A jersey has no float for a wire to catch

Only a float can be raised is the first of these essays and it is a clean piece of arithmetic. A raising machine drags wire teeth across a cloth; the teeth need something unsupported to hook; what they hook is a float; so which fabrics can be napped at all is a question about the matrix, decidable exactly, and over the whole four-by-four census the answer is two.

Every knitted fabric in this collection is outside that census, and knitted fabrics are raised constantly — a brushed jersey, a fleece, a sweatshirt back are all raised knits and they are the largest tonnage of raised cloth there is. So either the criterion says something about them or the criterion is about weaving rather than about raising.

It says something, and what it says is not what a reader would expect.

A knitted float is a different object #

The woven criterion reads a float off point paper: a run of face, a thread on the surface with nothing over it. A knit has no point paper of that kind, and a second bed changes what a float is — the knitted float defined there is a segment of yarn between two consecutive loops that passes one or more wales, and where it lies depends on which beds its two ends are on.

Three cases and no others. Both ends on the front bed: the yarn lies on the front fabric’s technical back, and if any back-bed wale is spanned the back fabric closes over it and the float is interior. Both ends on the back bed: the mirror image. One end on each bed: the yarn crosses the gap and is inside the cloth by construction.

An interior float is unreachable. Whatever a wire does at the surface, it cannot get at a length of yarn the other fabric is lying on top of. So the raising question for a knit is not “has it a float” but “has it an exposed float”, and the two are very different counts.

A plain jersey has none at all #

The first answer is the sharpest and it needs no census.

A plain jersey’s yarn goes from every wale to the next and passes none of them, so every segment of it is a sinker loop rather than a float. There is nothing unsupported anywhere in the fabric, at any length, and the woven criterion returns zero rather than a small number.

That is a stronger statement than “hard to raise”. It says the thing the woven criterion is about does not exist in a plain jersey, so any account of what a raising machine does to one has to be about something else.

And a brushed jersey is an ordinary commercial fabric. So the account has to be about the hair layer: what the wire catches on a jersey is fibre ends standing off the loops, not lengths of yarn, and raising a woven cloth moves the surface on to the hairs as a consequence of catching floats, while raising a jersey does it directly with nothing in between.

They are two different operations sharing a machine, and the accounts so far have treated them as one. The woven case starts at the matrix and ends at the hairs; the knitted case starts at the hairs and has no matrix in it. That is why the essay beneath it — what holds a nap in a knit — could compute an anchorage without ever asking what was being anchored: it was fibres all along.

Twenty structures of eleven hundred #

The census puts the named structures in context, and the context is thin.

Twenty of 1,135 is 1.8 per cent, and it is worth setting that beside the woven figure rather than against it. The woven census asks which of 22,874 drafts has a float of two or more anywhere, and nearly all of them do — the raising criterion there is easily met and the interesting count was the two that have crown line nowhere. Here the criterion is barely met at all.

The reason is the second bed. In a woven cloth a float is exposed by construction: there is one fabric and a run of face is on its face. In a two-bed knit most floats are swallowed — the enumeration finds 1,248 interior float segments against 24 exposed — because a structure that floats across one bed usually has the other bed knitting underneath it.

Every raisable knit is raisable on one side #

The census’s other finding is a zero and it is the one with a consequence.

Not one structure in the census is raisable on both faces. Ten are raisable on the face, ten on the back, and none on both — and the reason is immediate once stated: an exposed float lies on the face or on the back according to which bed holds its two ends, and a single float cannot be on both. A structure would need two exposed floats in opposite directions, and nothing this size manages it.

So a knit has a raisable side in a way a woven cloth need not. A woven cloth with a long float in both systems can be napped on either face and often is; a knit’s raisable face is decided by the structure, and a specification that names a raised knit without naming a face has left out something that is not a preference.

That also explains the shape of the fabrics in the trade. A sweatshirt fleece is raised on its back and a brushed jersey on either face, and the arithmetic says why: the first is a laid-in structure whose float is on the technical back, and the second has no float and is being raised on its hairs, which both faces have.

Which is what a fleece is for #

The structures that qualify are the laid-in ones, and that is not a coincidence — it is the construction being what it is for.

A fleece is a jersey ground with a third yarn laid in across the back, caught at intervals and floating between. The float is exposed by construction, its length is the tucking interval, and the whole point of putting it there is that a raising wire can hook it.

So the criterion does not merely classify fleece; it explains its geometry. The tucking interval is the float’s length, a wire needs a float of at least two wales, and a longer float raises more and holds less — which is exactly the trade-off the woven case prices as strength against warmth, arriving here as a choice of tucking interval rather than of weave.

The census cannot express a laid-in third yarn at all: its alphabet is knit, tuck and miss on two beds, and a laid-in yarn is a fourth thing. So the twenty structures it finds are the two-bed shadows of a construction that is really three-yarn, and the practical list is longer than twenty for a reason the enumeration is not equipped to see. That is a limit worth stating plainly rather than a hole: the census answers exactly the question it poses, which is about two-bed structures, and fleece is not one.

What the criterion is actually good for here #

Reading the two censuses together says what the criterion does and does not decide, and the division is clean.

It decides whether a wire can lift yarn. For a woven cloth that is the whole operation; for a knit it is a small and specific class of structures, and for the commonest raised knits it returns nothing.

It does not decide whether a wire can lift fibre. Fibre ends stand off every fabric ever made, in a population the hair layer describes, and a wire catches them whether or not there is a float underneath. That is the operation a brushed jersey undergoes.

And the two produce different naps. A nap lifted from a float is yarn pulled up and broken, so the nap’s fibres come from a length of thread that was carrying nothing anyway. A nap lifted from the hairs is the hair layer combed out and extended, so it takes fibre from loops that are carrying load — and a fibre in a knit is anchored by a metre of burial it does not have, so it sheds for the whole of its life.

That is the account’s own two findings meeting. The account below computed an anchorage and found it hopeless; this one says why the question arose at all, which is that a knit’s nap is fibre rather than yarn and fibre is what has no anchorage.

The numbers the two censuses produce, side by side #

Setting the woven and knitted counts in one place makes the difference between the two operations legible, and it is a difference of kind rather than of degree.

The line that matters is the third. In a woven cloth a float is exposed because there is one fabric and a run of face is on its face; in a two-bed knit the second fabric closes over most of them, and 1,248 of the 1,272 float segments the enumeration finds are interior.

That is the structural reason a knit is raised on its hairs and a woven cloth on its floats, and it is not a fact about machines or about fibre. A two-bed knit is two fabrics and the thing a wire wants is between them. A single-bed knit has only one fabric and no float at all, so it is short of the thing at both ends of the argument: nothing is hidden and there was nothing to hide.

The woven case, for the comparison #

The two cloths the woven census admits are worth drawing beside the knitted answer, because the contrast is what makes the knitted zero a finding rather than a null result.

A woven cloth’s problem is that there is too much to catch, not too little. The 2/2 twill offers a wire a float at every crossing pair, the raising census over the four-by-four catalogue finds the criterion met by nearly everything, and the design question is how much to take rather than whether anything is there.

A plain weave is the woven cloth that behaves like a knit, and the parallel is exact rather than approximate: no run of two, no float, nothing to hook, and whatever nap it takes comes off its hairs. So the knitted answer is not a new kind of result — it is the plain weave’s result, holding over almost the whole of a second field.

That is a satisfying place for the two accounts to meet. The property that made the plain weave the exception in every woven census is the normal case in knitting, because a knit’s yarn goes from wale to wale and passes nothing, exactly as a plain weave’s goes from crossing to crossing and floats nowhere.

What a specification should say #

The arithmetic ends at a practical point and it is worth stating because it is the kind a specification gets wrong.

A raised knit’s face is a property of its structure, not a finishing choice. Ten structures in the census are raisable on the face and ten on the back, and no structure is both — so “raised” without a face is an incomplete instruction for a laid-in fabric and a redundant one for a jersey, where both faces raise identically because both carry hairs.

And the two operations wear differently. Yarn lifted off a float is yarn that was carrying nothing; fibre lifted out of a loop is fibre that was carrying load. So a raised float costs the fabric nothing in strength and a raised jersey costs it the fibres it lost — which is the woven account’s exchange rate with its sign reversed, because there the raised fibre came out of a float too.

A specification that says how much nap it wants and not which of the two it is buying has priced neither.

What was counted, and how #

Each structure’s yarn path is traversed course by course, every segment between consecutive loops is classified by which beds its two ends are on and which wales it passes, and a segment passing one or more wales is a float. A float is exposed when the other bed’s fabric does not close over it, which is decided by whether any of the spanned wales belongs to the other bed. A structure is raisable at a stated minimum when it has an exposed float spanning at least that many wales. The census enumerates every assignment of knit, tuck or miss to each needle of each course on both beds, admits only those a machine could make, and asks the question of each.

Five things are checked. A plain jersey has no float at all, so the criterion returns zero rather than a small number. Some named structures are raisable and most are not. Every raisable one is raisable on one face only, which is the zero the census produces and would fail if the two classes had been confused. Over the whole two-bed census the raisable structures are under a tenth of the fabrics. And a longer float admits no more structures than a shorter one, at every step, which is the monotonicity a slip in the span count would break.

The frame — two needles by two courses, rib gated, with a tuck held at most four courses — is an input, and the longest exposed float it can hold is two wales.

Where the census stops #

The frame is small and the alphabet is short. Two needles by two courses is 6,561 candidates and admits 1,135 fabrics, which is enough to answer the question about exposure and not enough to say anything about long floats: the longest exposed float anywhere in it is two wales, because there is nowhere for a longer one to go.

A laid-in yarn is outside the alphabet, which is the largest omission and is the construction that matters commercially. A three-yarn fleece is not an assignment of knit, tuck and miss on two beds.

And the hairs are not counted. Everything here is about yarn, and the operation the census says a plain jersey cannot undergo is one it undergoes daily — on a population this criterion cannot see and the hair-layer arithmetic can.

Still open: what tucking interval a fleece wants #

The construction the census cannot express is the one with a real design question in it, and the question is a single number.

A fleece’s laid-in yarn floats between tuck points, and the interval decides two things at once. A longer float gives a wire more to catch, so a coarser interval raises more fibre for the same passes. And a longer float is held at fewer points, so it pulls out more easily and the nap sheds sooner — which is the account below’s anchorage question asked of a yarn rather than of a fibre, and which this collection’s capstan arithmetic can answer.

So there is an interval that maximises nap per unit of shedding, it is computable from the tuck’s wrap angle and the yarn’s friction, and nothing here has computed it. What the census does supply is the floor: a float of under two wales is not a float a wire can hook, so the interval is at least two and the question is only how much more.

Who found it, and when #

Raised knits are ordinary trade practice and the construction of a fleece is universal knowledge. The knitted float’s classification into face, back and interior is new here, arriving from the two-bed field. Putting the woven raising criterion to it, and finding that a plain jersey offers a wire nothing and that nothing in the two-bed census is raisable on both faces, was done here.