The cloth gains weight by losing size

Grams per square metre is the number a fabric is bought and sold by. It appears on every specification, it is what people mean by a “heavy” or “light” cloth, and it is the closest thing the trade has to a single figure of merit.

It is also a ratio, and finishing does not touch its numerator.

The arithmetic #

A piece of cloth contains a definite mass of yarn. Relaxation changes its length and width and cannot change its mass — no material enters or leaves — so

mass per unit area after = mass per unit area before ÷ (1 − warpwise)(1 − weftwise)

For the standard cloth in this field, losing 7.94 per cent of its length and 2.84 per cent of its width, that factor is 1/(0.9206 × 0.9716) = 1.118.

An eleven point eight per cent rise in the number a fabric is judged by, produced by taking something away from it.

Why this is not a curiosity #

Three consequences, and each of them is a place where a real decision gets made on the wrong number.

A specification can be met by finishing rather than by construction. A mill asked for 150 g/m² can weave a cloth that is 134 in the loom state and relax it into specification. That is not cheating — the fabric delivered genuinely weighs 150 — but it contains eleven per cent less yarn than a cloth woven at 150 and finished to stay there, and the difference is entirely in how much of the thread’s length is standing up in bends rather than lying flat.

Two fabrics at the same mass per unit area can differ substantially in yarn content. Everything that follows from yarn content — cost, strength per unit width, opacity in some directions, thermal resistance — differs with it. Mass per unit area is a good proxy for those things among fabrics finished the same way and a poor one across finishing routes.

And the number rises again every time the fabric relaxes further. A cloth that has been dry-relaxed weighs less per square metre than the same cloth wet-relaxed, and both are honest measurements of the same piece.

What it is not #

It is worth being careful here, because there is a nearby claim that is false.

The fabric is not denser in any material sense. The yarn’s packing factor has not changed, the fibres are where they were, and if the cloth is unravelled and weighed thread by thread every measurement is identical. What has changed is the projected area the same yarn occupies.

Nor is the fabric thicker in proportion. Thickness rises somewhat — more crimp means a greater crimp height, and this site computes the thickness as h₁ + d₁ — but not by eleven per cent. So the volumetric density rises less than the areal density does, and the two are often conflated.

The honest statement is narrow and it is the one that matters commercially: mass per unit area is a state-dependent quantity, and it is quoted almost universally without its state.

The relative thread count is state-dependent too #

The same argument applies to every quantity of the form count per unit length, which is most of the descriptive vocabulary of woven fabric.

Threads per inch. Picks per centimetre. The cover factor, which is a sett multiplied by a diameter. All of them have a length in the denominator and all of them rise when the length falls.

Take the standard cloth again. A fabric woven at 60 ends and 60 picks per inch in the loom state finishes at 60/(1 − 0.0284) = 61.8 ends and 60/(1 − 0.0794) = 65.2 picks per inch. A balanced cloth on the loom is not balanced when it is finished, because the two directions relaxed by different amounts — and the imbalance is a consequence of the machine rather than of the design.

This is worth putting beside what this site has already said about thread count. That essay argued that thread count is a poor proxy for quality because it can be inflated by plied yarns counted as singles. Here is a second and independent way the number moves without the fabric improving: it rises by however much the cloth was allowed to relax.

The same argument for every per-unit-area quantity #

Mass is the one that gets quoted, and it is not alone. Anything divided by an area moves with the area, and the fabric vocabulary is full of such quantities.

Thermal resistance per unit area rises, because the same fibre is packed into less area and the still air it holds is held in a smaller footprint. Air permeability falls, for the same reason and more steeply, because the interstices close as the threads crowd. Water-vapour resistance rises. Bursting strength, quoted as a pressure, rises because the same yarns span a smaller area.

None of these is a change in the fabric’s material behaviour. Every one is the same yarn doing the same thing in a smaller footprint, and every one of them is quoted in specifications without a state.

The one that is least affected is tensile strength per unit width, and the exception is instructive. Strength across a given width is decided by how many threads cross that width and how strong each is. Relaxation brings the threads closer, so a given width contains more of them, so the strength per unit width rises — but the strength per thread is unchanged, and the strength of the whole piece across its whole width is exactly unchanged, because it contains the same number of threads it always did.

A quantity per unit width moves and a quantity per piece does not, which is the same distinction one dimension down.

Why a heavier number reads as a better fabric #

There is a reason this particular quantity is worth an essay rather than a footnote, and it is about what the number is used for.

Grams per square metre functions as a proxy for quality across the whole trade. A heavier suiting is a better suiting; a heavier shirting is a better shirting; a heavier canvas is a stronger canvas. The proxy is not foolish — for fabrics of similar construction in similar fibres, more yarn per unit area really does mean more durability, more opacity and more of most things anybody wants.

What the proxy assumes is that the extra mass is extra yarn. And relaxation adds mass per unit area without adding yarn, so it moves the proxy without moving the thing the proxy stands for.

That puts this alongside thread count as the second quantity on this site to be a genuine measurement, honestly obtained, that fails as a figure of merit for a structural reason. Both fail the same way: the number is a ratio, and the denominator is adjustable by somebody other than the person choosing the yarn.

The third member of the family is cover factor, and it fails for both reasons at once — its sett moves with relaxation and its diameter moves with swelling and flattening.

What was counted, and how #

The mass gain comes out of relaxed() alongside the two shrinkages, as 1/((1 − warpwise)(1 − weftwise)) − 1, and it is returned rather than printed anywhere on its own because it is not an independent quantity — it is the area shrinkage inverted.

That relationship is the check worth stating. Area shrinkage and mass gain are the same fact written two ways, so a figure quoting both is quoting one measurement twice, and any presentation that lets them drift apart is wrong by construction. The function computes each from the same pair of shrinkages so they cannot.

The two shrinkages themselves are computed by the route this field’s first rung sets out: the relaxed state from Peirce’s geometry, the loom state as that thread with a stated fraction of its crimp removed, and the shrinkage cross-checked against the spacings.

A note on which way the trade rounds #

Since the quantity moves and everyone knows it moves, there is a settled practice for handling it, and it is worth recording because it is not the obvious one.

A mill does not quote a range. It quotes a single finished mass per unit area, achieved by setting the stenter and the shrinking range to land the fabric there, and it holds the number as a process target rather than as a measurement of what the construction gives. The construction is then chosen with enough margin that the target is reachable from either side.

That inverts the apparent causality. The specification does not describe the fabric; the fabric is finished until it matches the specification, and the finishing route is the adjustable part. A fabric’s areal density is a decision more than a property, which is the strongest form of everything this essay has been saying.

Where the model stops #

Mass is assumed conserved and it is not, quite. Finishing removes things. Desizing takes the size off a cotton warp — which can be several per cent of the piece’s mass. Scouring removes waxes and residues. Singeing burns off protruding fibre. Against that, a resin finish or a softener adds mass. A real finishing route changes the numerator as well as the denominator, and this essay’s arithmetic is about the denominator alone.

The two shrinkages are model outputs, not measurements, and carry the inputs described in the earlier rungs.

And nothing here is about thickness or bulk, which move differently and are the quantities a hand assessment actually responds to.

The specification that would not have this problem #

Since mass per unit area is state-dependent, it is fair to ask what would not be, and there is an answer: mass per unit length of thread, or equivalently the yarn count and the thread count in the loom state.

A specification written as so many ends and picks of such-and-such a count names quantities that no finishing operation changes. The yarn is the yarn. The number of ends in the piece is fixed when the warp is beamed and is the same number when the garment wears out.

That is how fabrics are specified for weaving, and it is not how they are specified for buying — which is the whole difficulty. A weaver’s specification and a buyer’s specification describe the same cloth in vocabularies that are not convertible without knowing the finishing route.

The convertible quantity is the one this site has been computing all along. Thread count in the loom state plus crimp gives thread count in any state, because crimp is exactly the exchange rate between a thread’s length and the cloth’s. A specification carrying the crimp would be state-independent and nobody writes one, because measuring crimp means destroying a sample.

The numerator moves too, and by the same order #

The limits section records that finishing changes the mass as well as the area, and leaves it as a caveat. It is not a caveat; it is the same size as the effect the essay is about, and it points the other way.

Desizing is the large one. A cotton warp carries a size add-on of five to fifteen per cent of the warp’s own mass, and the warp is roughly half the cloth, so desizing removes two and a half to seven and a half per cent of the piece.

Put that through the same ratio. The geometry alone gives 1/(0.9206 × 0.9716) = 1.118, and multiplying by what is left of the mass:

So the same greige cloth can arrive at anywhere between three and fifteen per cent above its loom-state areal density, depending on nothing but which finishing operations it passes through — and every one of those numbers is an honest weighing of the same construction.

That is the essay’s strongest claim reached by a second route. It is not merely that a mill can choose where on the relaxation curve to measure; it is that the two large levers, one on each side of the ratio, are both in the finishing department, and they act in opposite directions with comparable magnitudes. A specification hit by finishing can be hit from either side.

The conversion nobody writes down #

The essay says the weaver’s vocabulary and the buyer’s are not convertible without the crimp, and that a specification carrying it would be state-independent. The conversion itself is one line and worth setting down, because it is what makes the discrepancy above measurable rather than merely arguable.

A square metre of cloth contains, per system, one metre of cloth-length for every thread across the metre of width, and each thread is longer than the cloth by its crimp. So with setts in threads per metre and counts in tex,

areal mass (g/m²) = [n₁(1 + c₁)·T₁ + n₂(1 + c₂)·T₂] ÷ 1000.

For an ordinary sheeting — 2,400 ends and 2,200 picks per metre, 25 tex both ways, nine and four per cent crimp — that is 65.4 from the warp and 57.2 from the weft: 123 g/m².

Every term in it is either invariant (the counts) or state-dependent in a stated way (the setts and the crimps), which is exactly the property the essay says a specification wants. Quote a construction and its crimps and the areal density follows; quote an areal density alone and nothing follows.

Which makes the discrepancy a measurement #

The practical use is not the forward direction, which a mill already knows, but the backward one — because a buyer usually has both numbers and never compares them.

Compute the areal density from the quoted construction and subtract the quoted areal density. The two should agree. If the quoted figure is low, the cloth has lost mass — it has been desized and scoured and not resined, or it has been measured before it finished relaxing. If it is high, mass has been added, and a resin or a softener is the usual suspect.

The residual is therefore a measurement of the finishing route, taken from two numbers that appear on the same specification sheet and are never set against each other. It will not say which operation, and it does not need to: it says how much of the fabric is not yarn, which is the question a buyer paying for yarn was asking in the first place.

The number that would not move #

It is worth asking what a state-independent measure of a fabric’s substance would be, since mass per unit area is not one.

Mass per unit length of the piece is invariant, because the piece contains the yarn it contains. It is also useless as a comparison, since it depends on the width.

Mass per unit area in a named state works and is what the standards do. It is the same quantity with the omission repaired, and the cost is that two fabrics can only be compared if they were measured in the same state — which is precisely what a specified conditioning and relaxation procedure buys.

Yarn count and thread count in the loom state is the weaver’s specification and is genuinely invariant, and it is the one a mill uses internally. From it, the finished mass per unit area in any state follows once the crimps are known.

The pattern across those three is the pattern this whole field keeps producing. The invariant descriptions are the ones a maker uses and the state-dependent ones are the ones a buyer sees, and the two vocabularies are not convertible without information neither party normally records.

Why the direction of the error matters #

One last observation, and it is about which way the omission cuts.

Relaxation always raises mass per unit area, because it always shrinks the fabric. There is no operation in this field that lowers it except stretching, which is not durable. So a fabric measured in an incompletely relaxed state reads lighter than it will be, and one measured after full relaxation reads at its maximum.

A mill wanting to hit a minimum mass specification therefore has an incentive to measure late, and a mill wanting to hit a maximum has an incentive to measure early. Both are honest measurements of the same cloth and the specification is met or missed depending on when the tape went round it.

That asymmetry is why the standards specify the state rather than merely recommending one, and it is the clearest practical argument for everything this field has been saying. A quantity whose value depends on a choice, made by the party the number is used to judge, has to have that choice pinned down by something other than good intentions.

Who found it, and when #

The effect has been known as long as fabrics have been sold by weight, and the trade’s response is visible in its documents: a fabric specification quotes the finished mass and the finishing route, and a mill’s internal cloth particulars quote the loom-state construction. Both exist because neither alone is enough.

What has changed more recently is which number is public. Consumer-facing descriptions quote grams per square metre and thread count, both of which are state-dependent, and quote neither the yarn count nor the finishing route, both of which are not. The result is a vocabulary in which two fabrics can be compared on numbers that are genuinely measured, genuinely honest and not comparable.

That is not a scandal and it needs no villain. It is what happens when a ratio becomes a figure of merit and its denominator turns out to be adjustable.

Where the ladder goes next #

Two of this field’s three ladders remain. One is the surface: the yarn flattened between rollers and the fibre swollen in caustic soda, both of which change what the cloth looks like and leave its dimensions where they were.

The other is felting, which is the only operation in this field that cannot be undone and which needs a mechanism the site did not have.