How dense a knitted fabric is

A fabric is specified by its areal weight — grams per square metre — and that number is exact, easy to measure and computed here without a fitted constant. It is also, on its own, almost uninformative about what the fabric is like, because two fabrics of the same weight can be a thin dense sheet and a thick open one.

The quantity that separates them is a density: the weight per unit area divided by the thickness. Until a knitted fabric had a thickness there was nothing to divide by.

The arithmetic #

Areal weight is yarn per unit area times the yarn’s linear density, and both come from the fabric’s own dimensions.

A 20 tex cotton at a 3.5 mm loop puts one loop length of yarn in one wale spacing by one course spacing — 3.5 millimetres of yarn in 0.518 square millimetres. At 20 grams a kilometre that is 135 grams per square metre, which is an ordinary weight for a jersey and is exactly what the trade would report.

Divide by the thickness of 0.334 millimetres:

0.404 grams per cubic centimetre.

Cotton fibre is 1.52. So the fabric is 26.6 per cent fibre and 73.4 per cent air, which is the number every other property of the fabric turns on.

What the fraction decides #

Three things at least, and each of them has its own rung on this ladder.

Warmth, because a fabric’s effective conductivity is a mixture of the fibre’s and the air’s at that fraction. A fabric that is three quarters air conducts very nearly as badly as air, which is what an insulator is.

Compression, because the fraction says how much room there is to close before the yarn itself has to be squashed.

And permeability, because air moves through the space and not through the fibre.

None of those follows from the areal weight, and all of them follow from the density. A specification that gives the weight and not the thickness has given the fabric’s mass and withheld its character.

The number that does not move #

The areal weight of a knitted fabric is a plan quantity: yarn per unit area. So it depends on the loop length and the two spacings, and it depends on the fabric’s thickness not at all.

The thickness, on a single-bed fabric, depends on the yarn’s diameter and nothing else — not the loop length, not the gauge.

So for a single-bed fabric the two move independently: loosen the loop and the weight falls while the thickness stands still, and the density falls with the weight. A loosely knitted jersey is genuinely a bulkier fabric in the sense that matters, and the reason is that it has less yarn rather than more room.

And the number that moves a great deal #

Put the fabric on two beds and the thickness becomes a machine setting, and the density becomes one too.

Hold the yarn, the loop length and the plan dimensions fixed and open the beds:

Every one of those fabrics weighs 135 grams per square metre. They differ by a factor of three in density, and a specification that named only the weight would call them one fabric.

The whole of that factor is air, and it can be read straight off the table. Fibre fraction runs 26.6 per cent down to 8.9 — so the jersey is three quarters air and the widest rib is nine tenths of it. Nothing has been added or taken away between the first row and the last; the same yarn in the same loop has simply been given more room to stand in. That is the single most useful thing to know about a knitted fabric and it is invisible in every quantity a mill actually quotes.

And the fibre fraction is the reciprocal of the thickness, exactly. Thickness rises 0.334, 0.501, 0.668, 0.835, 1.003 — one yarn diameter a step — and the fraction falls 26.6, 17.7, 13.3, 10.6, 8.9, whose products with the thicknesses are 8.88, 8.87, 8.88, 8.85, 8.93 in units of per-cent-millimetres. They agree to within the rounding, because the numerator of the fraction is the fibre in a stitch and that has not moved. So the table has one degree of freedom in it rather than four columns, and the degree of freedom is the gap.

Which is why the comparison a knitter actually cares about is the wrong way round from the one a specification makes. Two fabrics at one weight can differ threefold in what they feel like, and two fabrics at one density can differ threefold in weight; the only pair of numbers that pins a fabric down is a weight and a thickness together, and thickness is the one nobody measures because it is not well defined without a pressure.

Which is the case for reporting a density #

That table is the whole argument for the quantity. A trade specification of a two-bed fabric that gives its areal weight has said nothing about the setting that decides its bulk, its warmth and its feel, and the setting is not recoverable from the weight.

The honest specification of a knitted fabric is three numbers: an areal weight, a thickness and the state and load the thickness was measured at. Two of the three are usually absent.

The comparison at fixed dimensions, stated #

Every row of that table uses single jersey’s relaxed spacings, because a rib’s have never been published in a form this collection could quote. A real rib is far narrower than a jersey of the same yarn — its wales fold to opposite faces and each hides the one beside it — so its areal weight is far higher than 135.

So the table is a comparison of what the bed gap does at a fixed plan, and it is the only comparison available without a measurement nobody has made. A real rib is denser than these rows say in the plan direction and exactly as thick, so its density is higher and its fibre fraction larger. The direction of the bed gap’s effect is unchanged.

What the trade’s own numbers hide #

A knitted fabric is bought and sold on two figures — an areal weight and a gauge — and it is worth saying exactly what each of them determines.

The gauge is needles per unit width, which with the loop length sets the plan. The areal weight follows from the plan and the count and adds nothing the plan did not already have.

So the two numbers between them describe the fabric’s plan twice and its thickness not at all. That is fine for a single-bed fabric where the thickness is fixed by the yarn and recoverable from the count — and it is not fine for a two-bed one, where the thickness is a machine setting nobody records.

The practical form of the complaint is narrow and specific: a rib’s specification should carry its bed gap, or a measured thickness, and it carries neither.

What the fibre fraction cannot be #

There is a check on the whole arithmetic and it is one this collection uses elsewhere: the fraction has to be between none of the fabric and all of it.

It is asserted rather than assumed, because a fraction is exactly the kind of quantity that can silently exceed one when a unit conversion goes wrong. This collection has been caught by that shape before — an areal weight out by a factor of ten, discovered only because the assertion that used it then solved for a sett of six hundred threads per centimetre and printed it.

Here the fractions run from 8.9 per cent to 26.6 and the check has nothing to complain about. It is worth having anyway, for the day a bed gap or a packing factor is passed in the wrong units.

The packing factor, which is the weak link #

The fibre fraction depends on the yarn’s diameter, and the yarn’s diameter depends on a packing factor: how much of the yarn’s circular cross-section is fibre rather than air between fibres.

This collection uses 0.6, which is a standard figure for a ring-spun staple yarn and is a modelling choice rather than a measurement of any particular yarn. A real yarn’s packing runs from about 0.4 for a soft open yarn to 0.7 for a hard-twisted one.

That range moves the diameter by twenty per cent and the thickness with it, so it moves the density by the same twenty per cent in the other direction. It is the largest single uncertainty in every number on this page, and it is worth naming because the arithmetic downstream of it looks exact.

What it does not move is the comparison between the rows of the table, since the same packing enters every one of them.

Two fractions, and they are different #

There is a distinction here that is easy to lose and this collection has had to draw before.

The plan fill is how much of a fabric’s area, seen from above, has yarn in it. For a relaxed jersey it is over ninety per cent, and it is over one for a tight one — the yarn overlaps itself in projection.

The fibre fraction is how much of a fabric’s volume is fibre. It is 26.6 per cent.

The two are not versions of each other. A fabric can be visually solid and mostly air, and a jersey is: seen from the face it has almost no holes, and three quarters of it is nothing.

That is the geometric reason a knitted fabric is opaque and warm at the same time, and it is a combination a woven cloth of the same weight does not manage as well.

What a woven cloth does #

The comparison is instructive and it goes the other way from what the weights suggest.

The woven cloths in this collection’s table have measured thicknesses between 0.16 and 0.44 millimetres and areal weights of a similar order to the jersey’s, so their densities are in the same range — a poplin comes out denser and a cheesecloth much less so.

The difference is where the air is. A woven cloth’s air is in its holes, distributed through the plane between threads that are pressed hard together at their crossings. A knitted fabric’s air is in its thickness, in a plan that is nearly closed.

Same fraction, different arrangement — and it is the arrangement, not the fraction, that decides whether the fabric passes air, which is why permeability and density are separate subjects here.

What this does not settle #

A real rib’s areal weight. That needs relaxed dimensions this collection does not hold, and it refuses to invent them.

The density of a tubular fabric. No thickness, so no density. The refusal propagates.

And what happens under load. Every number here is at the relaxed thickness. A fabric under a hand is denser, and by a fraction that depends on how hard the hand is pressing — which is not a small correction here, because a fabric that is nine tenths air has nine tenths of its volume available to be squeezed out of it. The compression is most of the quantity, not a perturbation on it.

Nor does it settle which of these fabrics is the warm one, though the table looks as though it should. Still air is the insulator and the widest rib holds the most of it, so the density column reads like a thermal ranking; but air only insulates while it stays still, and a fabric a millimetre thick with nine tenths of its volume open is a fabric whose air convects. The warmth argument needs the pore size as well as the pore fraction, and the pore size is not in this table at all.

And it settles nothing about a fabric that has been finished. Every row is the fabric as knitted. Milling, calendering, raising and setting all move the thickness without moving the weight, which means every one of them moves the density — so a density quoted for a finished fabric is a statement about the finishing route and not about the structure. That is the same trap the weight column sets, one process further on.

What density predicts that weight does not #

Three quantities follow the density and not the weight, and they are the three a wearer would name.

Warmth, which is a thickness over a conductivity and therefore falls as the density rises at constant weight. A knit is warm because of where its yarn is not is the arithmetic.

Firmness under a hand, which is the through-thickness force spread over an area and therefore rises with the density. What a knit gives up when it is pressed is that force.

And how much a fabric can be compressed before it stops giving, which is the air fraction directly: a fabric that is 9 per cent fibre has a great deal further to go than one that is 27.

Three properties, one quantity, and the specification names a different one.

Where the density sits beside other materials #

A number in grams per cubic centimetre invites comparison and the comparisons are informative.

The fibre the jersey is made of is 1.52. The fabric is 0.404 — a quarter of it. Cork is about 0.24, balsa about 0.16, expanded polystyrene about 0.02. A wide rib at 0.135 is denser than a foam and lighter than a softwood.

That is the right company for a fabric to be in, and it is a reminder of what a knitted structure is: a way of arranging a solid so that most of the volume is air while the solid remains continuous. The continuity is what a foam does not have and is why a fabric can be pulled.

The comparison also says why a fabric’s own conduction is dominated by its air. At 27 per cent solid, the fibre’s conductivity is being diluted about four to one, and at 9 per cent it is being diluted eleven to one. A knit is warm because of where its yarn is not is that dilution, worked through.

Why the packing factor is where a measurement would bite first #

The single largest uncertainty on this page is a modelling constant, and it is worth saying what would replace it.

The yarn’s diameter comes from its count, its fibre’s density and a packing factor — how much of the yarn’s circle is fibre rather than air between fibres. Everything here inherits it: the thickness directly, the fibre fraction twice over, the density inversely.

A measured yarn diameter would remove it entirely, and a yarn diameter is a much easier measurement than a fabric thickness: it needs a microscope and a slide rather than a compression tester, and it has no state, no load and no hair layer in it.

So the cheapest single improvement to every number on this ladder is not a fabric measurement at all. It is a yarn measurement, and this collection has never made one.

What is genuinely new here #

Two quantities and one argument.

A knitted fabric’s bulk density and fibre fraction, from its own geometry — 0.40 grams a cubic centimetre and 26.6 per cent fibre for an ordinary jersey, neither of which was computable while the fabric had no thickness.

And a case against the trade’s own specification. Five fabrics of one areal weight differ threefold in density, and the specification that names the weight cannot tell them apart. A knitted fabric needs its thickness quoted, with the load and state it was measured at, or the number that is quoted is the least informative of the three.

What the pictures cannot show #

The bar chart on this page is a chart of warmth rather than of density, because the two are the same information and warmth is the one a reader can weigh against experience. A chart of five densities would be five bars falling as the gap opens and would say the same thing less usefully.

Neither picture shows the yarn’s own internal air, which is the packing factor, and which is the largest uncertainty in every number here.

What this does not reach #

A fabric’s density under load, which is what a hand feels. Every figure here is at the relaxed thickness, and a fabric being handled is at some fraction of it.

And a fabric with hair on it. A raised or brushed knit has the same structure, the same weight and the same structural thickness, and a gauge reads it much thicker — so its measured density is much lower. Which number is right depends on what the density is for: a warmth calculation wants the hair included, because the hair holds air, and a compression calculation does not.

That is the third instance on this ladder of the same distinction between a structural thickness and a measured one, and it is the reason a density has to say which thickness it was computed from.

What a weight-per-unit-area cannot see, in one sentence each #

Which of two fabrics is warmer — the thicker one, at equal weight.

Which is firmer under a thumb — the denser one, because the same through-thickness force is being spread over fewer stitches per unit area in the open fabric.

Which drapes more softly — neither follows from the weight alone; drape is a bending rigidity over a weight, and the rigidity carries the fabric’s own geometry.

And which will feel like more fabric in the hand — the bulkier one, which is the density read the other way up.

Four questions a buyer asks, and the specification answers none of them.

Which numbers here are measurements and which are not #

Measured: Munden’s two spacing constants, the fibre’s density, and the yarn’s linear density. Those are the inputs.

Modelled: the packing factor, which sets the yarn’s diameter and therefore the thickness.

Computed: everything else — the areal weight, the thickness, the density, the fibre fraction, and the warmth and firmness that follow from them.

That division is worth stating because the one modelled quantity is the one carrying the uncertainty, and because everything computed inherits it in a known direction: a denser yarn packing means a thinner yarn, a thinner fabric and a higher density.

Where the ladder goes next #

A fabric that is three quarters air is a fabric whose warmth comes from the air rather than from the fibre: a knit is warm because of where its yarn is not.

And a density that depends on a bed gap is a density that depends on a setting nobody has measured, which is the standing gap in this whole two-bed account: a rib’s relaxation is not its bending either.