A knit's weight nearly names its yarn

What a fabric weighs found that a woven cloth’s areal weight is a sum of four products — two setts times two counts — so that a single number in grams per square metre admits a whole family of cloths. A weight fixes the fibre and not the drape drew that family for plain cotton at 150 grams and found it running from 20 tex to 200 and beyond, with the thickness trebling along it and the cover falling in step.

It ended by asking the question for knits. A knitted fabric has a different geometry and one extra freedom, the loop length, and whether its weight is as uninformative as a woven cloth’s was not obvious.

It is far less uninformative, and for a reason that takes one line.

A jersey’s weight is one product #

A relaxed plain jersey has $k_c/\ell$ courses and $k_w/\ell$ wales to the centimetre, so $k_s/\ell^2$ stitches to the square centimetre — its dimensions come from its loop — and every stitch is one loop length of yarn. Multiply the stitches by the yarn in each and by the yarn’s mass per length and the weight comes out as

$$\text{g/m}^2 = 0.1 \cdot \frac{k_s \cdot \text{tex}}{\ell},$$

with ℓ in centimetres. A 20 tex yarn at a 3.5-millimetre loop gives 135 grams, which is the weight the density essay found for the same fabric.

Where a woven cloth had four numbers to trade against one another, a jersey has two: the count, and the loop. Any count can make any weight if the loop is free to be whatever the weight needs.

The loop is not free #

It is not. A loop cannot be arbitrarily short — the needle has to draw it round a yarn of finite diameter — and it cannot be arbitrarily long without the fabric becoming a net. The trade’s measure of where a jersey sits between those is the tightness factor, the square root of the count in tex over the loop length in millimetres, and plain jersey is knitted between about 1.3 and 1.6 of it. The tube essay used the same band to bound a seamless taper, and it is stated there and here as an empirical range.

Both ends of the band are set by the same loop doing two jobs. At the tight end the loop is so short that the yarn is bent round a needle hook barely wider than itself, the knitting tension rises and the yarn starts to break or the fabric to feel like card. At the loose end the loop is so long that nothing holds a stitch’s shape: the fabric spirals, snags and changes dimensions at every handling. Neither end is sharp, which is why the band is quoted as a range rather than two numbers to the decimal, and neither end depends on the weight being asked for — they are properties of a loop and the yarn inside it.

Put the tightness factor into the weight and the loop leaves:

$$\text{g/m}^2 = k_s \cdot \mathit{TF} \cdot \sqrt{\text{tex}}.$$

That is the whole essay in one line. The weight is a constant times the tightness times the root of the count. At a fixed weight, the count can move only as far as the tightness can move to compensate, and the tightness moves over a band of 1.6 to 1.3.

At one weight, the count is fixed to within half again #

Solve for the count and the band becomes

tex from (g/m² / 1.6 k_s)² to (g/m² / 1.3 k_s)²,

a ratio of $(1.6/1.3)^2$ = 1.51 at every weight. The loop has been used up absorbing the tightness band, and there is nothing left to absorb a change of count.

At 150 grams, fully relaxed, that is 15.8 to 23.9 tex. A 150-gram plain jersey is knitted from a yarn between about sixteen and twenty-four tex, and from nothing else; a sixteen-tex yarn makes it at the tight end of the band and a twenty-four at the loose end.

The woven cloth at the same weight could be made from 20 tex or 200 — a ratio of ten, and the chart simply ran out of counts. A woven weight says almost nothing about the yarn; a knitted weight almost names it.

Why the two constructions differ so much #

The difference is where the fabric keeps its freedom.

A woven cloth sets its threads apart by a sett that the loom chooses independently of the yarn — thread count is not quality precisely because the sett and the count are separate specifications — and the only thing binding them is the jam, which is far away at most weights. So a fine yarn set close and a coarse yarn set open can weigh the same, and the family is wide.

A jersey sets its threads apart by the loop, and the loop is bound to the yarn at both ends: too short and the yarn cannot be knitted, too long and it cannot hold a shape. The knit has no sett. Its spacing is a consequence of its yarn, within a band, and so its weight is too. Two knits with one tightness factor are one knit found the same thing from the shape side: the loop’s geometry is fixed by one dimensionless number, and a fabric with little freedom in its shape has little in its weight.

And in each relaxed state it names a different yarn #

The constant k_s is the one thing in the weight that is not about the yarn or the loop. It is the stitch-density constant, and it depends on which relaxed state the fabric is in: 19.0 dry-relaxed, 21.6 wet-relaxed, 23.6 fully relaxed.

So the band moves with the state. A 150-gram jersey is 24.3 to 36.9 tex if it was weighed dry-relaxed, 18.8 to 28.5 wet-relaxed, and 15.8 to 23.9 fully relaxed. The dry band and the fully relaxed band do not overlap. A yarn that makes a 150-gram jersey in one state cannot make one in the other.

That turns a weight specification into a trap. A buyer specifying “150 grams” of jersey is naming a yarn to within half again — and naming a different yarn depending on whether the fabric is weighed off the machine or after it has been washed and tumbled, which is the difference between the fabric the mill delivers and the one the customer owns.

The same fabric gains a quarter in weight by relaxing #

Read the other way, the state moves the weight of a fabric whose yarn and loop are fixed.

Knitted and rested, a 20-tex jersey at a 3.5-millimetre loop weighs 108.6 grams. Soaked, 123.4. Soaked and tumbled, 134.9 — 24 per cent heavier. No yarn has been added. The fabric has relaxed for as long as it was allowed to, its courses and wales have moved closer, and the same yarn covers less area.

That is shrinkage seen from the scale rather than the tape measure, and it is exactly the ratio of the two stitch-density constants, 23.6 over 19.0. A woven cloth relaxes too, but its weight moves by its own shrinkage, a few per cent; a jersey’s moves by a quarter, because a knit’s dimensions are set by its loop’s shape rather than by a sett the loom imposed.

One count, a narrow band of weights #

The band read the other way says what a yarn can make. A 20-tex yarn knits into plain jersey of 137 to 169 grams fully relaxed, a ratio of 1.23 — the tightness band itself — and nothing outside it.

So a knitter who has chosen a yarn has very nearly chosen a weight, and one who has chosen a weight has very nearly chosen a yarn. The two specifications are almost the same specification, which is the opposite of the woven case, where they were almost independent.

A weight and a count together are a check #

Because the weight and the count are nearly the same specification, a jersey specification that names both is over-determined, and the extra number is a check a buyer can run without a sample.

Divide the weight by the stitch-density constant and the root of the count, and the result is the tightness factor the mill must have knitted to: $\mathit{TF} = \text{g/m}^2 / (k_s\sqrt{\text{tex}})$. A specification for a fully relaxed 150-gram jersey in 30-tex yarn gives 1.16 — looser than plain jersey is usually knitted, and a warning that the fabric will be open, unstable or not plain jersey at all. The same weight in 12-tex yarn gives 1.83, tighter than the band, a board rather than a knit. The count that decides how flat found the tightness factor deciding how hard a knit’s yarn is pressed; here it decides whether the specification describes a fabric that can be made.

A woven specification has no such check. Its weight and its count are consistent with almost any sett, and only the jam, far away, can refuse them.

Heavier jersey is tighter jersey, or coarser #

The formula says what a knitter can do to make a heavier fabric, and the answer is two things only.

From the same yarn, a heavier jersey is a tighter one, in exact proportion. A 20-tex yarn makes 137 grams at a tightness of 1.3 and 169 at 1.6, and a jersey of that yarn at 180 grams would need a tightness of 1.70 — past the band’s tight end. Beyond the band the only way up is a coarser yarn: 200 grams fully relaxed needs 28 to 42 tex, a different yarn altogether.

That is the reverse of the woven freedom, where the same yarn makes a heavier cloth simply by being set closer, all the way to the jam. A jersey’s weight is set by its yarn to within the tightness band, and the band is narrow because the same loop has to be both knittable and stable.

Why the ratio is the same at every weight #

The 1.51 is not a coincidence of the weights chosen. It is the square of the tightness band’s own ratio, and the weight, the constant and the state all cancel from it.

So the knitted band is equally narrow at 100 grams and at 250, and equally narrow dry and fully relaxed; what moves is only where the band sits. That makes the band’s width a property of the knitting practice — of how far a jersey’s tightness can range and still be jersey — and not of any fabric. A mill that knits a wider range of tightness widens every band by the square of what it gains.

The state trap, in grams #

The trap is worth putting in the customer’s units.

A jersey delivered at 150 grams in its wet-relaxed state — finished, but not yet washed and tumbled by the person who buys it — weighs 164 grams fully relaxed, because its stitch density rises by the ratio of the two constants, 23.6 over 21.6. The same garment, measured flat before and after its first wash, has lost area in that ratio as well. None of this is a fault in the fabric; it is the fabric reaching the state its constants describe, and a specification that did not name the state has not described it.

What the weight cannot say about a knit #

The weight nearly fixes the count, and it still says nothing about the fabric’s bulk. How dense a knitted fabric is found fabrics of one weight differing threefold in density — a jersey and a range of ribs, all of the same yarn and loop — because a rib’s two beds stand apart and a jersey’s do not. So the weight names the yarn and not the structure: every number here is for plain jersey, and a rib of the same weight and the same count is a different fabric entirely.

That puts the knitted weight in an odd position. Among plain jerseys it is nearly a complete specification; across structures it is hardly a specification at all.

The woven comparison, drawn at its own weight #

For the woven side, the weight line at 150 grams is the one already drawn, with its crimp solved rather than assumed.

Along it the thickness trebles and the cover falls by the same factor. A knitted weight line has no room for that: across its 1.51 of count, a jersey’s thickness — about two yarn diameters — moves by the square root of 1.51, 23 per cent, and its loop by the whole 1.51, from 2.48 to 3.76 millimetres.

The model named #

The jersey is Munden’s: courses, wales and stitches per unit area from the loop length and three constants per relaxed state, 5.0, 4.0 and 19.0 dry-relaxed, 5.3, 4.1 and 21.6 wet-relaxed, 5.5, 4.3 and 23.6 fully relaxed. The weight is stitches times loop length times count, with no allowance for the yarn’s own take-up in the loop beyond what the loop length already measures. The tightness band is 1.3 to 1.6, empirical and stated as such. The woven line is the crimp-solved plain weave of the essay that fixed the fibre and not the drape.

Required of the arithmetic, not shown: that a jersey solved for its loop at a weight weighs exactly that weight; that its tightness factor equals the weight over $k_s\sqrt{\text{tex}}$; that the band’s two ends sit exactly on the band’s two tightness factors; and that the band’s width in ratio is $(1.6/1.3)^2$ at every weight.

What was counted #

Three weights, 100, 150 and 250 grams, in three relaxed states each, for the knitted band; the same three weights on the woven line, over counts from 10 to 200 tex. One jersey, 20 tex at 3.5 millimetres, weighed in the three states. Nothing was fitted; the only inputs are Munden’s constants and the tightness band.

Where the model stops #

The tightness band is a practice, not a law. A jersey knitted tighter than 1.6 or looser than 1.3 exists — a very open fashion knit, a very firm sock — and each extension widens the count band in proportion to its square. The claim is about plain jersey knitted as plain jersey usually is.

The constants are cotton-derived and the fabric is plain. Wool jerseys relax to somewhat different constants, and any structure with a tuck, a miss or a rib has constants of its own that do not compose from the plain ones.

And “fully relaxed” is a state, not the end of the story. A jersey that keeps relaxing through its first few washes keeps gaining weight towards the fully relaxed figure, and a fabric weighed partway along is in no named state at all.

Who found it, and when #

Munden’s constants are from 1959 and the tightness factor from the knitting technologists who followed him. That a knitted fabric’s weight rises as it relaxes is familiar to every knitter who has washed a swatch. What is added here is the cancellation — the loop falling out of the weight once the tightness band bounds it — and its two consequences: that a jersey’s weight names its yarn to within a ratio of 1.51, and that it names a different yarn in each state.

Still open: whether a knit’s drape also sheds its weight #

The woven line’s surprise was that at the free bound of yarn stiffness a cloth’s bending length has neither the count nor the weight in it — only the fibre. A jersey’s bending is a loop’s, not a straight yarn’s, and its rigidity per unit width is the wales per centimetre times the rigidity of each wale’s legs. Along the knitted weight line the wale spacing goes as the loop, and the loop as the count, so the same kind of cancellation is possible. Whether a jersey’s bending length at the free bound belongs to its fibre alone, as a woven cloth’s does, is one more division, and the knitted weight line is narrow enough that the answer could be checked on a handful of swatches.