Textile Structure
how cloth is put together
Concept

Veil — where it appears

The light a hair layer returns of its own, which has no azimuth in it because a hair population points every way at once. Blocking a specular ray leaves a contrast untouched; adding an isotropic term to both its ends destroys it, which is why a shot fabric is filament.

Named by 7 essays across 2 fields — each of them below, with the objects they name alongside it.

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 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 shot effect needs a fibre with no ends. The peak-to-trough contrast of an eight-end satin in sheeting as the cloth is turned in the light, against how much hair stands on it. Bare, the contrast is 37 to one, because a straight thread's normals lie in the plane across it and the warp and the weft therefore reflect a quarter turn apart. A hair layer does two things and only one of them matters: it blocks, which takes the same factor off the peak and the trough and changes no contrast at all, and it returns light of its own, which is added to both. A hair population points every way at once, so its return has no azimuth in it — and adding a constant to both ends of a ratio of 37 destroys the ratio. On an ordinary spun cotton the contrast is already down to 5.1 to one; singeing recovers it to 29; raising kills it outright at 1.00. The one fibre with no staple length is the one fibre with no fibre ends, and every shot fabric ever woven is made of one.

A hair layer veils a highlight

An eight-end satin's shine swings by a large factor as the cloth is turned, because a straight thread's normals lie in the plane across it. Put fibre ends on it and the swing disappears — not because the hairs block the light, which changes no contrast at all, but because they return light of their own that has no direction in it.

weaves · Shine 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

Named alongside it

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

OpacityOpen areaClear openingScatteringTransmittanceFigure and groundCanopy criterionCover factorHair coverageHair layerSingeingAir permeability

All concepts