Raising spends the cloth's strength

A raising machine does not add anything. Every fibre in the nap was in the yarn before the operation, and every fibre standing up on the surface is one that used to be lying along a thread, contributing to that thread’s strength.

So a nap is not free and its cost is exactly its benefit: the fibre is worth more as insulation on the surface than it is as strength inside the yarn, which is a judgement about the fabric’s job rather than a fact about cloth.

What the nap is worth #

The reason to raise a cloth is thermal, and the mechanism is not the fibre.

Still air is the insulator. Its thermal conductivity is about 0.025 W/m·K, against roughly 0.05 for wool fibre itself and 0.6 for water. A fabric’s warmth is very nearly a measure of how much still air it can hold and how well it can stop that air from moving, and the fibre’s role is to hold the air rather than to insulate on its own account.

A nap is a layer of fibre ends standing off the surface, and the space between them is air that cannot easily circulate. So raising converts a fabric of a given thickness into a thicker one at almost no cost in mass — the mass was already there — and thickness at low density is exactly what a thermal insulator is.

That is why a raised fabric is so much warmer than its weight suggests, and it is why the operation survives its costs. Doubling a cloth’s effective thickness by rearranging fibre it already contains is a considerable return.

What it costs #

Three things, and they are not equally serious.

Tensile strength falls. Fibre pulled out of a yarn’s body no longer carries load along that yarn. The loss is not proportional to the fibre removed — a yarn’s strength depends on fibre length, twist and the whole distribution of how the load is shared — but it is real and it is in the direction the arithmetic suggests.

Abrasion resistance falls at the surface and rises at the yarn. This one is genuinely two-sided. The nap itself abrades away readily — it is loose fibre — so a raised fabric loses its nap with wear. But underneath, the nap has been protecting the yarn crowns from the abrasive contact, which is where this site computed the wear actually happens. A raised fabric wears its nap out and then wears like the fabric underneath.

And the surface pills. A fibre pulled part-way out and left is a fibre with one end anchored and a free length, and free lengths tangle with one another under rubbing into the small balls that make a garment look old. Pilling is raising’s characteristic failure mode and it is the same mechanism as the intended effect, continued past the point where it was wanted.

The conflict is structural #

Here is the part that makes this a rung rather than a list, and it is the axis this site has followed since its second essay.

A good nap needs long floats. The longer the unsupported span, the more the tooth can lift, the deeper the nap, and the fewer passes it takes. The previous rung established that a float is necessary; the depth of the nap goes with its length.

Long floats mean few interlacings. That is what a float is. And this site has computed, over a long stretch of work, what few interlacings do to a fabric:

• Lower tear strength retention under abrasion, because a long float is a long unsupported length exposed at the surface — the same property the raising machine exploits.
• Lower firmness, more slippage, more seam-slip.
• Higher tear strength, because free yarns group up ahead of a tear and share the load, which is the one place the trade-off runs the other way.
• Lower crimp and therefore less relaxation shrinkage.
• More lustre and more drape.

So the fabric that raises best is the fabric that was already weakest in the ways a raised fabric is used, and this is not a coincidence to be engineered around. The float length is one number and it appears in all of these consequences at once.

How the trade resolves it #

Not by optimising, which is the interesting part. The resolution is to build a cloth with two different jobs on its two faces.

A raised fabric is usually asymmetric by design. A moleskin is a heavy sateen: a dense warp-faced construction with a great many ends carrying the load, and a weft-faced back with long floats that are raised. The load path and the nap are in different systems, so raising the back takes fibre out of the picks and leaves the warp, which is carrying the strength, untouched.

That is the general solution and it is available because a weave has two systems. A backed cloth takes it further: an extra weft or warp is put in solely to be raised, bound loosely into the back of a cloth whose face and structure are decided independently — which this site computed the structure of earlier here, for a different purpose.

A raised fabric’s nap fibre and its structural fibre can be different fibres, and in a blanket they usually are: a strong warp of a long-stapled fibre, a weft of a soft, short, weakly twisted one chosen entirely for what it gives up to a wire.

So the conflict is real, and it is resolved by separating the two jobs rather than by finding a construction that does both. That is the same move the whole subject makes whenever a single system is asked for two contradictory things — it is why pile fabrics have a third thread system and why a double cloth exists.

What was counted, and how #

This rung computes less than the ones around it and it is worth being clear about that.

The catchable fraction on each face comes from raisable(), which walks the float map and sums the runs at or above the threshold. That is exact and it is a statement about the matrix.

The strength cost is not computed anywhere on this site. A yarn’s tensile strength as a function of how much surface fibre has been removed is a fibre-mechanics question — it needs a fibre length distribution, a migration model, and a load-sharing argument — and this site has none of that machinery. What is stated above is the direction and the mechanism, and no number is quoted for the loss because none would be defensible.

That is a deliberate limit and it is the same one the previous essay drew: the boundary of what this site can compute about finishing is the boundary of what geometry can say about a fibre.

The thermal argument is likewise qualitative here. Air’s conductivity is a physical constant and it is quoted as one; how much still air a given nap holds is not something the float map decides.

The same trade, in one sentence #

It is worth compressing the argument, because it is short once the machinery is in place.

Fibre is either in the yarn or on the surface, and it cannot be both. In the yarn it carries load; on the surface it traps air. A raising machine moves fibre from the first place to the second, and how much it can move is decided by how much unsupported thread the draft exposes.

So the fabric that offers the most to a raising wire is the fabric that has the least fibre bound into its structure per unit length — and that is the same statement as the fabric with the longest floats, which is the same statement as the fabric with the fewest interlacings, which is where every argument on this site about float length arrives.

A ceiling on the cost, which needs no fibre mechanics #

The strength loss is refused a number above, and rightly, because it needs a load-sharing model this collection does not have. What can be had without one is a ceiling — how much fibre a raising wire could conceivably remove from the load path — and it is computable from the geometry alone.

A wire catches what is at the surface. A fibre buried in the middle of a yarn is not at the surface at any point of its length and no tooth reaches it, so the fibre available to be raised is the fibre in the yarn’s outer shell, on the floated face, over the fraction of the cloth those floats occupy.

The shell’s share is arithmetic. A yarn of N fibres has a radius √(N/φ) fibre radii, so an annulus one fibre thick occupies about 4 ÷ √(N/φ) of the section — 29 per cent for a 20 tex cotton at a hundred and eighteen fibres, 18 per cent for a coarse 60 tex, and less for anything coarser still.

Multiply by the face that is floated and by nothing else, and the result is a bound:

a nap cannot take more than about a third of the fibres from the threads it is raised from, and it takes them only where the floats are.

Three readings, and the second is the one that constrains a design.

The bound is far above what a real nap takes. A singed cloth loses under one per cent of its mass and a heavily raised one carries a few per cent of it in the nap, so a real raising operation is using a small fraction of the ceiling. That is reassuring about the strength cost and it says the cost is not bounded by geometry in practice — it is bounded by what the machine can lift.

The bound falls as the yarn gets coarser, as one over the root of the fibre count. So a coarse-yarn cloth has proportionally less of itself available to be raised, and a nap of a given depth costs it a larger share of the fibre it can spare. A fine-yarn cloth raises more freely, which is the arithmetic behind the trade’s preference for finer wefts in raised goods and is not the reason usually given.

And the bound is per face. A cloth raised on both sides — a blanket, a double-faced flannel — draws on two shells from the same threads, so the two operations compete for one reservoir. That is a real constraint on a construction nobody computes, and it is why a double-raised cloth is built with a heavier weft than a single-raised one of the same weight.

None of that names a strength. What it does is bound the quantity the strength loss is a function of, from the same float map the previous rung uses, with no fibre mechanics anywhere — which is the most this collection can honestly say and rather more than nothing.

Where the model stops #

No strength number. The whole cost side is a mechanism without an arithmetic, and the essay says so rather than supplying a plausible figure.

The nap’s depth is not derived from the float length, only argued to increase with it. The relation depends on the wire, the number of passes, the moisture content and the fibre, and a model of it would be a model of a machine rather than of cloth.

Pilling is described and not modelled at all.

And the two-face resolution is a design pattern rather than a computation. Which system carries the load in a given construction is decidable from the draft — the balance machinery does it — but how much strength each carries is not.

Why a cost with no number is still worth an essay #

There is a temptation, on a site whose whole proposition is computing rather than quoting, to leave out anything that cannot be computed. That temptation should be resisted here and the reason is worth stating.

A trade-off whose two sides are the same variable is a structural fact, and it is provable without either side being quantified. The argument in this essay does not need to know how much strength is lost. It needs only that the loss increases with float length while the nap improves with float length, and both of those follow from the mechanism.

That is enough to establish the useful conclusion: there is no clever raised fabric that is also strong at the raised face, and a designer who wants both must use two systems rather than a better construction. A quantified version would say where on the curve to sit; the unquantified version says that the curve exists and which way it runs, which is the part that decides the architecture.

The site’s fourth invariant — say which model produced a number — has a corollary that this essay is an instance of: when no model produced a number, say that too, and say what survives without one.

The operation that takes it back off #

There is a second machine that belongs in this essay because it is applied to the same cloth immediately afterwards, and it is the reverse of raising in one respect and not in another.

A cropping or shearing machine cuts the nap to a uniform height — a spiral blade against a ledger blade, exactly a lawnmower — and everything a raised cloth is finished with has been through one. The purpose is uniformity rather than removal: a raised nap is uneven, and cropping produces a level pile of a chosen height.

What that means for this essay’s accounting is that the fibre removed by cropping is lost entirely. It is cut off and taken away as flock. So the raising operation takes fibre out of the load path, and the cropping operation takes some of that fibre out of the fabric altogether, and a raised-and-cropped cloth is genuinely lighter than the cloth that went in.

That is measurable and it is a real yield loss — a few per cent of the piece. It also means the areal density of a raised fabric moves in the opposite direction from every other operation in this field, which mostly raise it by shrinking the cloth.

Why a raised fabric wears the way it does #

The wear sequence of a napped cloth follows from everything above and is worth stating, because it explains a familiar object.

First the nap flattens. The lifted fibres lie over under pressure and friction, especially where a garment is rubbed — elbows, cuffs, seat. The cloth there looks darker and shinier, because a flattened nap reflects specularly where a standing one scatters.

Then the nap goes. The flattened fibres abrade away, and the area returns to the appearance of the unraised fabric underneath.

Then the fabric wears normally, and it wears slightly faster than the same fabric unraised, because the fibre that was removed to make the nap is fibre no longer contributing to the yarn.

That sequence — shine, then bare, then wear — is what an old woollen coat looks like at its elbows, and every stage of it is this essay’s trade-off being paid back in order. The warmth was borrowed against the fabric’s life, and the borrowing is repaid at exactly the places the garment is used hardest.

It is worth adding that the exchange has a floor as well as a slope. A raising machine cannot lift fibre that is not there, so a yarn spun from continuous filament raises hardly at all — there are no fibre ends to pull up, only loops of filament that either break or do not move. Raising is a staple-fibre operation, and the filament equivalents reach a napped surface by other routes: sanding, or knitting a pile in as a third system, both of which are different mechanisms with different costs.

Who found it, and when #

The construction answers are old. Moleskin, swansdown, flannelette and blanket cloth are all pre-industrial or early-industrial fabrics, and every one of them is built with the nap and the strength in different systems. Nobody derived that; it is what remained after everything else was tried.

The thermal argument — that still air rather than fibre does the insulating — is nineteenth-century physics applied to clothing in the twentieth, and it is the reason the modern versions of these fabrics are lofted synthetics rather than better wool. Once the insulator is understood to be trapped air, the design problem becomes how to trap the most of it per gram, and a raised woven cloth is a fairly inefficient answer to that question compared with a needled batt.

Which is why this field’s fabrics survive on their other properties: a raised woven cloth is durable, windproof, tailorable and repairable, and a batt is none of those. The nap is not what a melton overcoat is for.

Where the ladder goes next #

Three ladders have now run: shrinkage, felting and the surface. The last essay in this field collects what they have in common, which is a single unstated assumption running under every quantity on this site — and a rule for what to do about it.