Textile Structure
how cloth is put together
Concept

Lustre — where it appears

The specular reflection a run of uninterrupted parallel yarn gives, which is why a satin shines and a plain weave does not. It follows the float length and nothing about the fibre, so it is decidable from the matrix and is one of the widest consequences the float has.

Named by 19 essays across 6 fields — each of them below, with the objects they name alongside it.

Where the floats are in the 5-end satin. Every longest run of warp on the face, marked. A float is smooth because nothing interrupts it, which is the same reason it snags: there is a length of thread lying on the surface with nothing holding it down.

The float decides

How far a thread runs on the face before it goes under is one number, and it sits behind lustre, drape, snagging, abrasion, tear strength and how densely the cloth can be set. Almost nothing else in the subject has that reach.

weaves · Float Figure and ground on 8 ends. A damask is a satin and its own complement. The figure is warp-face and the ground is weft-face, they carry the same longest float and need the same shafts on the same threading, and the whole of the pattern is carried by which system is on top.

A damask is its own complement

The pattern is carried by direction alone. Figure and ground are the same satin, one warp-face and one weft-face, with the same longest float, the same shaft count and the same threading — so the cloth's most famous effect costs it no structural difference whatever between the two areas.

fancy · Jacquard 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 The same yarn, flattened. One yarn's cross-section at five degrees of flattening, all drawn at one scale and all of the same area. Nothing is added: the yarn is wider because it is thinner. The cover rises for that reason alone, which is why a calendered cloth is more opaque than the cloth that went into the machine.

Calendering is the cloth arriving at the other model

This site has carried two thread sections side by side since its foundation — Peirce's circle and Kemp's racetrack — and has been careful to say which produced any number. They are not two opinions about one yarn. They are one yarn on either side of a finishing machine.

finishing · Lustre finish 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 Swelling, at the same count. The same yarn before and after mercerisation, drawn to one scale. Its linear density has not changed — the same grams per kilometre go into the cloth — but the fibre occupies more volume, which is a lower packing factor and a larger diameter. Every consequence in this field follows from that single number.

Mercerising is a packing factor

Cotton held in caustic soda swells, and everything the treatment is famous for follows from one number in this site's diameter calculation. The lustre it is actually sold for does not, and saying which consequences are computed and which are not is the whole of the discipline here.

finishing · Lustre finish 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 Which move to use on 16 ends. For each satin move the order admits, the distance from an interlacing to its nearest neighbour, measured on the torus the repeat lives on. A move whose interlacings crowd gives the eye something to find; the one that scatters furthest is the one to weave.

Which satins are worth weaving

Manuals give the moves a satin admits as a list, as though the survivors were interchangeable. They are not. Measure how far apart the interlacings sit and the traditional counter turns out to be the best move at the orders a weaver mostly uses — and to fail first at thirteen, where the square root names four and five scatters further.

weaves · Satin From a calender's line load to a force at one crossing. A sheeting through a nip loaded at 30 N per millimetre of bowl width, with the cloth in contact over 5.0 mm. The pressure is the first divided by the second, 6.00 N/mm², and the force at one crossing is that pressure times the area a crossing owns — the product of the two thread spacings, 0.1374 mm². So the crossing carries 0.824 N, the sections flatten to 2.42 and 2.63, and the cloth thins from 0.388 mm to 0.218 mm. What the drawing cannot show is that two cloths through the same nip are not given the same treatment: the area a crossing owns varies fivefold across this site's table, and it is a factor in the force.

A calender spends the compression for good

Calendering was described on this site as moving a cloth from one thread-section model to another, which was right and had no number in it because the amount of the move was a free parameter. It is a pressure now — and the same nip setting turns out to give two cloths quite different treatments, because the force at a crossing is the pressure times the area a crossing owns.

finishing · Lustre finish A damask's figure and ground trade places when the cloth is turned. A satin 8 figure on a sateen 8 ground in sheeting — one cloth, one set of threads, one sett, and the ground is the figure's own complement. Their total specular areas are within a few per cent of one another, so neither is intrinsically the brighter. What differs is the direction: the figure's crowns run with the warp and the ground's with the weft. So the contrast between them is 2.0-to-one with the light coming from 8° and 0.47-to-one from 90° — it reverses, exactly, a quarter turn apart. That is what makes a damask visible in one colour, and it is not the step in its surface: the step is fifty micrometres and returns no light at all under a diffuse illumination, while this contrast is a factor of 2.0 and is present whenever there is a direction in the light.

A figure shows by its shine, not its step

A damask is one cloth in one colour and its pattern is plainly visible. This collection attributed that to the step in its surface — fifty micrometres of relief, computed from the interlacing rates. The step is real and returns almost no light. What makes the figure visible is that its crowns run at right angles to the ground's, so the two trade places when the cloth is turned.

pattern · Blocks Twist is not torsion: a straight rod, twisted. A rod drawn with a cross painted along it, and the cross turned through 2 full turns from one end to the other. The rod is straight, so it has no Frenet frame at all — a straight line has no osculating plane to turn. The two discs above are the rod's ends seen down its own axis, which is where the twist is an angle rather than a foreshortened wiggle. The twist is the rotation of the painted cross about the rod's own tangent, and it is 2 turns whatever the centre line does. That is the quantity a torsional rigidity resists, and it is why a collection that solved a plane curve had not thereby dealt with torsion.

A shadow stripe is two twists

A cloth striped in one colour, where the stripe is visible only because alternate bands are spun the other way round. The pattern is carried entirely by which way the fibres lie on the yarn's surface, and it disappears when the light moves.

pattern · Stripe The two diameters of a 20 tex yarn. The pressure inside a twisted yarn is zero at its surface, so the outermost fibres are held by nothing but their own buried ends and some of them stand off as loops and ends. A yarn therefore has two diameters: a mass diameter of 167.1 µm, which is a volume divided by a length and is the one every other calculation on this site uses, and a contact diameter of 217.1 µm, which is what a neighbouring thread, a finger or an air stream meets. The gap is a hair layer of 25.0 µm on each side and it is measured, not computed — nothing here predicts hairiness. What is computed is the consequence, and it is 29.9% of the diameter every cover factor on this site was built from.

Singeing is the cheapest change to a surface

Pass a cloth through a flame fast enough and it loses under one per cent of its mass. What it loses is the part of itself that was doing most of the touching, and lustre, friction, printability, pilling and measured cover all move at once.

finishing · Hairiness Z twist at 1600 turns per metre. A 20 tex cotton yarn, 0.167 mm across, with its surface fibres drawn as the helices they are. The angle between a surface fibre and the yarn's axis is 40.0°, and it is the only quantity in this family: the yarn is 13.8% shorter than the fibre in it and carries 59% of the strength the same fibre would give lying straight.

The other crepe is in the yarn

A crepe weave puts the texture in the matrix. A crepe yarn puts it nowhere the matrix can see: the cloth is a plain weave, and the surface comes from a thread twisted so hard that it shortens by a seventh and spends the rest of its life trying to untwist.

weaves · Texture weaves 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 How much every four-by-four draft can shine. All 22,874 four-by-four drafts in which every end and every pick interlaces, at sheeting's construction and a tolerance of 2°, counted by specular area. The range runs from 0.02% to 0.93%, a factor of 60.0, and the distribution is not smooth — it clusters, because the quantity behind it is a count of whole crossings and takes only certain values. The dullest drafts in the catalogue are the plain weaves, which have no plateau at all and shine only from the crowns of their turns; the brightest carry the most float on the face, with the fewest turns interrupting it. Lustre over the catalogue is a length census, and nothing about the yarn enters it.

Lustre is a length times a width

The specular area of a cloth factors exactly: a length of crown line, which the draft supplies, times a width of section within the tolerance, which the yarn and the finish supply. Neither factor knows anything about the other, and over the four-by-four catalogue the first alone spans a factor of sixty.

weaves · Shine A calender multiplies the highlight by 32, and all of it is width. A 2/2 twill in sheeting pressed at increasing force, with the specular area recomputed at each state from the site's own compression model. It rises from 0.91% of the plan to 28.9%, a factor of 32, while the cloth thins from 381.6 µm to 186.1 µm. The gain is not in the length of the crowns: that moves by 5 per cent. It is in their width, which moves by 31.8 times, because pressing puts a flat top on the section and a flat top has one normal rather than a fan of them. The finish does not polish the thread. It changes the dimension of the highlight, from a line to a band, and the arithmetic says so by refusing to put any of the gain in the other factor.

A calender buys the width

Press a cloth and its lustre multiplies by twenty-four. None of that comes from the length of its crowns, which moves by six per cent; all of it comes from their width, because a flattened section has a plane on top of it and a plane has one normal rather than a fan of them. The arithmetic refuses to put any of the gain in the other factor.

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 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 Three rules for how hard to fold a yarn, and which one the trade uses. For 2, 3, 4 folds of 20 tex cotton at 800 turns a metre: the ratio that makes the fold's surface helix angle equal its singles', the ratio that sets the fold's net moment to zero, and the ratio the trade actually folds at. The surface rule is 1/√n exactly, because a fold of n singles is √n times the diameter. The torque balance is C/(B+C), which for this fibre is 0.201 and is the same at every count, every twist and every number of folds. The trade's brackets contain the surface rule in all three rows and the torque balance in none of them.

The folding rule is a surface angle

Fold at two thirds for two singles, six tenths for three, a half for four. Those are one over the square root of the fold count, they are what makes a fold's surface twist angle equal its singles', and all three of the trade's brackets contain the number exactly.

setting · Ply

Named alongside it

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

Crown lineSpecular areaFloatSpecular reflectionHelix angleYarn diameterCalenderingFloat lengthSatinTwist factorWarp-facedAbrasion

All concepts