Textile Structure
how cloth is put together
Generator

Whether a cloth's hairs can reach one another

Whether a cloth's hairs can reach one another
Whether a cloth's hairs can reach one another. n_A λ² for each construction in this site's table — the hairs per square millimetre times the square of their own length, which is the pure number that asks whether a hair can touch its neighbour. It is a count times an area, so it has to be a pure number. Every one of them is under one, which means no ordinary woven cotton cloth has a hair layer at all: it has isolated whiskers on a bare surface. The dashed line is the threshold. The spread across the whole table is only 1.9-fold, because the density goes as the sett times the root of the count and those move in opposite directions as a cloth is made finer — so construction is almost powerless here, and everything that crosses this threshold does so by finishing rather than by weaving.

n_A λ² for each construction in this site's table — the hairs per square millimetre times the square of their own length, which is the pure number that asks whether a hair can touch its neighbour. It is a count times an area, so it has to be a pure number. Every one of them is under one, which means no ordinary woven cotton cloth has a hair *layer* at all: it has isolated whiskers on a bare surface. The dashed line is the threshold. The spread across the whole table is only 1.9-fold, because the density goes as the sett times the root of the count and those move in opposite directions as a cloth is made finer — so construction is almost powerless here, and everything that crosses this threshold does so by finishing rather than by weaving.

6 essays call hair-bars. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the weave its essay argues about.

Where it is called

Changing this generator changes every one of these figures.

A yarn's diameter is a contour, not a length. The fraction of the space beside a 20 tex cotton yarn that is occupied by hair, against height, grossed up from the modelled population by the measured split between the long and short populations. At the yarn's own surface it is 8.9% — the layer is almost entirely gap — and it falls away exponentially from there. Every instrument that reports a yarn diameter is picking a contour of this curve, and the contours are far apart: a threshold that needs half the space filled is never met at all, one that needs a twentieth is met at 355 µm, and a hair counter triggers out at 2353 µm. The earlier model gave the layer a single thickness of 25 µm, which is a fair description of where most of the material is and wrong about its extent by more than a decade. What the curve cannot say is which contour any particular instrument uses, which is a fact about the instrument. Pattern and colour

A cloth is more opaque than it is closed

Opacity is not cover — this collection established that already and left the discrepancy attributed to the thickness of the threads. Part of it is not in the threads at all. A hair standing in a hole blocks light exactly as well as a thread does and costs nothing in air.

 Whether a cloth's hairs can reach one another. n_A λ² for each construction in this site's table — the hairs per square millimetre times the square of their own length, which is the pure number that asks whether a hair can touch its neighbour. It is a count times an area, so it has to be a pure number. Every one of them is under one, which means no ordinary woven cotton cloth has a hair layer at all: it has isolated whiskers on a bare surface. The dashed line is the threshold. The spread across the whole table is only 1.9-fold, because the density goes as the sett times the root of the count and those move in opposite directions as a cloth is made finer — so construction is almost powerless here, and everything that crosses this threshold does so by finishing rather than by weaving. Knits and other structures

A knit gives up its fibres more easily

Knitwear pills and shirting does not, and the fibres are often the same fibres. The difference is a count of yarn per unit area and a pressure between threads, and both of them push a knit over a threshold that a woven cloth of the same yarn cannot reach.

 Hair, nap and pile are one construction at three settings. 12 mm of sheeting at one pair of scales, carrying each of this site's three protruding surfaces — 50 pixels to the millimetre along the cloth and 29 off it. They are the same object, fibre standing off a cloth with a density, a length and an anchor, and they differ by 9-fold in density and 4.8-fold in length. What actually separates them is the third line under each name: hairs are held by whatever the twist happened to leave, a nap by the float it was pulled from, and a pile by a W or a V through three picks. Only the last two were chosen. The pile's tufts are drawn in the float colour because that is what a woven pile is, and they are all one length because a blade cut them; the hairs and the nap are drawn as measured quantities and their lengths come from the population's own exponential. Each panel clips to the room it has, and the densest of the three is drawn at the model's own number rather than thinned. Compound and figured cloths

Hair, nap and pile are one construction

This site now has three surfaces made of fibre standing off a cloth, arrived at from three different directions and in three different fields. They are the same object at three settings, and what separates them is not what they are but how much of them anybody decided.

 How much of an abrasion loss is not damage. The share of a reported abrasion mass loss that is hair rather than cloth, for sheeting as woven and raised 64-fold. The first material off a fabric is its hair layer, which is 0.107% of a bare cloth's mass and 6.84% of a napped one's — and which regenerates, so it keeps coming off. A bare cloth is through it by 5344 cycles and the test then reaches the crowns, where the loss means damage. A napped cloth is not through it by 342000, which is more cycles than any standard test runs, so a Martindale on a fleece never measures the fabric at all. Two cloths taken to the same mass loss have therefore not lost the same thing, and the more heavily napped one may not have been damaged. a-cloth-loses-its-strength-before-its-mass made the same point about a different pair of quantities; this is the same failure one layer further out. Cloth doing a job

Abrasion takes the hairs first

An abrasion test reports milligrams lost against cycles, and the first milligrams off any fabric are not fabric. On a bare cloth that stage is over in a few thousand cycles. On a napped one it is not over by the end of the test, so a Martindale on a fleece never measures the fleece.

 The strong fibre is the one that pills. Standing pills per unit area by fibre, relative to wool, at one and the same fuzz supply — every row is the same cloth raised the same amount, so the only thing varying is how long a pill survives once it exists. A pill is not made, it is kept: rubbing generates it and rubbing breaks the anchor fibres that hold it, and an anchor survives in proportion to how much force it takes to break. So polyester carries 18 times wool's standing population from the same generation rate, and the ordering here is exactly the ordering of tenacity and nothing else. Wool sheds its pills because wool anchors break. No two real fabrics have the same fuzz supply, which is why a wool knit still pills more than a cotton shirting in practice — the comparison drawn here isolates the anchor and says nothing about the generation, and reading it as a ranking of fabrics would be wrong. Cloth doing a job

A pill is anchored, not made

Every account of pilling starts with how a ball of fibre forms and stops there, which explains why fabrics pill and not why some of them stay pilled. A pill is not a thing that happens; it is a standing population, and the number on a fabric at any moment is a generation rate times a lifetime.

 Warmth is a canopy, and a canopy grows as a logarithm. Thermal resistance of sheeting against how much its hair population has been multiplied by raising, both faces counted. The unraised cloth is given no still air at all, because its hairs cannot reach one another — n_A λ² is under one and there is no canopy to hold air still. Past the threshold the canopy's depth is λ·ln(n_A λ²), so every doubling of the hair population adds the same depth of nap and no more: the steps here are 434 µm apiece, all the way up. At 256× the nap is 3.07 mm deep and worth 39 times the cloth it grows on, which is the whole reason a flannel is warm and a poplin of the same yarn is not — a canopy is two parts in ten thousand fibre, so its conductivity is air's, while the cloth itself is a quarter fibre. What is claimed is a conduction resistance across a depth of nearly still air; whether the air is still is a question about flow and is not asked here. Mechanics and drape

Warmth is mostly the hairs

This collection established that a fabric's thermal resistance is its thickness and not its fibre, and that twice the thickness is twice the warmth. It never asked what the thickness was made of. On a raised cloth almost none of it is cloth.

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