Textile Structure
how cloth is put together
Concept

Tuck — where it appears

Taking new yarn into a loop without casting the old one off, so that loop is held for another course and pushes its neighbouring wales apart. It is the cheapest way to widen a knit without changing its yarn, and its cost is paid in stitch density and in the yarn the held loop borrows.

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

half-cardigan 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.

Knit, tuck and miss

A weave is a matrix over two symbols and a weft knit is a matrix over three. The site's central question survives the translation intact: a weave falls apart when its above-and-below relation is disconnected, and a knit falls apart when a needle never knits.

knits · Stitch notation Yarn per needle, by structure. Wale spacings of yarn per needle position, at one loop length. A knitted loop is 4.30 of them — Munden's constant, measured rather than derived — a float across one needle is exactly one, and a tuck is taken as a stated multiple of a loop. Everything else follows by counting, so the percentages beside the bars are not estimates.

What a tuck costs

A knitted loop is about four wale spacings of yarn and a float across one needle is exactly one, so replacing a knit with a miss removes three quarters of a loop. That much is a count. What it does to the fabric's size is not, and this essay is careful about which is which.

knits · Stitch notation How much of a fabric's yarn crosses between the beds. The share of half periods that cross from one bed to the other, read off each structure's own traverse rather than quoted. It is the mechanical difference between these fabrics in this account: a half period that crosses climbs the whole bed gap and one that does not climbs a yarn diameter. Single jersey and a tubular fabric come out at zero — the tubular one because its two faces are made on separate courses and never meet — and a one-by-one rib comes out at one, with every sinker loop crossing. A two-by-two rib is at a half, which is the number a reader would guess and is here counted.

Where a two-bed fabric's yarn is

Thirteen named structures, and for each of them the share of its yarn that crosses between the beds — read off its own traverse rather than quoted. It separates the fabrics into three groups, and one of the groups turns out not to be a fabric at all.

knits · Two-bed Which knitted fabrics lie flat, counted from the structure matrix. The curl balance of every named two-bed structure this site holds, with a tuck counted in full on the bed that took its yarn: the yarn a repeat puts on the front bed minus the yarn it puts on the back, over the total. A fabric lies flat exactly when it is zero, and the criterion has to put single jersey at one end and a one-by-one rib at the other or it is worth nothing — which it does, at 1.00 and 0.00. What it is for is the rest: a tubular fabric balances because it is two jerseys facing opposite ways, both cardigans balance because a tuck holds yarn on the bed that took it, and half-milano and a three-by-one rib come out front-heavy — which is what they are and what they do. 6 of the 13 structures curl.

Which knitted fabrics lie flat

Curl was explained here by counting face changes between courses, which works for stockinette and garter and reaches nothing else. The same question turns out to be a signed sum over a structure's own grid — and it answers for every fabric a two-bed machine can make, including the ones nobody has a rule for.

knits · Two-bed 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.

knits · Spirality 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.

knits · Spirality

Named alongside it

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

MissTwo-bedCensusCourseWaleInterlockLoopNeedle bedResidual torqueRibSpiralityStitch notation

All concepts