Textile Structure
how cloth is put together
Concept

Opacity — where it appears

Whether a fabric hides what is behind it, which is not the same as how much light it stops. The covering rule treats a thread as a bar that transmits nothing, and a fine thread plainly does not — so what a cloth passes is its open area plus its threads' own transmittance times the fraction they cover.

Named by 11 essays across 4 fields — each of them below, with the objects they name alongside it.

How open a batiste is, against where the light is. One minus the cover is a cloth's openness to a light directly behind it, and for this batiste it is 40.1 per cent. Move off the normal and a line of sight has to clear the hole at the top of the cloth and the same hole one thickness below, so what it can use falls as t·tan α is taken off each side — reaching nothing at 39.0° across the ends. Averaged over the whole sky with Lambert's cosine weighting, the cloth is 6.42 per cent open — 6.3 times less than the covering rule says, and the whole of the difference is the thickness. One minus the cover is the openness of a cloth with no thickness, and no cloth has none.

Opacity is not cover

The covering rule counts a thread as a bar that stops everything, and a single fine cotton thread held to a window plainly does not. What a cloth transmits is the open area plus whatever comes through the threads, so the covered fraction is a lever rather than a barrier — and the lever is longest exactly where the rule says the cloth is most closed. Nothing here computes a thread's transmittance, and saying why is the useful half.

pattern · Opacity 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.

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.

pattern · Opacity How open a muslin is, against where the light is. One minus the cover is a cloth's openness to a light directly behind it, and for this muslin it is 37.9 per cent. Move off the normal and a line of sight has to clear the hole at the top of the cloth and the same hole one thickness below, so what it can use falls as t·tan α is taken off each side — reaching nothing at 36.1° across the ends. Averaged over the whole sky with Lambert's cosine weighting, the cloth is 5.36 per cent open — 7.1 times less than the covering rule says, and the whole of the difference is the thickness. One minus the cover is the openness of a cloth with no thickness, and no cloth has none.

One minus the cover is a cloth with no thickness

The covering rule says a cloth's openness is one minus its cover factor, and this collection derived it and has used it ever since. It is the answer for a light directly behind the cloth. Move the light and a line of sight has to clear the hole at the top of the fabric and the same hole one thickness below, so the openness falls, and it reaches nothing at thirty-six degrees. Averaged over the whole sky a muslin is a seventh as open as the rule says.

setting · Cover 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.

A yarn has a diameter for every instrument

Conservation of volume gives a yarn one diameter and every other route gives a different one. The disagreement is not experimental scatter: a yarn's outside is a coverage that falls away exponentially, and each instrument stops at whatever contour of it will trigger the instrument.

cloth · Hair layer A print is as sharp as the hairs are long. How far ink carried on a hair reaches past a printed edge into the unprinted cloth, for sheeting in three states. A hair lying near the edge bridges as far as its own length, and the number bridging at least a distance x is (n_A λ/2)e^(−x/λ) — an exponential with the population's own decay length — so the visible feather is a quantile rather than a mean, taken here at one hair per 50 millimetres of edge. As woven the feather is 1911 µm, which is a fifteenth of an inch and coarser than any screen worth engraving: the cloth cannot hold better than 7 lines to the inch whatever the printer does. Singeing caps it at the flame's own reach of 200 µm and takes the cloth to 63 lines — a factor of 10, bought by burning off a fraction of one per cent of the cloth's mass. That is why singeing comes before printing and why nobody prints a fine figure on a raised cloth.

A print is as sharp as the hairs are long

Singeing comes before printing in every finishing route ever written down and the reason given is that the cloth must be smooth. The reason is sharper than that: ink carried on a fibre end reaches as far as the fibre is long, so the feather on a printed edge is a quantile of a hair population and nothing else.

finishing · Coating Seeing through a white voile, from the street and from the room. How much of a scene's contrast survives a white voile, whose open area is 49%, looked through from the street into the room and from the room out to the street, against how much brighter the street is than the room. The scene comes through the clear lines of sight and nothing else; everywhere else the viewer sees thread lit from the viewer's own side, which returns light with no image in it. On a bright day, a hundred times brighter outside, 0.5% of the room's contrast reaches the street and 65% of the street's reaches the room. At equal light both are 28% — the curves cross at a ratio of one whatever the cloth — and with the lamps on after dark the room is the side on show, at 63%. What the plot cannot show is the threads' own optics: their reflectance and transmittance are assumed values for a white sheer rather than measurements, and only the crossing point is independent of them.

A sheer hides whichever side is darker

A net curtain hides a room by day and shows it at night, and the cloth has nothing to do with which. What a viewer sees through a sheer is an image through its clear lines of sight against a veil of lit thread, and the only thing that decides their balance is how much brighter one side is than the other. At equal light the two views are identical for every cloth there is. And a black sheer of the same openness shows twelve times more of the room by day than a white one.

pattern · Opacity A white thread 70% open figure in a white thread 49% open ground at 30 : 1, from both sides. A lozenge figure in a sheer, drawn as the street sees it and as the room sees it, with the street 30 : 1 as bright as the room. The ground is white thread 49% open and the figure white thread 70% open. Each region glows with the scene behind it through its holes and with its threads lit from both sides; from the street the figure's contrast against the ground is −24.6% and from the room +5.4%, a negative number being a figure darker than its ground. Each panel is shaded relative to its own brighter region, as an eye adapted to that view would see it, and both panels share one gain so that the two steps are to scale against each other. The contrast is stretched 3 times to be visible at all, so the numbers rather than the depth of the shading are the measurement. What the drawing cannot show is the absolute glow, which from the street is 9.35 and from the room 7.02 times the room's illuminance for the ground, nor the thread optics, which are assumed values.

A figured sheer is a negative from one side

A net curtain with a pattern in it carries two patterns, one for each side, and by day they are opposites. A more open figure in a white voile is a dark figure a quarter below its ground from the street and a light one five per cent above it from the room, and after dark the two views trade places exactly. The figure vanishes from the street at one light ratio and from the room at another. And a figure can be made that the room cannot see at all while the street sees it nearly black — along one line of openness and thread tone, and never from both sides at once.

pattern · Opacity A white thread 70% open figure behind a net 60% open, from both sides. A lozenge figure in the inner curtain of a pair, drawn as the street sees it and as the room sees it through a plain net 60% open, with the street 30 : 1 as bright as the room. From the street the figure's contrast against its ground is −7.0% where a single curtain would have given −24.6%; from the room it is +6.9% where a single curtain would have given +5.4%. Each panel is shaded relative to its own brighter region, both at one gain, so the two steps are to scale against each other, and the contrast is stretched 9 times to be visible at all — the numbers rather than the depth of the shading are the measurement. What the drawing cannot show is the light between the two curtains, which is 19.80 times the room's illuminance from the street and 0.57 from the room, nor the thread optics, which are assumed.

A net in front gives the figure to the room

The commonest double curtain is a plain net outside a patterned one, and the plain net does not merely dim the pattern. It weakens the figure from the street by a factor of three and a half and strengthens it from the room by a quarter, so a pattern four and a half times stronger outside than in becomes one the room sees slightly better. A figure designed to be invisible from indoors reappears at nearly three per cent, and the day-and-night exchange a single curtain obeyed exactly stops holding at all.

pattern · Opacity A voile hung at 2.5 times its window, seen in plan. A curtain of voile gathered to 2.5 times the width of its window, drawn in plan with the window above it and a line of sight crossing a flank. A length of cloth spans its own length times the cosine of its flank angle, so a fullness of 2.5 stands every flank at 66.4 degrees and a line of sight normal to the window meets the cloth at that incidence. This cloth's holes close completely at 47.3 degrees, which is a fullness of 1.48, so at 2.5 times every flank passes no line of sight at all and the whole of what comes through arrives at the crests. Flat the cloth is 49.3% open and hung it is 3.0%. What the plan cannot show is the cloth's own drape, which rounds every fold drawn here as a corner.

A curtain is gathered so that it is seen edge-on

A curtain is hung with more cloth than window, and the surplus is not decoration. Laid in folds, a length of cloth spans its own length times the cosine of its flank angle, so the fullness is the secant of that angle exactly — and a line of sight through the window meets the cloth at it. A voile's view halves at a fullness of 1.08, its flanks shut completely at 1.48, and at the two and a half times a curtain is actually hung at, every flank passes nothing and the whole of what comes through is the crests.

pattern · Opacity What a passer-by is looking at, for rooms of four reflectances. The street's view of a window behind a sheer white thread 49% open at 30 : 1, split into the part that is an image of the room, arriving through the holes, and the part that is the cloth's own threads lit by the street. a room reflecting 8% contributes 0.4% of the view; a room reflecting 20% contributes 1.0% of the view; a room reflecting 35% contributes 1.8% of the view; a room reflecting 60% contributes 3.1% of the view. The veil is identical in every row because the cloth and the street are: only the furniture changes. What the chart cannot show is where in each room that reflectance sits, and a dark room with a lit lamp in it is not its own average.

What a sheer hides is decided by the furniture

Every result these essays have produced assumed the room and the street reflect the same three tenths of the light on them. That was never a fact about cloth. A room reflecting a twentieth is hidden two hundred and thirty-eight times better than the street it faces and one reflecting four fifths only fifteen times, with the same curtain at the same window — and the day-and-night exchange they rested on, exact for equal scenes, is out by more than half the glow for an ordinary pair of unequal ones.

pattern · Opacity The section the fabric asks for, beside the one the model drew. A 20 tex cotton yarn in cross-section, at 900 times life size. The circle is what every solve in this collection has assumed: a diameter of 0.167 mm from the count and the packing factor. The ellipse has the same area and a minor axis of 78% of it, which is the closest the fabric's own adjacent courses come to one another — 0.130 mm. Nothing about that number was fitted to a fabric. It falls out of a solve that knew nothing about flattening, and it lands inside the range the trade reports for yarn in cloth, which this collection has carried as a free parameter ever since it first put a number on a sett.

What a flattened yarn does to its cover

A cover factor is a sett times a diameter, and it decides how much of a cloth is thread and how much is hole. A flattened yarn is a third wider than a round one of the same area, so a cloth of flattened yarn covers more at the same sett — and every opacity, permeability and shade computed from a round diameter is wrong in one direction.

setting · Cover

Named alongside it

The objects these essays reach for when they reach for this one.

Open areaCover factorVeilClear openingScatteringTransmittanceYarn diameterFigure and groundHair coverageHair layerCanopy criterionCloth thickness

All concepts