Raising moves the surface onto the hairs

Everything in this ladder has been about a surface made of yarn: crowns where threads come to the top of the cloth, plateaux where they float, and the distribution of heights between them. A raised cloth does not have one. Its outside is a layer of loose fibre ends, standing off the fabric, pointing in every direction, and there is nothing underneath them that participates in anything at all.

The claim #

Raising replaces a cloth’s surface with a different kind of object, and the criterion for whether it can be done is exactly the criterion for whether the cloth had any crown line to lose.

Three statements, and the second is an exact coincidence that is not one.

A raised surface has no crowns, no plateaux and no orientation. Every result in this ladder — the bearing exponent, the specular area, the azimuth selectivity, the crown line census — is about a woven surface, and none of them survives a nap.

Raisability and crown line are the same criterion. A raising tooth needs a float to catch, which means a run of two crossings or more; crown line is contributed by a run of two crossings or more. Both censuses over the four-by-four catalogue return the same answer, and it is the same two drafts.

And what is spent is the shine. The floats that carry the crown line are the floats the teeth pull apart. A cloth cannot be both lustrous and napped, and the reason is not a matter of degree.

The two censuses, which are one census #

Only a float can be raised settled the raisability question over the whole four-by-four catalogue: of the 22,874 drafts in which every end and every pick interlaces, 22,872 have a catchable float on one face or the other and two do not. The two are the plain weave and its translation.

Two drafts of twenty-two thousand settled the crown-line question over the same catalogue and returned the same pair. Every draft with a run of two carries crown line; the only drafts without a run of two are the plain weaves.

The two questions are the same question. A run of two is a float a tooth can get under and it is a plateau a light can reflect from, because both are consequences of a thread being on the face at two consecutive crossings — one asks for something to catch and the other asks for something flat, and a horizontal length of thread is both.

That is worth stating because the two essays were written a long way apart, about two apparently unrelated finishing questions, and arrived at the same two matrices. A census that keeps returning the same exception is measuring the same property under two names.

What the new surface is #

A raised layer is not a surface in the sense this ladder has been using. It is a brush: a population of fibre ends, of varying length, standing at varying angles, with air between them.

Three consequences follow and all three are qualitative rather than numerical.

It has no bearing curve of the sort computed here. A brush’s contact area is a function of how far it has been compressed, but the function comes from the statistics of fibre lengths and angles, not from any geometry of the cloth beneath. It is also enormously compliant: a raised layer compresses by a large fraction of its own height under a pressure that would move a woven surface by a micrometre.

It has no orientation, or rather it has a weak one. A raising machine works in one direction, so the fibres are combed and lie preferentially with the machine — which is why a napped cloth has a way of the nap and why it is cut with the pile running one way. But the fibres are individually at every angle, so the specular selectivity that makes a shot cloth switch is gone. A napped cloth is matt from every direction, and the small directional effect it retains is a shading rather than a highlight.

And it interpenetrates. The hairs are what touch established this for the spun yarn’s own hair layer, and a nap is that layer deliberately enlarged: two napped surfaces pressed together do not meet at a plane, they mesh, and the contact between them is a matter of fibres bending past one another.

What was counted, and how #

Nothing new was computed for this essay. That is the point of it.

The raisability census is raising’s and is exact: for each draft, the float map is read and the longest run on each face is compared with the tooth’s minimum. At a minimum float of two, 22,872 of the catalogue are raisable; at three, 22,784; at four, none — because a four-by-four repeat cannot hold a run of four with every thread interlacing.

The crown-line census is the surface’s and is also exact, and its zero set is the same two masks.

What the surface arithmetic cannot do is describe what happens after the raising. It can say what has been destroyed, exactly, and it has no model of what replaces it.

How high the new surface stands #

The one quantity that can be estimated without a model of the nap is where the new outside is, and it settles how thoroughly the old one has been buried.

A raised layer on a flannel stands between half a millimetre and two millimetres above the cloth. The woven surface it covers has a peak-to-valley relief of about 380 micrometres on an ordinary sheeting and less on a lighter cloth. So the nap is between one and five times the whole depth of the surface it replaces, and anything pressing on the fabric has to compress the entire fibre layer before it reaches the first crown.

That is a large ratio and it explains why the transition is total rather than partial. If a nap stood a few tens of micrometres proud, a firm touch would push through it and meet the crowns, and a fabric would have two contact regimes with a crossover between them. At half a millimetre and above there is no crossover in any range a person applies: the woven surface is simply not reachable.

The exception is the worn cloth. A napped fabric in use loses its nap where it is rubbed — at an elbow, a cuff, a seat — and when the layer is gone the crowns are back. A worn flannel is shiny at exactly the places it has been worn, and the shine is the crown line reappearing from under a layer that has been rubbed away. That is a visible everyday phenomenon with an exact account: the fabric has reverted to the surface this ladder computes.

The exchange, priced three ways #

This collection already prices raising in one currency, and the surface adds two more.

Strength, which is already computed: fibre standing up on the surface is fibre no longer in the load path, and the float length that makes a good nap is the float length that weakens the cloth.

Lustre, which is exact: a napped cloth’s specular area is not reduced, it is replaced. The crown line is still there under the nap and is returning light into a fibre layer that scatters it. The measurable consequence is that a fabric’s gloss falls to the floor of the instrument, and the floor is set by the fibre rather than by the weave.

And contact, which is a reversal. A woven surface touches on a per cent or two of its plan and concentrates pressure by a factor of twenty to fifty; a napped surface touches on a great many fibre ends and concentrates far less. A nap is a pressure-distributing layer, which is a large part of why a raised cloth feels soft, and it is the same argument that makes a cut pile behave as it does arrived at by tearing rather than by cutting.

Why a filament cloth cannot be napped #

The float criterion is necessary and it is not sufficient, and the missing condition is about the yarn rather than the weave.

A raising tooth catches a fibre end. A continuous filament has two ends per bobbin and none anywhere in the cloth, so there is nothing for a tooth to lift: dragging wires across a filament satin abrades it and raises nothing.

So raisability has two conditions and this collection has computed only one. The weave must offer a float, which is exact and censused; the yarn must be staple, which is a fact about the yarn and is binary. A filament cloth with the most raisable draft in the catalogue is not raisable, and a staple cloth in a plain weave is not either — for two entirely different reasons that both come out as no.

That is a useful shape to notice. A property with two independent necessary conditions cannot be predicted from a census of one of them, and the census of drafts here says which cloths are not excluded by the weave, which is a weaker statement than it looks.

What a napped cloth measures like #

Three instruments give different readings on a raised cloth, and the differences are all consequences of the layer rather than of the fabric.

A thickness gauge reads the nap. A presser foot at a kilopascal compresses a fibre brush a long way — much further than the micrometre or two it sinks into a woven surface — so a napped fabric’s measured thickness is a strong function of the pressure, far more so than a woven one’s. Every standard for raised fabrics specifies a lighter foot for exactly this reason.

A gloss meter reads the fibre. The crown line is still under there and is still returning light, into a layer that scatters it in every direction. What comes back at the mirror angle is the fibre’s own surface reflection, which is a fibre property.

And an abrasion tester reads the nap first and the cloth afterwards, in two clearly separate phases: a fast initial loss of fibre with no loss of strength at all, and then a slow loss of the fabric itself. That two-phase curve is a familiar nuisance in wear testing and standards instruct the operator to discard the first part of it. It is the layer being removed, and it is the only phase of the test in which mass loss really is uncoupled from damage.

How much of a flannel is nap #

The two-phase abrasion curve is described above and left as a shape. It has a corner in it, and the corner can be located, because the first stage removes exactly the fibre that raising put on the surface and that fibre can be weighed.

Take a nap standing half a millimetre proud on average at ninety fibre ends per square millimetre, in fifteen-micrometre cotton. The fibre volume above the cloth is then 8 × 10⁻³ cubic millimetres per square millimetre of fabric, and at cellulose’s density that is

about 12 grams per square metre.

Against a flannel at two hundred grams per square metre, the nap is six per cent of the cloth’s mass.

So the corner in the abrasion curve is at six per cent. Below it a test is removing fibre that was already out of the load path — raising took it there — so mass falls and strength does not move at all. Above it the test has reached the threads, and strength then falls faster than mass, because the damage concentrates on the crowns.

A flat then a steep, with the knee at six per cent of mass, is a specific prediction about a curve that standards currently handle by instructing the operator to discard its first part. It is also the only phase of any wear test in which mass loss is genuinely uncoupled from damage, which is why discarding it is right and why knowing where it ends is worth something.

Which also dates the shiny elbow #

The same number says how far a garment has to wear before the surface underneath comes back.

A napped cloth reverts to its woven surface when the layer above it is gone, and the layer is six per cent of the local mass. So a flannel elbow goes shiny after it has lost about six per cent of its fabric there — not after it has worn thin, and not as a gradual dulling, but at a fairly definite point where the last of the nap goes and the crown line is exposed.

That matches the way the defect appears. A worn flannel does not shade gradually from matt to glossy; it develops a shiny patch with a recognisable edge, and the edge is where the nap ends. The transition is sharp because the two surfaces are different objects rather than two states of one, which is the essay’s whole point arriving as an everyday observation.

It also says the repair works and why. Brushing a shiny patch raises what fibre is left and restores the layer partially, and it stops working when there is no fibre left to raise — which is well before the cloth is worn through, and is the point at which a tailor calls a garment finished.

And it prices the protection #

The last section says the nap protects the threads and calls it the reason a raised cloth wears comfortably despite being weaker. The six per cent puts a figure on both halves.

The cost is the fibre pulled out of the load path, which is what raising spends and which is that same six per cent of the mass — though not six per cent of the strength, since the fibre is drawn from the floats rather than cut.

The benefit is that the same six per cent is spent first, before any wear reaches a thread. So the exchange is a fixed quantity of fibre moved from the inside of the cloth to the outside, where it is sacrificed instead of the threads.

Whether that is a good bargain depends on how a garment fails. If it fails by abrasion at a few places, the nap is spent where it is needed and the trade is excellent. If it fails by tearing or by seam slippage, the fibre has been given up for nothing. A raised cloth is a cloth that has pre-paid its abrasion and has no defence against anything else — which is a fair description of what flannel is good for and what it is not.

Where the model stops #

There is no model of the nap at all. Everything above says what raising destroys. What it creates — the height distribution of the fibre ends, the compliance of the layer, the friction between two napped faces — needs a statistics of fibre lengths and protrusion that this collection does not have and that would be a spinning subject rather than a weaving one.

The raising process is not modelled either. How many fibres a tooth lifts per pass, how deep it reaches and how much it breaks are machine questions, and the strength essay treats them as an exchange rate rather than as a mechanism.

And the nap is reversible in one direction and not the other. A crushed or worn nap can be brushed back up, partly; a cloth that has been raised cannot be un-raised, because the fibre has been pulled out of the yarn’s body and will not go back. The surface arithmetic has nothing to say about either.

The float criterion is for a four-by-four repeat. Real napping cloths — flannel, moleskin, blanketing — are woven on longer repeats with much longer floats than four ends can hold, precisely because a longer float gives the teeth more to work with. The census establishes the boundary case, not the practice.

The generalisation #

When a finish replaces a surface, every property computed from the old surface stops being about the object.

That is obvious stated baldly and is easy to forget in practice, because the fabric still has a draft, a sett, a thickness and a weight, and all the arithmetic that produced its surface still runs. The arithmetic is describing something that is now buried.

The more useful form is a rule for reading a finishing route: ask what the outermost few hundred micrometres is made of after each step, and expect every surface property to be a property of that layer and of nothing beneath it. A calender leaves the yarn as the outer layer and changes its shape; raising replaces the outer layer entirely; a coating replaces it with a film. Three finishes, three different answers to the same question, and only the first leaves this ladder’s arithmetic applicable.

One more consequence of the same rule is worth carrying, because it cuts the other way. A finish that replaces the surface also protects it. A napped cloth’s crowns are not merely hidden from the light, they are hidden from the abradant, and every micrometre of fibre layer is a micrometre the rubbing has to remove before it can reach a thread. That is the whole of why a raised fabric wears comfortably despite being weaker: the strength has gone into the nap and the nap is spent first.

Who found it, and when #

Raising is medieval and the teasel is older than the wire card. The float criterion is this collection’s own, from the work that priced what a finish does to a cloth.

What is new here is the identification: that the raisability criterion and the crown-line criterion are the same criterion, so the census that says which cloths can be napped is the census that says which cloths have a specular surface to lose. Two essays written a long way apart returned the same two matrices, and the reason is that both were asking whether a thread is ever on the face twice running.

Where the ladder goes next #

To the finish that replaces the surface with something computable rather than statistical: a coating fills the crowns before it bridges the holes, where the volume above the bearing curve says what the add-on has to be and where every gram spent on the crowns is a gram not spent on the holes.

Sideways, the knitted fabric’s own two surfaces — a jersey has two surfaces — which are made of loops rather than floats and which are the last place in this ladder where crowns are still crowns.