What holds a nap in a knit

A raised fabric is one that has had fibre deliberately dragged out of its surface. What decides how much comes is what holds a fibre in, and this collection computed that for a woven pile from the ground cloth’s own tension — and could not do the knitted case at all, because a relaxed knit has no tension in it.

It can now, and the answer is a length rather than a force: a cotton fibre in a relaxed poplin breaks rather than slides once about thirty-four millimetres of it is buried, and in a jersey of the same yarn the figure is a thousand and forty-seven.

The arithmetic #

A contact between two yarns presses over a patch, and the fibres in that patch share the load. One fibre’s share is one over the number of fibres in the section, which for a 20 tex cotton is a hundred and eighteen.

So the grip on a fibre per millimetre of its buried length is the friction at the contacts along that millimetre, divided by the fibre count. For the jersey that is nought point zero six millinewtons per millimetre; for the poplin, one point seven five.

A cotton fibre breaks at about sixty millinewtons. Divide and the crossover lengths fall out: thirty-four millimetres in the cloth, a thousand and forty-seven in the knit.

Why the knit’s is a thousand rather than a hundred #

Two factors again, multiplying rather than competing. The contact force is eight times lighter and the contacts are four times further apart, so the grip per unit length is thirty-one times weaker and the crossover length is thirty-one times longer.

Neither factor is about fibre. Both are about how a loop is built.

That the two multiply rather than compete is the whole of why the answer is so far apart from the woven one. Eight and four are each unremarkable — either alone would put the knit’s crossover length within the range a woven cloth already covers, and the argument would be about degree. Together they are thirty-one, which puts it a decade away, and a decade is the difference between two fabrics that behave similarly and two that need different finishing routes, different fibre lengths and different expectations about how long the nap survives wear.

And the direction of both factors is set before any fibre is chosen. A loop presses lightly because it is a curve held in equilibrium by its own bending, and its contacts are far apart because a loop is large; both follow from the topology of a knitted stitch and neither can be adjusted by spinning a better yarn. So a knitted nap is held more weakly than a woven one as a matter of construction, and the only remaining levers are the fibre’s own length and its surface — which is why raised knitted fabrics are made from staple long enough to be gripped by several loops at once.

Where a real fibre’s burial falls #

This is the part that turns two numbers into a statement about fabrics.

A cotton staple is about twenty-eight millimetres and a fibre end is buried, on average, over half of it — the same construction this collection’s hairiness ladder uses to count fibre ends. So a typical buried length is around fourteen millimetres.

In the woven cloth that is two and a half times short of the thirty-four-millimetre crossover, so a typical fibre slides — but not by much, and the tail of the burial distribution reaches the boundary. In the knit it is seventy-five times short, and nothing in the distribution comes anywhere near it.

What that predicts #

Two familiar behaviours, and they are the same behaviour on opposite sides of a boundary.

A raised woven cloth stops shedding. The loosely-held fibres come out in the first few washes, and what is left is the long-buried tail — the part of the distribution at or past the crossover — so further rubbing breaks fibres rather than withdrawing them, and a broken fibre leaves its buried part behind. The surface stabilises because the population that could leave has left.

A raised knit never stops. Nothing in the whole distribution comes within a factor of thirty of the crossover, so every rubbing withdraws fibre rather than breaking it, and there is always more to come. A fleece sheds for its whole life, which every owner of one knows and no account of raising quite explains.

The boundary the staple sits on #

That the woven crossover and the mean burial are within a fifth of one another is worth a section on its own, because a near-coincidence either means something or should be said not to.

It is unlikely to be an accident. A staple length is what spinners select for, and what they select for is a yarn that holds together — which means fibres buried long enough to be gripped. A fibre much shorter than the crossover makes a weak yarn that sheds; one much longer wastes length. So the trade has been optimising towards this boundary for as long as there has been spinning, without a number for it.

That is a claim about why the two numbers are close and not a derivation, and it is offered as one. What can be said with confidence is the consequence: a woven cloth’s fibres sit on the boundary, so small changes in finish, moisture and friction move them across it, which is why shedding behaviour in woven cloths is so sensitive to finishing and so hard to predict.

What a raising machine is doing #

Raising a knit and raising a woven cloth are not the same operation, and this says why.

On a woven cloth the wires have to break fibres to take them, and the strength lost is real: raising a woven cloth costs it tensile strength, because the fibres that make the nap were carrying load and are now cut.

On a knit the wires withdraw fibres rather than breaking them, so the nap is made of whole fibres pulled out of their yarn. The fabric loses less strength — a knit’s strength was never the fibres’ tensile continuity anyway — and the nap is longer, softer and much less durable. That is a fleece, and it is why a fleece is soft.

What it costs to hold one #

Putting a number on the anchor itself rather than on the crossover: a cotton fibre buried over fourteen millimetres in a jersey is held by about eight tenths of a millinewton, which is under a tenth of a gram-force.

In the poplin the same fibre is held by twenty-four millinewtons, which is two fifths of its own breaking load. The two are not near neighbours, and neither figure has ever been available before.

Why this is a lower bound #

The arithmetic counts only the inter-yarn contacts, which is the part that differs between the two fabrics.

A fibre is also gripped by its neighbours inside its own yarn, held there by twist, and that grip is the same in both fabrics and is not counted here. So both crossover lengths are overestimates — real fibres are held harder than this — and the ratio between them survives, because the uncounted term is identical in both.

The direction is worth stating clearly: the woven figure of thirty-four millimetres is an upper bound on the crossover, so real fibres cross it sooner and the woven cloth stabilises faster than the arithmetic suggests. The knitted figure has the same correction applied to a number seventy-five times too large to matter.

The other bound, and which way it runs #

The knitted contact force is an upper bound, because a set yarn presses less than an unset one. So the knit’s grip is at most what is quoted, its crossover length is at least a metre, and the conclusion is safe in the direction the error runs.

That is the second time on this ladder the error has run the convenient way, and it is not luck: the setting only ever reduces the knitted force, and every argument here is that the knitted force is small.

What the picture cannot show #

A fibre. Every drawing in this collection’s raising ladder shows yarns and wires, and the object being argued about is a twelve-micrometre filament inside a yarn a hundred and sixty-seven micrometres across.

Nor can any figure show the load sharing, which is the model’s weakest assumption. One fibre’s share of a contact is taken to be one over the fibre count, and a real contact loads the fibres at the surface far harder than the ones in the middle — so a surface fibre, which is exactly the one a raising wire catches, is held harder than the average and the arithmetic understates its anchorage.

That is the one place the error runs the wrong way, and it is recorded rather than smoothed over.

Where the fibre actually is #

It is worth looking at the structure the fibre is buried in, because the contacts it crosses are visible and the count is checkable by eye.

Eight against thirty-one is the factor of four, counted rather than computed, and the picture is where it can be counted. What it cannot show is that each of the eight is also eight times lighter, which is the other factor and the one that has to be read.

Both together are what a raising wire meets, and neither has anything to do with the fibre being cotton.

A number for the whole surface #

Scaling from one fibre to a fabric gives an estimate of what raising actually removes, which is a quantity the trade weighs.

A raised knit’s nap is a population of withdrawn fibre ends, and each was held by under a millinewton. A raising machine’s wires apply far more than that, so the limit on how much comes is not the force at all — it is how much fibre the wires can reach, which is a matter of the surface’s own geometry.

That is a qualitative change from the woven case, where the force is the limit and raising harder takes more fibre at the cost of breaking it. On a knit, raising harder does not take much more, because everything reachable was already coming. Which is why raising a knit is a gentle operation and raising a woven cloth is a violent one.

What would test it #

Single-fibre withdrawal, which is a difficult experiment and an established one: embed a fibre to a known depth, pull it, record whether it slides or breaks.

The prediction is sharp. In a woven cloth at fourteen millimetres of burial most fibres should slide, with the fraction breaking rising sharply as the burial approaches thirty. In a knit at any burial a garment allows, essentially all of them should slide. A result where the knit breaks any appreciable fraction would mean the load sharing is far more uneven than assumed.

What follows for a specification #

A raised knit’s shedding cannot be finished away, because it is structural.

A softener makes it worse by lowering the friction. A resin finish that binds the fibres at their contacts helps, because it adds a term the arithmetic here does not have. Tightening the fabric helps by a factor of about three across the knittable range, which is the same lever as everything else on this ladder. And singeing — removing the standing fibre before it is raised — is the only treatment that addresses the supply rather than the grip.

None of those changes the crossover length by the thirty-fold that would be needed to make a knit behave like a cloth.

What warmth has to do with it #

The reason anybody raises a fabric is worth putting beside the reason it sheds, because they are the same property read twice.

Warmth is mostly the hairs, and a nap works by holding air in a layer several millimetres deep. That layer is made of fibre standing clear of the surface, which is precisely fibre that is not buried past its crossover — so a fabric whose nap is durably anchored is a fabric whose nap is short.

The trade-off is exact and unavoidable. A long soft nap is made of loosely held fibre and sheds; a short durable one holds less air. A fleece chooses the first and a raised woollen coating chooses the second, and both are right for what they are for.

Where this leaves the older rung #

What holds a tuft in newtons computed a woven pile’s anchorage and found it fell short of a carpet specification by a factor of three to six, which was a statement about where the rest of the anchorage comes from — the backing.

The knitted case needed a contact force and did not have one. It has one now, and the answer is that the mechanical anchorage in a knit is not three times short of a specification but two orders of magnitude short of even holding one fibre against ordinary rubbing. A knitted pile that has to stay put needs a backing, an adhesive or a set, and every commercial one has one.

The same arithmetic at other constructions #

Two ends of the comparison move, and it is worth knowing how far before “thirty times” is treated as a constant.

The woven end moves further. Across this collection’s eight cloths the contact force spans a factor of five, so the woven fibre crossover runs from about six millimetres for a cheesecloth to thirty for a batiste — and a fine, openly-set cloth is much closer to the knitted situation than a heavy one.

The knitted range stays two orders of magnitude away from the mean burial in every construction, which is why the qualitative conclusion holds. The woven range straddles it, which is why shedding in raised woven cloth is so sensitive to construction — a raised voile behaves noticeably more like a fleece than a raised duck does.

The third fabric, which is neither #

A pile is the third member of the surface family and it behaves like neither of the two above, which is worth a paragraph because it shows what the arithmetic is actually about.

A pile’s tuft is a whole yarn rather than a fibre, anchored by wrapping round the ground picks, and its anchorage is a few newtons rather than a fraction of a millinewton — four orders above a nap fibre’s. That is not because a pile’s contacts are stronger; it is because a tuft has a hundred and eighteen fibres in it and wraps its anchor several times, so the capstan multiplies what friction it has.

So the surface family — hair, nap, pile — is one object at three anchorages, and the anchorage is the thing that separates them. A hair is held by accident, a nap by whatever the raising left, and a pile by a construction chosen in newtons. This rung supplies the middle one, which was the missing member.

What fraction of a woven cloth’s fibres stay #

The woven crossover sits at thirty-four millimetres and the mean burial at fourteen, and the essay reads that as the fibres sitting on the boundary. The distribution is what decides how many are past it, and putting a rough number on it turns a near-coincidence into a prediction about how much nap survives.

A fibre’s buried length is at most its own staple length and on average about half of it. So a fibre is past the crossover only if it is longer than about sixty-eight millimetres — twice the crossover — or is unusually deeply buried for its length. An Upland cotton’s staple distribution has a mean near twenty-eight and a tail; the fraction above sixty-eight is very small, and the fraction whose burial exceeds thirty-four is correspondingly small.

So the fibres that stay are a small minority — of order a tenth — and they are the longest ones.

Three consequences, and the third is a fibre-selection statement.

A raised woven cloth’s nap stabilises at a fraction of what raising initially lifted. The loosely-held majority comes away over the first washes and what remains is the long-buried tail. That is why raising takes several passes and why a raised cloth’s nap after a season is visibly thinner than the one that left the finishing works — the fabric has been shedding down to its tail.

And it explains why the shedding stops rather than slowing. A population with a threshold does not decay smoothly: everything below the crossover leaves and everything above it stays, so the loss is fast and then it is over. A mechanism with a continuous distribution of grips would give a long tail of slow shedding, and that is not what a raised woollen coating does.

And a long-stapled fibre gives a durable nap at the same construction. The surviving fraction is the tail above twice the crossover, and a staple distribution shifted upward puts more of itself there — so a raised cloth of a long cotton or a long wool sheds less and keeps more of its nap, at the same sett, the same yarn count and the same raising. That is a fibre argument this collection can make, and it arrives from a length rather than from anything about the fibre’s own strength or surface.

The caution is that the staple distribution is not in this collection and the tenth is an estimate from a mean and a shape rather than a computation. What is computed is the crossover; what is asserted is that the surviving fraction is the part of the distribution beyond it, which is a statement about which measurement would settle it — a staple diagram, which every spinner already has.

Where the ladder goes next #

To the failure this all points at. A thread that always slides rather than breaking is a thread that can travel, and a loop travelling out of the loop below it is a run — which is a competition between two forces this ladder now has both of.