Textile Structure
how cloth is put together
Concept

Racetrack — where it appears

Kemp's yarn section — a rectangle with semicircular ends, conserving the circle's area — which flattens as a cloth is set closer. Peirce's circle and this are the same cloth before and after something pressed it, which is what makes the aspect ratio a record of a force.

Named by 6 essays across 4 fields — each of them below, with the objects they name alongside it.

Two sections, one yarn. The same yarn given a circular cross-section and a racetrack one of equal area, both jammed. The spacing the two models allow is nearly the same; the cover and the cloth thickness they predict are not.

A tow is not a yarn

Every geometric model on this site assumes a thread with a diameter. A reinforcement tow has a width and a thickness instead, and the two are eight to one — which moves the jammed sett, the crimp, the cover and the cloth's thickness at once, in four different directions, from one change.

applied · Sett 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 A crossing before and after it is pressed. One warp end of a sheeting riding over three picks, drawn twice to the same scale. Unpressed, both sections are circles and the cloth is 0.388 mm thick. At 0.40 N per crossing the sections flatten to aspect ratios of 1.75 and 1.84, the cloth thins to 0.263 mm, and the warp runs flat for 0.109 mm over each pick before it begins to curve. What the drawing cannot show is why the cloth does not do this by itself: flattening shrinks the arc radius as well as the crimp height, so it costs bending energy, and a relaxed cloth keeps its threads round.

A flattened thread is a record of a force

A yarn in cloth is not round, and this site has modelled the flattening for as long as this collection has run with the amount of it left as a number somebody chose. Give the section a stiffness and ask what the cloth prefers, and the answer is a circle — at every stiffness, for every balanced cloth in the table. Flattening does not happen by itself; it happens because something pressed.

mechanics · Compression A crossing before and after it is pressed. One warp end of a sheeting riding over three picks, drawn twice to the same scale. Unpressed, both sections are circles and the cloth is 0.388 mm thick. At 0.42 N per crossing the sections flatten to aspect ratios of 1.79 and 1.88, the cloth thins to 0.260 mm, and the warp runs flat for 0.113 mm over each pick before it begins to curve. What the drawing cannot show is why the cloth does not do this by itself: flattening shrinks the arc radius as well as the crimp height, so it costs bending energy, and a relaxed cloth keeps its threads round.

Peirce and Kemp are one cloth at two moments

This site has run two thread sections side by side since the setting field was built — a circle and a flattened racetrack — and said honestly that they disagree and that the disagreement is the point. They are not rival descriptions of the same fabric. They are descriptions of the same fabric before and after something pressed it, and the difference between them is a pressure that can now be named.

setting · Sett The bracket that closes and the bracket that does not. A 25 tex cotton yarn at a packing factor of 0.6. Its bending rigidity lies between 0.00117 N·mm² — the sum of its fibres', with them free to slide — and 0.478, a solid rod of its own diameter: a factor of 408, and both ends are derivations. Its resistance to being squashed out of round has an upper bound of the same kind, 369 N/mm² for a solid section, and no lower bound at all, because fibres free to slide resist a change of shape with nothing. That is why the aspect ratio of a flattened yarn has been a free parameter here since the setting field was built: a quantity bounded below by zero cannot be estimated from its bounds, and has to be measured.

The stiffness with no lower bound

A yarn's bending rigidity lies between two derivable ends and the ratio is the fibre count — wide, but closed. Its resistance to being squashed out of round has an upper bound of the same kind and a lower bound of exactly nothing, because fibres free to slide resist a change of shape with nothing at all. That is why nobody could ever compute the aspect ratio of a flattened thread.

mechanics · Compression 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

Named alongside it

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

Cloth thicknessYarn diameterCompression energyContact forcePacking factorBending rigidityCalenderingCoverCover factorCrimp heightJammingLustre

All concepts