Pre-shrinking is a subtraction done in advance

A cloth that will lose eight per cent of its length is not a cloth anybody can sell to a shirtmaker. There are two ways out. The fabric can be designed to want less — fewer interlacings, an opener sett, a lower loom tension — and everything that buys costs something else. Or the shrinking can be done before the cloth leaves the mill, which is what the industry actually does.

The machine that does it is Sanford Cluett’s, patented in 1930, and the operation is called compressive shrinkage. It has been sold under his name ever since, which is why a shirt label carries a proper noun where an operation ought to be.

What the machine does #

The mechanism is worth describing because it is unusually direct — there is no chemistry in it and nothing is added.

The cloth is fed onto a thick rubber blanket that runs round a roller. Going round the roller the blanket’s outer surface is stretched, because it is on the outside of a curve. The cloth is laid onto it at that moment, in contact and gripped. Then the blanket comes off the roller and flattens, its outer surface contracts back to its unstretched length — and the cloth, held against it by friction and by a heated shoe, is carried along with the contraction.

The cloth leaves shorter than it arrived, by whatever the blanket’s compression ratio was set to. The length has gone into the crimp, exactly as it would have in a wash, and it has gone there by a mechanical route rather than by wetting and drying.

That is the whole operation. Its elegance is that the compression is set by a geometry — the blanket’s thickness and the roller’s radius — so it is repeatable and adjustable, and its limitation is that it only works in the length direction, which is where the problem mostly is.

The arithmetic that gets done wrong #

Here is the trap, and it catches people who are perfectly comfortable with percentages.

A fabric would relax by six per cent from its woven length. The machine takes out four and a half. What is left?

The answer that comes to mind is one and a half per cent, and it is wrong. Six per cent and four and a half per cent are fractions of the same starting length, so their difference is a length — but the number a customer experiences is a fraction of the length they were sold, which is the post-machine length.

Written out: the woven piece is 100. The machine leaves it at 95.5. It will eventually settle at 94. The customer measures the loss against 95.5, so the residual is

1 − 94/95.5 = 1.57 per cent

not 1.5. The difference is small here and it grows with both numbers, and more importantly it is systematically in one direction: the naive subtraction always understates the residual. A mill that computes it that way and sets its machine to hit a two per cent specification will ship fabric that misses.

Over-shrinking, and the cloth that grows #

The machine can be set past the fabric’s own relaxation, and what happens then is the interesting case.

Take a cloth that would relax by four per cent and compress it by six. It leaves the machine at 94 and it wants to be at 96. So it grows, by

96/94 − 1 = 2.13 per cent

in wear. A garment that gets longer after washing is a stranger complaint than one that gets shorter and it is a real one, and this is where it comes from.

The asymmetry is worth noticing: over-shrinking by two points produces a growth of 2.13 per cent, while under-shrinking by two points produces a shrinkage of about 2.08. The two errors are not quite the same size, for the same reason the residual is not the difference — the denominators differ.

What “pre-shrunk” is actually claiming #

The standards are careful here and the marketing is not.

Residual shrinkage is what a specified laundering procedure removes from the finished fabric. It is the number the standards define and the number a specification quotes, and it is measured against the fabric as sold. The common threshold is one per cent, and a cloth meeting it may still have had five per cent taken out of it in the mill.

So “pre-shrunk” does not mean the fabric will not shrink. It means the shrinking has been done at the mill’s expense rather than the customer’s, and that what remains is small enough to be inside a garment’s making-up tolerance. It also addresses only one of the two shrinkages a tape measure records: a pre-shrunk cotton is still two per cent smaller while it is wet, permanently, because there is nothing there to take out.

The phrase that gets used loosely is sanforized, which is a trademark and means the cloth has been through a compressive-shrinkage machine under licence, with the residual verified against the standard. It is a claim about a process and a test, not a claim that the number is zero.

The other three ways to do it #

Compressive shrinkage is the standard route for cotton and it is not the only one, and the alternatives are worth setting out because each addresses a different part of the problem.

Relaxation by wet processing. Running the cloth through a rope-form washing machine or a tumble dryer supplies the mechanical action that lets the yarns move past their own friction, and the fabric relaxes on its own account. This is cheap, it is often happening anyway for other reasons — scouring, dyeing — and its limitation is that it is uncontrolled: the fabric relaxes as far as the treatment happens to take it, which is not to a specification.

Setting. For a thermoplastic fibre the whole problem can be removed rather than pre-empted. Heat the fabric above the fibre’s glass transition, hold it at the wanted dimensions, cool it, and the fibre’s own structure is set to that state. A heat-set polyester is dimensionally stable because it has no memory of a different state to return to, which is a fundamentally different solution from taking the shrinkage in advance.

Cross-linking. For cotton, a resin finish forms covalent bridges between cellulose chains at the dimensions the fabric was in when the resin cured. The fabric then resists returning to its relaxed state because doing so requires breaking bonds. This is what a durable-press finish is, its cost is a substantial loss of tensile and tear strength, and the fabric is stable in a way that has nothing to do with its crimp.

Only the last two remove the mechanism. The first two run it to completion; the last two prevent it. That distinction decides how the fabric behaves when it is treated in a way the finisher did not anticipate — a relaxed cloth is stable because it has nowhere to go, and a set or cross-linked cloth is stable because something is holding it, which can be undone.

Why the residual is never zero #

A specification says one per cent and not zero, and the reason is in this field’s arithmetic rather than in anyone’s caution.

The eventual state is an asymptote. A fabric approaches its fully relaxed dimensions over many launderings, with each one supplying a little more mechanical action and moving it a little further, and there is no finite treatment that reaches the end. A machine set to the full expected relaxation over-shrinks the fabric relative to where it will be after one wash and under-shrinks it relative to where it will be after twenty.

So a residual figure is always a figure against a specified procedure, and the procedure is part of the number. Five domestic launderings is a common definition and so is one; they give different answers for the same fabric and both are correct.

The practical consequence is that a garment made from cloth with a one per cent residual against a five-wash test will go on moving slightly for the rest of its life. That is accepted, because the making-up tolerances absorb it, and it is the reason the specification is written against a procedure rather than against the asymptote nobody can reach.

What was counted, and how #

The pre-shrinking arithmetic here is three lengths and nothing else, and the reason it exists as a function rather than as a formula in a caption is that the two mistakes above are easy to make and hard to see.

It computes the post-machine length as 1 − applied, the eventual length as 1 − total, and the residual as 1 − eventual/afterMachine, which is the only one of the three that involves a division by something other than the original. It reports over-shrinking as a separate flag with the growth beside it, rather than returning a negative shrinkage — because a negative shrinkage is a number that reads as a small shrinkage at a glance, and the two cases are qualitatively different.

The figure draws all three lengths as bars against a common scale, with each fraction marked against the bar it is a fraction of. A single bar could not show the error, which is why the figure has three.

Which of the two inputs the residual is really at the mercy of #

The arithmetic has two inputs — the fabric’s total relaxation and the machine’s applied compression — and the residual is more sensitive to errors in them than to their own sizes. Differentiating says which of the two a mill should spend its attention on, and it is not the one the machine’s operator can adjust.

The residual is 1 − (1 − T)/(1 − A), so

a one-point error in the applied compression moves the residual by 1/(1 − A) points, and a one-point error in the fabric’s total moves it by the same factor.

At the essay’s own numbers that factor is 1.05. At a heavily shrinking cloth compressed by seven points it is 1.08. Both errors are amplified, by a few per cent, and always in the direction of making them worse. That is small and it is systematic, and a mill setting its machine to hit a specification exactly will miss on the unlucky side rather than the lucky one.

The useful part is the comparison between the two.

The applied compression is known well. It is a blanket thickness and a roller radius, both fixed by the machine, and a range holds its setting to a fraction of a point across a piece.

The fabric’s total is not known at all well. It depends on the construction, the loom tension, and everything the finishing route did before the cloth reached the range — and the cloth arriving has had an unknown fraction of its relaxation taken and an unknown fraction put back. A mill estimating it from a construction is working to a point or two at best.

So the residual’s uncertainty is essentially the fabric’s own total’s, amplified by five per cent. Tightening the machine buys almost nothing.

That points at a different practice from the one the arithmetic invites. Measure the total per lot rather than tightening the setting per lot: relax a sample of the incoming cloth to its own limit, read its total, and set the machine from that. The measurement is a wash and a tape measure, it takes an hour, and it removes the term that dominates the error — where a better-controlled range removes the term that does not.

And it explains a piece of mill practice that looks like caution. A finisher running an unfamiliar cloth sets the compression low on the first piece and works up, which is exactly the behaviour of somebody whose uncertainty is in the fabric rather than in the machine — and which the arithmetic above says is the right way round.

Where the model stops #

One direction only. Compressive shrinkage acts along the length. Weftwise stability has to come from elsewhere — from the stenter’s overfeed, from a resin finish, or from the fabric being designed not to need it — and a piece that is stable in length and not in width is a common and annoying result.

One relaxation, not a sequence. The model has a single eventual length. Real fabric approaches it over several launderings, and the standards’ procedures exist precisely to force it there quickly enough to be measurable.

Nothing here models the machine. The compression is an input; the blanket thickness, roller radius, shoe temperature and cloth moisture that decide it are not represented at all. What the model says is what a given compression is worth, not what setting produces it.

And the fabric is treated as uniform. A real piece varies across its width and along its length, and the shrinkage specification is met on average with a tolerance.

Why the operation is worth its cost #

A compressive-shrinkage range is a large, heavy, expensive machine that a mill runs everything through, and its whole output is the removal of a few percentage points. It is worth asking why that is worth doing rather than telling customers to allow for it.

The answer is that the allowance has to be made per garment and the shrinkage varies per fabric. A shirtmaker cutting from a stable cloth cuts to the pattern. A shirtmaker cutting from an unstable one must cut every piece oversize by the fabric’s own figure, in two directions — and a cloth cut on the bias skews as well as shrinking — and get it right — and any error shows up as a garment that fits before washing and not after, which is the worst possible time to discover it.

Doing the operation at the mill moves a per-garment problem to a per-piece one and makes it somebody’s specialised job. That is the same economic argument that puts any operation upstream, and it is the reason the machine exists rather than a table of allowances.

There is a second reason and it is about the ceiling. A fabric’s relaxation is bounded by its crimp, so the mill knows the worst case exactly, and a machine that can take out up to that bound can guarantee a residual. A tailor’s allowance cannot guarantee anything, because it is applied to a fabric whose history the tailor does not know.

Why the operation is placed where it is #

A finishing route is a sequence and compressive shrinkage sits at the end of it, which is not arbitrary.

Every wet operation before it — desizing, scouring, bleaching, dyeing — relaxes the cloth somewhat and then dries it under whatever tension the machine imposed, so the fabric arriving at the shrinking range has already had an unknown fraction of its relaxation taken and an unknown fraction put back. Putting the shrinking range first would mean shrinking a cloth that was then going to be stretched again by everything downstream.

So the operation goes last, after the stenter, and its input is a fabric in a state the finisher has just set. The machine is the last thing to touch the cloth, and that is the whole of why it can guarantee anything.

The corollary is that anything done to the fabric afterwards invalidates the guarantee. A cloth that is pressed, re-rolled under tension, or laid up wet after leaving the range is a cloth whose residual is no longer the residual that was measured.

Who found it, and when #

Cluett’s patent is 1930 and the commercial name followed almost immediately. What is notable is how quickly the operation became universal for cotton: within a decade the phrase was on labels, and by the 1950s a shirting that had not been through the process was a specialty item rather than the norm.

The standards followed the machine rather than preceding it. Once a mill could control residual shrinkage, a customer could specify it, and specifying it required a procedure — so the laundering test methods that define what the number means were written to give the guarantee something to be measured against.

The arithmetic in this essay is not in the patent and does not need to be. It is the sort of thing that gets discovered independently by everyone who has to hit a specification, and gets written down rarely because it looks obvious once it is right.

Where the ladder goes next #

The shrinkage ladder ends here, but the area it took out has to go somewhere in the bookkeeping. A cloth with the same mass over a smaller area weighs more per square metre, and the next essay follows that consequence — which is where a fabric appears to gain quality by having something taken away from it.