Textile Structure
how cloth is put together
Concept

Specular reflection — where it appears

Light reflected in one direction rather than scattered, which is what a run of parallel uninterrupted yarn does and what makes a float or a fibre line shine. It is why a satin shines and a plain weave does not, and the quantity behind it is the float length rather than anything about the fibre.

Named by 13 essays across 5 fields — each of them below, with the objects they name alongside it.

The highlights of a 8-end satin, move 3. Every unbroken run of warp on the face, drawn as the band of light it returns. A yarn is a cylinder and a cylinder reflects a line rather than a point, so a float's highlight is as long as the float — and how long that is, in inches, is the float divided by the picks per inch the weave can be set to.

Why satin shines

Lustre is usually filed under fibre, and silk gets the credit. It is a property of the weave: a cylinder reflects a line rather than a point, so the highlight a cloth returns is exactly as long as its longest float.

weaves · Float single float as an array. One cell per needle per course, over 2 repeats each way. K knits a new loop and casts the old one off, T tucks the yarn into the loop below without casting off, M misses the needle and floats past it. The margins carry the two conditions: a wale with no K in it never casts off, and a course with no K in it is never caught by anything. Both hold here.

The float in a knit

Five rungs of this anchor have taken the float to be a length of thread on the surface with nothing holding it down. A knit has one too, and it behaves the same way in the light and the opposite way in the hand — because a woven float lengthens its thread and a knitted one shortens its fabric.

knits · Float Z twill, Z twist. A square of cloth with two directions on it. The broad lines are the twill, whose angle 45.0° from the warp comes from the setts alone — 24 ends and 24 picks per centimetre. The fine lines are the surface fibres of the warp ends, at 25.3° from the warp because the yarn is twisted 900 turns per metre. Between them is 19.7°, and that is the whole of the rule.

Twist and the twill line

The oldest rule of thumb in weaving says to weave a Z twill from S-twist warp for a bold line and from Z-twist warp for a subdued one. Both halves of it are geometry: the twill's angle comes from the two setts, the fibres' angle comes from the twist factor, and the rule is their difference.

setting · Twist A round thread reflects a beam into a fan. A round thread seen end-on, with a beam arriving from straight above. Every point across the thread has its own normal, tilted by the angle it sits at, and mirrors the beam through twice that angle — so a single direction in becomes a whole fan out, spread across the thread and not at all along it. Seen from the front that fan is a highlight lying along the thread, exactly as long as the length of thread that is straight, which is the float. Nothing about this depends on the fibre. A cylinder of any material returns a fan, and the only way to narrow it is to stop the section being a cylinder — which is what a calender does.

A float reflects into a line

A cylinder cannot return a beam to a point. Its normals sweep the whole half-turn across it and nothing at all along it, so a straight thread throws light into a fan — seen as a highlight lying along the thread, exactly as long as the length of thread that is straight. The lobe of a satin is twice as narrow along the thread as across it; the lobe of a plain weave is exactly round.

weaves · Shine Turn the cloth and the highlight changes hands. A 2/2 twill in sheeting turned under a light, with the specular area of each system counted separately at each angle. The warp peaks at 0° and the weft at 83°, a quarter turn apart, and neither returns anything worth seeing where the other peaks. The reason needs no dye and no interference: a warp crown's normals all lie in the plane across the warp and have no component along it, so a warp float can only mirror light that arrives from across the warp. A cloth woven with one colour in the warp and another in the weft therefore shows one colour at one angle and the other a quarter turn away, which is the whole of shot silk — a geometric effect that has been sold as a mysterious one for three hundred years.

Turn the cloth and the shine changes hands

A warp crown's normals all lie in the plane across the warp and have no component along it, so a warp float can only mirror light that arrives from across the warp. Turn the cloth a quarter turn and the weft takes over. That is the whole of shot silk — a geometric effect with no dye that changes and no interference in it.

weaves · Shine Specular area against the size of the source. The share of a sheeting's face that reflects, for plain, 2/2 twill, 5-end satin, 8-end satin, against the angular half-width of whatever is lighting it. Plain weave's line has twice the slope of the others, because a specular area is a length times a width and both are proportional to the angle for a weave with no float — while a float contributes a crown line that does not shrink with the source at all.

No cloth shines under a sky

Every specular figure on this account is drawn at a tolerance of two degrees, which is a stand-in for how wide the source is. Sweeping it says something the account has not: the contrast between a floated weave and a plain one is inversely proportional to the source's angular size, exactly, because a float keeps a crown line as the source narrows and a plain weave has only turns. A satin outshines a plain weave by 177 under the sun's disc, by 22 under a small lamp, and by exactly nothing at sixty degrees.

weaves · Shine A lamp in front of a window: the contrast against the lamp's share of the light. The contrast an eight-end satin shows over a plain weave when a 1° lamp and a 16° window both lie in the direction the cloth reflects to the viewer, against the lamp's share of the light: 0.0% gives 3.01, 0.5% gives 3.22, 1.0% gives 3.43, 2.0% gives 3.85, 5.0% gives 5.11, 10.0% gives 7.21, 20.0% gives 11.39, 30.0% gives 15.57, 50.0% gives 23.88, 70.0% gives 32.16, 100.0% gives 44.48. The points lie on a straight line between the window alone and the lamp alone, to within 0.8 per cent: the room's contrast is its sources' contrasts averaged by power. The dashed curve is a single source as wide as the power-weighted average width, which gives only 3.30 at a tenth of the light where the room gives 7.21.

A room lights a satin at the harmonic mean of its lamps

A satin outshines a plain weave by a factor inversely proportional to the width of the light, which is a clean law for one source and says nothing about a room. A room has a lamp and a window at once. Sum each source's highlight and the average falls out by itself: the room behaves as a single source whose width is the harmonic mean of its sources' widths, weighted by the power each supplies. The harmonic mean is ruled by the narrowest source, so a small lamp carrying a tenth of the light more than doubles the contrast a large window gives.

weaves · Shine A satin's contrast as the lamp moves off the mirror. The specular area of an eight-end satin over a plain weave, both as a sheeting, for a source 2° wide moved away from the direction the viewer sees mirrored in the cloth. Moved across the satin's floats, the contrast is 22.4 on the mirror and 21.7 forty degrees off. Moved along them it is 22.4 on the mirror and 0.25 once the source is more than twice its own width away: the satin is darker than plain. A calendered satin falls to 1.83 across its floats as well. What the plot cannot show is shadowing, which a lamp far enough off the mirror brings in.

A lamp off the mirror lights a satin only across its floats

Every source in the account of a room was a source the viewer sees mirrored in the cloth. A lamp off to one side lights the cloth too, and which facets it reaches depends on which way it is off. Displaced across a satin's floats it is caught by the float's own curve and adds contrast like any lamp on the mirror; displaced along them by more than twice its own width it reaches only the turns, and the satin comes out a quarter as bright as plain weave.

weaves · Shine Floated weaves against plain under an overcast sky. The sky's radiance each weave's facets mirror into the eye, over the plain weave's, as the viewer's elevation above a sheeting falls from overhead to thirty degrees, under an overcast sky with a ground of albedo 0.2. 2/2 twill: 1.25 overhead and 0.99 at 30°; 5-end satin: 1.30 overhead and 1.01 at 30°; 8-end satin: 1.37 overhead and 1.01 at 30°. What the plot cannot show is the diffuse reflection, the same for every weave of one fibre, which a real cloth's sheen sits on top of.

A satin mirrors the top of the sky

A uniform source sixty degrees wide leaves every weave reflecting the same share of its face, and that was read as saying no cloth shines under a sky. A real sky is not uniform. An overcast one is three times as bright overhead as at the horizon, and it stands over a ground darker than itself. Every facet of a cloth mirrors one direction, and a satin's facets mirror the top of the dome while a plain weave's mirror the horizon and the ground — so seen from above, under cloud, an eight-end satin still sends back a third more sky.

weaves · Shine What a pane of glass does to a sheer's multiplier. The factor by which an error in reading a window is multiplied on its way into the room's reflectance, against the angle a passer-by looks at the glass from, at 30 : 1, for three sheers behind a pane of window glass. The dashed level beside each is the same cloth with no glass. white voile: 64.0 bare, 59.8 behind glass straight on, 65.7 at 60°, 92.7 at 75°; grey voile: 27.3 bare, 28.7 behind glass straight on, 34.7 at 60°, 61.7 at 75°; black net: 2.0 bare, 5.2 behind glass straight on, 8.8 at 60°, 25.4 at 75°. The white voile is easier to read through glass up to 56.7°, because the pane dims the street on its threads by more than it mirrors; the black net is harder at every angle. The pane mirrors a street reflecting 0.3; a sky in the mirror would be brighter, and nothing here models one.

Glass hides a black net and not a white voile

A window pane in front of a curtain mirrors the street, and a mirror is a veil with no thread in it. It also dims the street's light on the cloth. For a white voile the two nearly cancel, and straight on the dimming wins, so the voile is slightly easier to read through glass than without it. For a black net the mirror is most of what a passer-by sees: its multiplier goes from 2 to 5 head-on and to 25 from along the pavement. The glass makes the net private, not the voile. The angle at which it stops helping does not depend on the time of day, and a polarising filter at Brewster's angle takes the mirror out altogether.

pattern · Opacity A disc woven on one beam, as it catches a lamp. A disc of 5-float satin on a ground of float 3, twelve blocks square, woven on one beam so that every column is pulled to the tension that makes it consume what the others do, and drawn as its blocks catch a lamp. A block is lit when its warp's crossings still reflect into the eye; outlined blocks are figure. At the mirror every block is lit. Tilted by 10.8° along the warp, the ground in the columns that carry most ground — the tightest — has gone dark, while the ground in line with the figure's widest part, pulled least, still shines: a band as wide as the figure runs down the ground above and below it. What the drawing cannot show is the diffuse light every block also returns, which dilutes the contrast and does not reverse it.

A figure woven on one beam shows its columns off the mirror

A figured warp shares one beam by letting the columns that want more yarn pull tighter until every column consumes alike. With the figure allowed to give crimp as well as the ground, the tightest column of a satin disc on a twill needs 0.013 to 0.042 newtons, under a tenth of the working tension. Its warp lies tens of micrometres lower, a relief too small to see. At the mirror it shines exactly as a slack column does. A few degrees off the mirror, along the warp, its crossings stop reflecting before a slack column's do, and the figure's own columns appear as bands in the ground. Only a damask has none.

fancy · Jacquard What an upper window's glass does to a white voile. How many times harder a room is to read through a white voile behind glass than through the bare cloth, against how far the passer-by stands out from the façade, for a window centred 1.5, 4.5 and 7.5 m up in a street twelve metres wide between ten-metre terraces, under an overcast sky, at 30 : 1. Below one the glass helps. ground floor: 0.95 from 2 m, 0.95 from 5 m, 0.95 from 9 m; first floor: 2.34 from 2 m, 1.55 from 5 m, 0.94 from 9 m; second floor: 4.92 from 2 m, 1.86 from 5 m, 1.49 from 9 m. The first floor's curve drops by a step at 6.3 m, where its pane stops mirroring the sky and starts mirroring the terrace opposite. What the chart cannot show is a clear sky, which is brighter again near the horizon.

An upper pane mirrors a sky no curtain can afford

A pane in front of a sheer helps a reading only while what it mirrors is dim: for a white voile, below about half the brightness of a white wall lit like the window. A street-level pane mirrors the terrace across the road and stays under that. An upper pane, seen from the pavement below, mirrors the sky, and an overcast horizon — the darkest sky there is — is already twice the limit. Whether a first-floor pane shows sky depends on how far out from the façade the passer-by stands and on nothing else, so the same window is harder to see into from close up than from across the street.

pattern · Opacity What tilting a window pane does to a curtain behind it. How many times harder a room is to read through a white voile behind glass than through the bare cloth, against the tilt of the pane — leaned forward to the left, tilted back to the right — for windows centred 1.5, 4.5 and 7.5 m up, seen from 3 m out in a street twelve metres wide between ten-metre terraces, under an overcast sky. Each curve jumps where its pane starts to mirror the sky: the ground floor tilted back past 18.6°, the first floor leaned forward less than 9.7°, the second floor leaned forward less than 25.6°. Upright the three read 0.95, 1.82, 2.89; leaned forward 26°, 0.97, 0.94, 0.93. What the chart cannot show is a canopy or blind over a shop window, which a pane leaned forward would mirror instead of the street.

A pane leaned forward loses the sky and finds no darker mirror

A pane tilted by some angle sends a passer-by's line of sight off at twice that angle more, and the passer-by's place along the street still drops out. Tilted back about twenty degrees, a street-level pane mirrors sky from everywhere in the street and nearly doubles what a white voile hides. Leaned forward ten degrees, a first-floor pane stops mirroring sky from three metres out, and the voile behind it reads better through glass than bare. Leaning further finds nothing darker: under an overcast sky the road is a brighter mirror than the terrace opposite, by a seventh.

pattern · Opacity

Named alongside it

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

LustreCrown lineFloatSatinFloat lengthOpacityOpen areaSpecular areaTransmittanceVeilWeave angleAnisotropy

All concepts