Lapping — where it appears
Named by 6 essays across one field — each of them below, with the objects they name alongside it.
Also named here as warp knitting — the same set of essays touches all of them, so they are one junction rather than several.
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 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.
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 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 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.
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.
Named alongside it
The objects these essays reach for when they reach for this one.
Warp knittingThread lengthTricotAnisotropyBeamTensile locusWaleCloth integrityConnectivityCrimp interchangeEaserGreatest common divisor