Textile Structure
how cloth is put together
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The thread: Exactly this many — page 5

Page 5 of 5 of the essays on this thread.
The tucked-in edges of a 2/2 twill, 8 ends wide. A strip of 2/2 twill 8 ends wide over 8 picks, woven with tucked-in edges: every pick is cut at both edges and each tail is laid back into the next shed, so between every pair of picks there is a turn at both edges. 8 of the 16 tucked turns are caught, where the edge end is on the other face in the next shed, and 8 are not. Across all its edge placements the weave catches every tucked turn at 0 of 16. What the drawing cannot show is the tail itself, which lies alongside the next pick for the tuck's length and doubles the weft there. Weaves

A tucked-in edge asks every weave the odd repeat's question

A shuttle weft turns at one edge per pick, alternately, and that alternation is what let a 2/2 twill hold both selvedges with two ends re-entered on its own shafts. A rapier or air-jet loom cuts every pick at both edges and tucks both tails into the next shed, so every boundary between picks is a turn at both edges — the question an odd repeat always asked. Only a plain column answers it. Of the 22,874 four-by-four drafts, 10,382 can still hold their edges on their own shafts, against 13,238 under a shuttle; the 2/2 twill is among the 2,856 lost. And the tucked zone carries two picks in every shed, which lies flat only below between a half and two thirds of a weave's maximum pick density.

 What a 2×2 cable weighs as its cable twist rises. A cotton cable of 2 folds, each of 2 singles, with the folds set at 0.707 of the singles' twist and the cable twisted the singles' way at ratios from nought to 0.60, at twist factors of 3000, 3800, 4500. A little cable twist makes the cable lighter, because it takes twist out of folds set above their own crossing; then the cable's own helix wins and the count climbs. It crosses the singles' sum at 0.260 at 3000, 0.250 at 3800, 0.239 at 4500. At the rule as quoted, a cable twist of 0.500, the cable is +2.21%, +3.54%, +4.95% heavy; at the rule read in the finished thread, 0.293, it is +0.16%, +0.32%, +0.54%. What the curves cannot show is a real cable's folds pressed out of round, which shortens the cable's helix and moves every crossing right. Setting and geometry

A cable weighs its singles at the twists the finished thread keeps

Cabling untwists every fold and hands that twist back to the singles inside it, so beneath its own helix a cable is a fold folded at the difference of two twists — and the cable's helix is a length nothing below it can pay for. Twisted where the cabling rule is quoted, a two-by-two weighs three and a half per cent over its notation. Read in the finished thread, with every level's surface at one angle, the same rule sets the folding frame exactly where a plain fold's is and the cable at 0.293, and the cable comes back to within half a per cent.

 Where five two-bed structures hang straight, in the square of a single tuck's share and a held tuck's. The square of two unmeasured shares of a knit loop's torque: across, the share a tuck held for one course carries; up, the share each loop of a tuck held for two courses carries. Each line is where a named structure's every fabric balances, traced from its own count: a half-cardigan, single = 1.00, any held share; a held half-cardigan, held = 1.00, any single share; two loops against two, wherever the two shares agree; one hold against one, where a held loop carries half a single; a held tuck against a single knit, from (0.00, 0.50) to (1.00, 1.00). The diagonal is the account that treats every tuck loop alike, and the half-slope line the account in which a hold carries one tuck's torque however many loops it holds. What the square cannot show is where in it a real yarn sits, which is not measured. Knits and other structures

A tuck held two courses is a second unknown

Counting a tuck as a share of a knit loop's torque assumed every tuck loop carries the same share, however long its needle holds it. A needle that tucks on two courses running holds two loops in one hook and casts them off together, and nothing says that second loop carries what a single tuck does. Give the held loop its own share and every structure hangs straight on a line in a square of two unknowns rather than at a point on one. Of the 9,581 three-course fabrics that looked immune to the tuck, 1,788 are immune only if a held loop carries exactly what a single tuck does — and if a hold carries one tuck's torque however many loops it holds, 13,337 are immune instead. Two small structures, each straight under one account and leaning under the other, would say which.

 4 drops of 250 cm cut from one roll of a 64 cm repeat, three ways. 4 matched drops of 250 cm cut one after another from one roll of a cloth with a 64 cm repeat, drawn along the roll at its own scale, with the cloth lost between drops shaded and its length written below. A straight match has one place in the repeat where every drop must start, ticked above the roll, so each gap is 6 cm and 18 cm is lost. A half-drop's alternate widths start half a repeat lower, ticked below. Cut in the order the widths hang, A B A B, every gap goes from one class to the other and costs 38 cm, 114 cm in all; cut A A B B, the like gaps cost 6 cm and the job loses 50 cm. What the strip cannot show is the pattern itself, which is the same cloth in every row. What cloth is

A half-drop wastes less, cut in the right order

A straight match has one place in the repeat where every drop may start, so a cutting room loses half a repeat between drops on average and a whole one at worst, in any order. A half-drop has two, because alternate widths start half a repeat lower — and that gives the cutter a choice the straight match never offers. Cut in the order the widths hang, a half-drop loses exactly what a straight match loses. Cut with like drops together when the remainder favours it and alternated when it does not, four drops of a pair of curtains lose a third less, and a long run half as much: (r/4)·n/(n − 1) a gap, against r/2. The rule needs one subtraction before the first cut.

 What a thread of twos weighs as its levels of twist are added. A two-fold, a cable of two two-folds, a cord of two such cables and a cord of two cords, all of 20 tex cotton singles, each twisted so that every level's surface sits at one angle in the finished thread, at twist factors of 3000, 3800, 4500. At 3,800 they weigh fold −1.35%, cable +0.32%, cord +2.02%, cord of cords +3.75% against the sum of their singles: a fold light, a cable on its notation, and every level after it one helix heavier than the last. Dashed, the same four twisted to the rule as quoted on the frames, +0.46%, +3.54%, +4.54%, +6.98%. What the chart cannot show is the folds' and cables' real shape, which is taken round. Setting and geometry

The singles pay once and every level adds a helix

A cable twisted so that every level's surface sits at one angle weighs its notation, and it is tempting to read that as a law: equal angles, honest count. It is not one. With every surface at one angle the singles keep the same twist however many levels sit above them, so their saving is paid once, while every level adds a helix of the same length. A two-fold comes out light, a cable on its notation, and a cord of two such cables two per cent heavy — the cable's agreement is the walk passing through zero. For a cord to weigh its notation, everything above its singles has to sit at about half their angle.

 One repeat of two patterned fabrics, pulled two ways. One twelve-course repeat of a two-bar warp knit, each band a course drawn at its spacing and its kind: two tricot underlaps, two satin, or one of each. With the bars coincident the repeat is two bands, and narrowed to four fifths of its width the satin band opens to +150% while the tricot band opens to +26%; widened a fiftieth the satin band closes by −36% and the tricot band by −3%. Opposed, every course is the mixed kind and every course moves alike, by the smaller opening and the larger closing. The bands are drawn at the fabric's width to scale. What the drawing cannot show is the loops, held fixed here. Knits and other structures

Opposed bars even a warp knit by locking it

Two patterning bars knitting the same stripe can be set so that each bar's long underlaps fall where the other's are short. Neither bar's stroke changes, and every course then carries the same total yarn — but that is not why the cloth comes out even. Every course pairs a long underlap with a short one, the long one stops the width and the short one stops the length, and so every course gives like the stiffer bar in both directions. The evenness is bought with the stripe's give.

 A bay window's drops cut from one roll, three ways. Four drops of 250 cm and two of 140 cm cut from one roll of a 64 cm repeat, drawn along the roll to scale with the cloth lost between drops shaded. A straight match loses 76 cm at best. A half-drop cut in hanging order loses 154 cm. The same half-drop in its best order loses 44 cm, by keeping the long drops together, where each loses 6 cm, and changing class only after a short drop, which prefers to. What cloth is

A bay window wastes less than a wall

When a job's drops are all one length, a half-drop's best cutting order has one forced move, because the cutter has to change class once whatever the drops would prefer. Mix the lengths, as a bay window or a window over a radiator does, and each length sets its own price for what follows it. Six drops then lose a quarter of a repeat a gap instead of three tenths. Whether every drop can have its way is the bridges of Königsberg on two islands, and for a straight match mixing the lengths does almost nothing: its order can only choose which drop is cut last.

 A 2/2 twill line's ends where the reed leaves them. A light warp line 3 ends wide in a dark 2/2 twill, with the ends drawn at their true places at a cover of 60% and both boundaries traced. Set evenly the edge swings 2.00 thread spacings. With 3 ends to a dent, closed by 40% of a spacing so that they touch, and the line on the dent's edge, it swings 1.20. One end along in the same reed it swings 2.40, more than if it had been set evenly. The weave and the reed are the same in the last two. Only where the line starts has changed. Pattern and colour

A stripe's edge is cleanest inside one dent

No weave can draw a line with a straight edge, since the thread at the boundary must go under somewhere. A cloth has one freedom its weave lacks, which is the spacing of its ends, and it looked as though crowding a stripe's outer end could halve the swing. It cannot, in most cloth: two ends stop at a diameter apart, so the swing falls only as far as the cover. The freedom that costs nothing is another one. A line's narrowest unbroken width is exactly its swing plus one, so it fits one dent of a reed, and the same reed gives 1.2 thread spacings or 2.4 according to which end of the dent the line begins on.

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