What a knit gives up when it is pressed

Press a woven cloth and this collection has an account of what happens. Its thickness falls along a curve with two laws in series, the area in contact grows as the highest crowns flatten, the pressure at every depth is computable, and the whole thing is checked against eight measured thicknesses.

Press a knitted fabric and until now the answer was silence, for a reason that had nothing to do with compression. A loop solved as a plane curve has no thickness, so there was nothing to press.

The first point #

A relaxed 20 tex cotton jersey at a 3.5 mm loop is 0.334 millimetres thick and resists being made thinner at 15.1 kilopascals per unit of strain.

Those are the two numbers a compression curve starts from: where it starts and how steeply. Neither existed before the loop was allowed out of the fabric’s plane, and both come from the same solved shape — the thickness from the interlacing, the slope from the through-thickness component of the contact force divided by the area a stitch occupies.

What the resistance is made of #

This is where the two fabrics part company, and it is the substance of this rung.

A woven cloth resists compression by flattening its threads. Its crossings are already in contact at zero load — the crowns of the warp bear on the crowns of the weft — so the first thing a press does is squash the yarn itself, and the cloth’s compression curve is very largely a yarn compression curve seen through a geometry. That is why this collection’s woven curve is two laws in series: the crowns’ contact area growing, and the yarn’s own resistance to being flattened.

A knitted fabric resists by bending its yarn. Its loops are in point contact and the yarn between them runs free, so the first thing a press does is shorten the straight line between two interlacings and force the thread between them to bend harder. Nothing is being flattened; something is being bent.

The two fabrics store the work in different places. A woven cloth’s compression energy goes into the transverse deformation of its threads. A knitted fabric’s goes into the bending of a free run.

Which predicts a difference in shape #

That difference is not just an account of the mechanism; it says what the two curves should look like.

Yarn compression stiffens hard: pressing a thread flat gets rapidly more expensive because the contact area grows and the material runs out of room. A woven cloth’s curve therefore rises steeply almost from the start.

Bending a free run does not stiffen in the same way. The energy is quadratic in the curvature and the curvature grows smoothly as the chord shortens, so a knitted fabric’s resistance should rise far more gently over its first substantial fraction of strain — and then, when the loops finally come into contact with one another through the thickness, meet a wall.

That is a testable prediction about the shape rather than the value, and shapes are what this collection’s brackets do not eat.

The numbers side by side #

Per crossing, at rest, this collection’s woven cloths press their own crossings together with between 185 and 851 millinewtons. A jersey presses its interlacings with 38.3, of which 7.8 acts through the thickness.

So a woven cloth’s crossings press between five and twenty-two times harder than a knit’s, and the part of a knit’s force that acts through the thickness is smaller again by a factor of five. Taken at face value that says a knitted fabric is roughly two orders of magnitude softer through its thickness than a woven cloth of comparable yarn.

Anybody who has pressed both would agree with the direction. The factor is not to be taken at face value, for a reason set out below.

Why the factor is not to be trusted #

The two forces are computed by routes with nothing in common, and that is usually a strength here — but in this case one of them is measuring something the other is not.

The woven figure is obtained by inverting a measured thickness against a compression model: the cloth is known to be a certain thickness at rest, the model says what pressure would produce that thickness, and the answer is reported as the force the crossings are carrying. So it includes everything real that is holding a woven cloth open, whether the model names it or not.

The knitted figure is obtained by differentiating a solved shape, and it includes only what is in the model: bending, and nothing else. It excludes the yarn’s own transverse stiffness, the hair layer, and any contact between loops that the model lets pass through one another.

Comparing them is comparing a measurement’s residue with a model’s output. The direction is safe; the factor is not.

Why a woven cloth has no equivalent of the soft part #

The contrast is sharper than the two mechanisms suggest, because a woven cloth’s crossings are in contact at zero load and a knitted fabric’s loops are not in contact through the thickness at all.

A woven cloth at rest already has its warp crowns bearing on its weft crowns, with a normal force this collection computes at between 185 and 851 millinewtons a crossing. There is no gap to close before the resistance begins.

A knitted fabric’s two faces are held apart by yarn that runs free between its interlacings, and nothing on the front face touches anything on the back. Pressing it does not bring two things into contact until the loops have moved a long way — which is the geometrical statement behind the softness, and is also, uncomfortably, the regime where this model’s lack of self-contact bites hardest.

What is missing before this is a curve #

Three things, and each one bites at a different depth.

A compressible yarn. The model’s thread is a line of fixed diameter. Real yarn flattens, and at the crossings of a knitted fabric it flattens first — which means the fabric’s thickness starts falling before any loop has moved at all.

Self-contact. The model stops a thread reaching further than its own length and stops nothing else. Adjacent courses can pass through one another, which is why its extension ceiling is three times any real jersey’s. Under compression the same absence means nothing stops the fabric being squashed to zero thickness.

And a hair layer. A knitted fabric’s surface is crowns with fibre standing off them, and a gauge meets the fibre first. The first tens of micrometres of any real compression measurement are the canopy being crushed, and the loops have not begun to move.

So what exists here is a relaxed thickness and an initial slope, not a curve. Saying so is the honest position and it is a much better position than none.

Where the pressures a fabric sees actually are #

Fifteen kilopascals is a large pressure for a fabric and it is worth putting beside the ones a garment meets.

A finger pressing to judge a fabric’s handle applies a few kilopascals. A person sitting applies about ten over the contact area. A compression stocking applies two to five. A thickness gauge in a standard test applies one.

So every ordinary use of a knitted fabric is in the first fraction of its resistance, well below the pressure that would begin to close its loops. What is being compressed in all of those cases is the hair layer and the crowns, not the structure.

That has a consequence for measurement that is worth stating plainly: a standard thickness measurement of a knitted fabric is a measurement of its hair, not of the two yarn diameters this collection predicts. The two are not competing answers to one question; they are answers to different questions.

The tightness factor, which moves it a long way #

The resistance is a bending stiffness over a length squared spread over an area, so it moves fast with the gauge:

A factor of twenty across a range one machine can knit. That is much more variation than the fabrics’ thicknesses show — which do not vary at all — and it is the quantitative form of a familiar observation: a loose knit is soft and a tight one is firm, at the same thickness.

The pressure falls faster than the force does because the stitches spread out as the loop lengthens, so there are fewer of them per unit area to carry the load.

And a second bed moves it further #

A rib at a three-diameter bed gap has a through-thickness force of 10.1 millinewtons a stitch against a jersey’s 7.8, over a fabric twice as thick.

That is springier in the way a hand reads it: more force, more travel. The energy stored per unit area before the loops meet is larger by more than the ratio of the forces, because there is twice as far to go.

It is also the reason a rib feels like a different kind of fabric under a thumb rather than a firmer version of the same one. A jersey’s resistance is a thin fabric bending; a rib’s is a thick one.

The comparison that would settle it #

One measurement would tell most of this story, and it is a standard one.

Take a knitted fabric and a woven cloth of the same yarn and similar areal weight. Measure both on a compression tester from a very light load to a heavy one, and plot thickness against pressure on log axes.

The model says the knitted curve should start higher, fall further and be less steep over its first decade of pressure, and that both curves should converge at high pressure where both are compressing yarn rather than structure. If the knitted curve is steeper than the woven one at low pressure, the mechanism proposed here is wrong and something other than bending is carrying the load.

That comparison has not been made in this collection, and it is the most obviously available next step on this ladder.

What this rung does not claim #

It does not claim a knitted fabric is soft. It claims a knitted fabric’s structure is soft, and a fabric’s first few per cent of compression is not its structure.

It does not claim the woven and knitted numbers are commensurable. One is a model’s output and one is a measurement’s residue.

And it does not supply a curve. It supplies where a curve starts and how steeply, which is two of the several things a curve needs.

The bracket, and what survives it #

Every force here is a yarn’s bending stiffness over a length squared, and a spun yarn’s bending stiffness is a band a hundred and thirty wide. So the fifteen kilopascals is the free end of a wide bracket and the whole column of pressures inherits it.

Three things survive. The thickness, because it is a length and has no stiffness in it. The ratio between two fabrics’ resistances, because the stiffness divides out — a rib against a jersey, a tight knit against a loose one. And the shape of the curve, which is a statement about which mechanism is operating rather than about how hard it pushes.

Which is why this rung’s claims are put as a mechanism and a shape rather than as a table of pressures. The table is there because a number with a stated bracket is more useful than no number, and it should be read as an order of magnitude.

What is genuinely new here #

Two things.

A knitted fabric has a compression resistance at all, computed rather than asserted: 15 kilopascals of initial slope on a relaxed thickness of two yarn diameters.

And the two halves of this collection resist for different reasons. A woven cloth flattens its threads and a knitted fabric bends them, and that is a statement about where the work goes rather than about how much of it there is.

What the pictures cannot show #

Neither figure here is a compression curve, because there is not one to draw. The first is the energy against a climb, whose slope is the resistance; the second is a section showing where the force acts.

A reader looking for a thickness-against-pressure plot will not find one on this page, and the reason is in the section above about what is missing. Drawing one would mean extending the model past the point where it is honest.

What is worth taking away #

A relaxed jersey is two yarn diameters thick and resists at fifteen kilopascals per unit strain, and that is a compression curve’s first point rather than a curve.

The mechanism is the substance: a woven cloth resists by flattening its threads and a knitted fabric by bending them, so the two curves should have different shapes as well as different heights — and a shape is a claim this collection’s brackets do not swallow.

What a compression measurement would decide #

One experiment settles three claims at once, and it is a standard test.

That the relaxed structural thickness is two yarn diameters, which is the knee in a load sweep rather than any single reading.

That the initial slope is of order fifteen kilopascals, which is the flat part’s gradient.

And that a knitted curve is less steep than a woven one over its first decade of pressure, which is the mechanism claim and the one this rung actually rests on.

Three predictions, one apparatus, and none of them run here. That is the honest state of the knitted compression account: a first point, a slope, a shape and no measurement.

Which rungs this stands on #

The thickness, at how thick a knit is, which is where the curve starts.

The through-thickness force, at the force that holds a knit open, which is its initial slope.

And the woven curve it is being compared with, at a cloth compresses along its own bearing curve, which is a measured account rather than a modelled one and is the reason the comparison’s factor cannot be trusted.

Nothing else is added here. What is new is the mechanism claim, and a mechanism claim is a statement about which of two already-computed things is doing the work.

The regime a garment actually lives in #

It is worth ending on where the pressures a fabric meets sit against the fifteen kilopascals, because the answer decides how much of this rung is about fabrics in use.

A thickness gauge applies about one kilopascal. A finger judging handle applies a few. A person sitting applies about ten over the contact area. A compression stocking applies two to five.

Every one of those is below the fabric’s own initial slope, so every ordinary use of a knitted fabric is in the first fraction of its structural resistance — and the first fraction of a real fabric’s resistance is its hair layer and its crowns rather than its loops.

So this rung’s numbers describe a regime a garment rarely reaches. That is not a reason to leave them uncomputed; it is the reason the mechanism claim matters more than the value, because the mechanism is what decides the shape of the part a garment does reach.

The one comparison this collection can already make #

There is a pair of numbers on either side of the site that are commensurable, and it is worth ending on them because they are the strongest form the contrast takes.

A woven cloth’s crossings press with between 185 and 851 millinewtons and all of it is through the cloth, because a woven thread’s plane stands at a right angle to the fabric. A jersey’s press with 38.3 and a fifth of it is.

So through the thickness the two differ by between twenty-four and a hundred and nine times, where the raw forces differ by five to twenty-two. Two thirds of the contrast is the size of the forces and the remaining third is where they point — and the second third was not available at all until the loop had a third coordinate.

Where the ladder goes next #

A thickness that resists is also a thickness that insulates, and the two are the same geometry read for different purposes: a knit is warm because of where its yarn is not.

And what a gauge actually reads on a knitted fabric — as against what the structure is — is the subject of what a thickness gauge reads on a knit.