Generator

The tricot lapping

A warp-knit lapping drawn from the guide bar's movement. Each thread is coloured by the group of wales it belongs to, so a lapping that leaves the wales independent shows as several colours. This one joins them into 1 group.

6 essays call lapping. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the weave its essay argues about.

Where it is called

Every figure listed here is drawn from this one rule.

Knits and other structures

Warp knitting, which is a different thing entirely

Every wale has its own thread, and if the thread never leaves its wale the fabric is a set of independent cords. Whether a lapping makes cloth is decided by a coprimality condition — the satin theorem, in a knit.

What a second guide bar buys. Independent fabrics left by each lapping across 12 wales, counted by walking the wale graph and checked against the greatest common divisor of the shogs with the width. A bar that leaves more than one is not making cloth; a second bar can put right what the first could not.

Knits and other structures

What a second guide bar is for

One warp-knit bar leaves the wales in as many independent fabrics as its shog shares factors with the width. Two bars leave the greatest common divisor of both — so a pair of shogs that each fail alone can succeed together, and a pair that share a factor cannot.

What a second bar wants that the first does not. How much more yarn each guide bar needs than a tricot bar, per wale, over a 100 metre piece at 14 courses a centimetre — which is 140000 courses. A cord bar wants 111.3 metres more and a satin bar 232.3, both of which are more than the piece is long. A shared beam is one course spacing out after 0.28 courses.

Knits and other structures

Two bars cannot share a beam

Two guide bars each make one overlap a course and one underlap, and the overlap is the same object on both — the same needle, the same loop. So the difference in what they consume is exactly the difference in their underlaps, with no model of a loop in it: a cord bar wants 111 metres more yarn per wale than a tricot bar over a hundred-metre piece, and a satin bar 232. A shared beam is one course spacing of slack out after less than half a course.

The locus a warp knit's underlaps put it on. Width against length for each shog, at 28 needles an inch and 14 courses a centimetre. An underlap keeps its own length, so the two spacings lie on a circle and every fabric moves along an arc of it. A tricot can be pulled 27.3 per cent wider and 62 per cent longer; a cord 7.5 and 173. The shog decides which.

Knits and other structures

The shog is the anisotropy

An underlap is a straight run from one needle to another on the next course, so it is a hypotenuse — and its length is fixed while the two spacings are not. Pulling the fabric wider turns it towards the horizontal and pulls the courses together, on a circle. Every state a warp knit's underlaps allow lies on that circle, its as-knitted point sits where the shog puts it, and the ratio of the length it can give to the width it can give runs from 2.3 at a tricot to 218 at four needle spaces.

A patterning bar's thread through one repeat. One guide-bar thread followed through a 12-course repeat, needle places across and courses down, with each course's underlap drawn beside it as a bar against the beam's steady delivery, the repeat's mean of 1.984 mm. The shogs are 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3: 6 of 1 space (1.155 mm) and 6 of 3 spaces (2.814 mm), at 28 gauge and 14 courses a centimetre. The overlaps, the same on every course, are not drawn. What the drawing cannot show is the tension: a course whose bar runs past the mean is a course the beam has not yet paid for.

Knits and other structures

A patterned warp knit needs a stroke as long as its stripe

A guide bar that changes its shog from course to course takes yarn at a changing rate from a beam that delivers at one. The overlap is the same on every course, so it cancels again, and the running shortfall is the sum of each course's underlap less the mean — exact, with no loop in it. It returns to nought every repeat and strays inside it by a stroke that something must absorb. For a stripe the stroke is about the stripe's own height in the cloth, whatever the machine's gauge. The same twelve courses of tricot and satin need six times the stroke in two blocks as alternating, and of all 924 orderings exactly one pattern needs the least.

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.

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