Lustre finish — the series · Textile Structure

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.

part 1 · finishing

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.

part 2 · finishing

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 the standard cloth table, and it is a factor in the force.

A calender spends the compression for good

Calendering was described here 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.

part 3 · finishing

An operation multiplies a spread by its own log-slope. A transformation does not leave a population's spread alone: if y goes as the kth power of x then a small spread in x becomes k times that spread in y, exactly in the limit and nearly so at the CVs a yarn has. So an operation with an exponent below one narrows the population it acts on — a thickness that goes as the square root of a load comes out at half the spread it went in with — and one with an exponent of four widens it fourfold. This is the same derivative that decided every bias in this ladder, read for its magnitude rather than for its curvature, and it is why a finish can be a variance-reducing operation without anyone having chosen it for that. The straight line through the origin is the whole of the rule; the departure from it at the right-hand end is the second-order term arriving, which is where the linearisation stops being one.

A finish spends a spread before it spends a mean

Every operation on a cloth multiplies the variation it inherits by its own log-slope, so an operation with an exponent below one makes the cloth more even and one above it makes the cloth less even. Calendering, which is bought for evenness, has an exponent of 1.4.

part 4 · finishing

Where a calender works, and where recovery has been measured. Each fibre's measured elastic-recovery span drawn against the shape strains a calender imposes, on one axis. The settings run from 11.2 per cent shape strain at a flattening of 1.25 to 54.9 per cent at 3. cotton is measured to 5 per cent; wool is measured to 20 per cent; silk is measured to 5 per cent; flax is measured to 2 per cent; viscose is measured to 5 per cent; nylon is measured to 8 per cent; polyester is measured to 8 per cent. Only wool reaches any setting at all, and only the lightest.

A calender works where nothing has been measured

This account has twice recorded that the missing piece is plasticity — what fraction of a flattening survives the nip. The piece is missing for a sharper reason than nobody having written it down. A calender's flattening is a shape strain, and at the lightest setting in this account's own series that is 11 per cent while cotton's elastic recovery is measured from 2 to 5. Six fibres of seven have no data at any setting the machine has, and wool reaches only the lightest. The law cannot be had from the measurements; what can be had is the bracket, and it is a factor of twenty-four.

part 5 · finishing

How much plateau a cloth of stated cover can be given. The flat run a calender can put on a 200 micrometre yarn, against the cover the cloth already has. A thread may widen until it meets its neighbours, so the flattening is capped where the section's width equals the pitch; at a cover of 0.3 that is a flattening of 13.9 and 619 micrometres of plateau, and at 0.9 it is 1.32 and 53 micrometres. At full cover both are nothing.

A covered cloth cannot be calendered

A calender widens a section at conserved area, and a thread may widen until it meets its neighbours. So the flattening is capped by the cover the cloth already has — ×30 on a scrim, ×1.32 at a cover of nine tenths, and exactly one at full cover. The plateau a calender buys falls to nothing along with it, which makes the lustre a nip can add and the cloth's opacity the same constraint read twice: a cloth that cannot be seen through is a cloth a calender cannot help.

part 6 · finishing

A calender's best cloth is the one its nip fills

A calender's lustre is a length of crown line times a width of plateau. A closer cloth has more crown line and less room to widen each thread into, and the product was expected to peak at some interior cover that would move with the weave. It does not peak at all on the cap alone — per unit of crown line it falls all the way from the most open cloth. The peak is made by the nip: a nip that flattens by f has one best cloth, the one it exactly fills, at a cover of d over the flattened width, and there the lustre is (f − 1)/f. No yarn, and no weave, moves it.

part 7 · finishing