Textile Structure
how cloth is put together
Series

Spirality — the series

4 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. Which knitted structures spiral, at a twist factor of 4.0. A yarn leaves the spinning frame with a torque it has not been allowed to release, and a loop knitted from it leans. The lean per unit of twist factor above balance is measured; what is counted here is the structure. A loop on the front bed and one on the back are mirror images, so their torques have opposite signs, and a fabric that knits equally on both beds nets to zero whatever the yarn is doing — which is why 1x1-rib, 2x2-rib, interlock do not spiral and plain, half-cardigan, tubular do. The count has to be made per fabric and not per structure: an interlock and a tube both knit equally on the two beds, and they are opposite cases, because an interlock's two components each straddle the beds while a tube's are each wholly on one. The integrity criterion, which asks what nothing holds together, is what tells them apart. What the bars cannot show is the tube's second face, which leans the other way.

    A jersey leans because its yarn still turns

    A single-jersey T-shirt comes back from the wash with its side seam spiralling round the body, and a rib does not. The difference is not the yarn: it is a count. Loops on opposite beds are mirror images, so their torques oppose, and a fabric that knits equally on both nets to zero whatever the yarn is doing.

    part 1 · knits
  2. The course helix of a 30-inch machine with 96 feeders, unrolled. A knitted tube from a 30-inch machine with 96 feeders unrolled flat, one round wide, with its wales drawn straight along it and its courses climbing across it. The machine lays 96 courses in each turn, so each course climbs 96 course spacings — 48 mm of fabric — in one round of 2,262 wales, 162 cm: an angle of 1.70° from the tube's cross-direction. The course drawn heavy is followed round one turn. The vertical scale is exaggerated 6 times. What the drawing cannot show is the hand of the helix, which is set by the direction the cylinder turns.

    A circular machine leans its courses whatever the yarn

    Spirality is blamed on the yarn, and the yarn is most of it. The rest is the machine's. A circular knitting machine's needles make wales that run straight along the tube, and its feeders lay one course each per turn, so every course climbs its feeder count in every round: on a 96-feeder machine, 48 millimetres round 162 centimetres of tube, an angle of 1.7 degrees. The helix has no machine size in it, its hand is set by the way the cylinder turns, and it survives every remedy aimed at the yarn — a steamed yarn, a plied one, S and Z on alternate feeders, and a rib.

    part 2 · knits
  3. Imbalance against the torque a tuck carries, for six named structures. For six named two-bed structures, the imbalance of front-bed loops against back-bed loops in the worst fabric, as the share of a knit loop's torque a tuck carries runs from nought to one: single jersey from 1.000 to 1.000; a one-by-one rib from 0.000 to 0.000; a half-cardigan from 0.333 to 0.000; a full cardigan from 0.000 to 0.000; a rib that both tucks and floats from 0.333 to 0.143; a half-milano from 0.333 to 0.333. Structures without tucks are flat lines; a half-cardigan falls from a third to nought and a rib that tucks and floats from a third to a seventh. What the lines cannot show is where along them a real tuck sits, which is not measured.

    A tuck decides whether a third of two-bed fabrics lean

    A jersey leans because every loop is on one bed and a rib does not because its loops are mirrored across two, and the count that says so treated a tuck as nothing. A tuck is a loop of the same lively yarn wrapped round a needle of one bed, and nobody here has measured how much of a knit loop's lean it carries. It matters. Of the 1,135 two-bed fabrics a two-needle, two-course frame can make, 135 are balanced whatever a tuck carries and 612 lean whatever it carries — and 388, a third, are balanced under one answer and lean under the other. A half-cardigan leans a third of a jersey if a tuck carries nothing and not at all if it carries a full loop's torque, which makes it the instrument that would settle the question.

    part 3 · knits
  4. 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.

    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.

    part 4 · knits

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