A circular machine leans its courses whatever the yarn

A jersey leans because its yarn still turns: a spun yarn carries a torque it has not been allowed to give back, every loop on one bed rotates the same way under it, and a structure that knits equally on both beds cancels it exactly. The remedies the trade uses all go after that torque — a lower twist, a plied yarn, a steamed one, S and Z yarns on alternate feeders — or after the count, by knitting a rib.

Every one of those remedies works on the yarn or on the structure, and a spirality reading is not only about either. Part of it is laid down by the machine before any yarn has had a chance to turn, and none of the remedies reaches that part. It is small against a hard-twisted yarn’s lean and large against a well-set one’s, and it is the reason a tube knitted from a perfectly balanced yarn is still not square.

Needles make the wales, feeders make the courses #

A circular knitting machine is a cylinder of needles turning past a ring of feeders. Each needle rises and falls in one slot as it passes each feeder, and the loops it makes hang one below the other in the fabric: a wale is one needle’s output, and it runs straight down the tube because the needle never moves sideways in the cylinder.

A course is different. A feeder lays yarn into every needle that passes it, so each feeder draws one course round the tube as the cylinder turns. A machine with F feeders therefore lays F courses in every turn — and a course cannot close on itself, because by the time the cylinder has brought its first needle back to the same feeder, the other F − 1 feeders have each laid a course of their own in between. Each feeder’s yarn runs on as one continuous helix, and the helices of all F feeders interleave.

So the courses are not rings. Each is a turn of one of F interleaved helices, and each helix advances F course spacings in one round of the tube.

A course climbs its feeder count in every turn #

Take a large single-jersey machine: thirty inches across, twenty-four needles to the inch round its circumference — 2,262 needles — and 96 feeders, knitting a jersey that relaxes to 14 wales and 20 courses to the centimetre.

In one turn a course climbs 96 course spacings, and at 20 courses a centimetre that is 48 millimetres of fabric. Round the relaxed tube it has 2,262 wales to cross at 14 to the centimetre, 162 centimetres. A rise of 48 millimetres in 162 centimetres is a slope of about three per cent, which is 1.70 degrees from the tube’s cross-direction.

A degree and three quarters is too small to see on a plain jersey and large enough to measure on any of them. It is the angle between the courses and the perpendicular to the wales, in the fabric as it comes off the machine and before the yarn’s torque has done anything at all.

The angle has no machine size in it #

The rise is the feeder count times the course spacing, and the round is the needle count times the wale spacing, so the angle’s tangent is the feeders per needle times the ratio of the fabric’s wales per centimetre to its courses per centimetre. The diameter of the machine does not appear.

That makes the angle a property of how densely a machine is fed and of the fabric’s own shape. The 30-inch machine carries 42 feeders per thousand needles. An 18-inch body-size machine with 54 feeders on 1,357 needles carries 40, and its courses climb at 1.60 degrees. A 20-inch machine with only 12 feeders, knitting a coarser jersey at 10 wales and 14 courses, carries 11 per thousand and climbs at 0.43.

The fabric’s ratio matters as much as the machine. The same machine knitting a jersey that relaxes to eight tenths as many wales as courses rather than seven tenths climbs about a seventh more steeply, because its courses are further apart for the same wales.

Why the large machines all sit near a degree and a half #

Feeders are not added to a machine for its looks. Why a knit shows a thick place found the design tension behind them: every feeder added lays another course per turn, which is more production, and every feeder added lengthens the period at which a difference between packages repeats down the fabric. A builder who wants the most fabric from a cylinder fits as many feeders as the circumference has room for, and room goes with the diameter.

So production machines are built at roughly a constant number of feeders per inch of diameter, and needles are set at a constant gauge per inch of circumference, and the ratio of the two is nearly the same on every large machine. The course helix is therefore not an accident of one machine. It is the price of fast knitting, paid at nearly the same angle on every production machine of a given gauge, and paid far less on a slow machine with few feeders.

Two leans with two owners #

A spirality reading is an angle between a fabric’s wales and the perpendicular to its courses, and there are now two reasons for that angle to be other than nothing.

The yarn’s torque leans the wales. It rotates every loop the same way once the fabric is free to relax, and the wales follow. The angle is fitted rather than derived — about nine degrees for each unit of twist factor above a balanced 2.4 — and its sign is the yarn’s twist direction.

The machine leans the courses. The helix is laid before the yarn has been released, and its hand is the direction the cylinder turns: a machine turning the other way lays the other helix. Nothing about the yarn enters it.

The reading is the sum of the two, with signs. When the cylinder’s helix leans the same way as the torque, they add; when it leans the other way, they subtract. The two owners do not consult each other, and the same yarn on two machines turning opposite ways gives two different readings.

The same yarn reads two ways on two machines #

At a twist factor of 3.2 the fitted torque lean is 7.2 degrees. On the 96-feeder machine the reading is 8.9 degrees with the cylinder turning with the lean and 5.5 with it turning against. The difference between the two machines is 3.4 degrees, twice the helix, and it is nearly half of the torque lean itself.

The lower the twist, the larger the machine’s share. At a twist factor of 2.8 the torque lean is 3.6 degrees, and the two machines read 5.3 and 1.9 — one nearly three times the other, from one yarn. At 4.0 the torque lean is 14.4 and the readings are 16.1 and 12.7, which is a difference a test lab would put down to scatter.

So a comparison of spirality between two mills is a comparison of their machines as well as their yarns, and the finer and better-set the yarns, the more of the difference belongs to the machine.

What every yarn remedy leaves #

Every remedy for spirality aims at the torque, and the helix is not torque.

Knit the same singles on alternate feeders with S and Z twist, and the torques cancel course by course: the reading is 1.70 degrees. Steam the yarn until it has no torque left, or ply two singles against each other: 1.70 degrees. Knit a 1×1 rib from the original singles, and the structure cancels the torque exactly: the rib’s wales do not lean, and its courses still climb at 1.70 degrees.

The remedies are right about what they remove and silent about what they leave. A fabric knitted with every one of them applied at once still has its courses running at a degree and three quarters to its wales, because nobody removes a helix by changing a yarn. A half-cardigan, whose torque is a third of a jersey’s, reads 2.4 degrees of torque and 4.1 or 0.7 in all.

Reading the two leans apart on one machine #

Because the two leans have different owners, they can be separated without knowing either in advance, and the separation needs nothing but the machine a mill already has.

Knit the yarn twice on the same machine: once as a jersey and once as a 1×1 rib. The rib’s structure cancels the torque, so its reading is its own course helix and nothing else. The jersey’s reading is its torque lean plus or minus its course helix. Subtract the jersey’s helix from its reading and what is left is the yarn’s torque lean with the machine taken out, measured on the machine that will knit the production.

There is one correction, and the arithmetic says exactly what it is. The helix depends on the fabric’s own ratio of wales to courses, and a rib relaxes to a very different ratio from a jersey — narrower, with many more wales to the centimetre — so its helix is not the jersey’s. The rib reading establishes the machine’s hand and its feeders per needle; the jersey’s own helix then follows from the jersey’s own counts, and it is that helix, not the rib’s, that comes off the jersey’s reading. Two counts a technician takes with a pick glass are the whole of the correction.

The reverse test is a machine turning the other way, and most mills do not have one. The rib test needs only the machine in front of it, which is why it is the one worth running.

A rib has straight wales and leaning courses #

The rib is the case that shows what kind of lean the helix is.

A jersey’s torque rotates its loops, so its wales lean and a tube’s side seam — which follows a wale — walks round the body. A rib’s wales do not lean, so its seam stays where it was put. But its courses are on its machine’s helix like any other fabric’s, so a rib knitted in the round has courses that are not square to its wales, at whatever angle its own machine’s feeders per needle and its own counts give.

So the torque moves the seam and the helix moves the hem. The first is a rotation of the wales and the second a rotation of the courses, and a garment shows them in different places: a side seam spiralling round the body is the yarn; a hem that will not lie parallel to a stripe is the machine.

Where the machine’s helix shows #

On a plain jersey the helix is invisible, because nothing marks a course. It shows wherever something does.

A stripe marks a course. A jersey striped by feeding colours at the feeders is striped along its courses, so its stripes are helices too, climbing 48 millimetres a turn. A tube flattened for a garment has two faces, and each face’s stripes climb half a turn’s rise across it — 24 millimetres across the chest of a garment from the large machine, and 13.5 from the body-size one. A striped T-shirt cut square to its wales has its stripes running uphill across it by that much. A weft stripe is counted in pairs of picks because a loom’s shuttle has to come back; a knitted stripe climbs because a feeder never does.

A hem marks a course. A hem cut along a course runs at 1.7 degrees to the wales, and a hem cut square to the wales runs across the courses. On open-width fabric a straightener can shear the helix out as a skew — a skew a bias panel also suffers from shrinkage — but a garment knitted as a tube has no edge to pull on, and its helix goes to the customer.

And a straightener chooses what to square; it cannot square both. The angle between a wale and a course is knitted into the loops, so pulling the courses square to the fabric’s edge shears every loop by the helix angle and leaves the wales leaning by it instead. A jersey loop sheared a degree and three quarters is a loop held away from the shape it was knitted in, and a held position is the kind of distortion that a wash can give back. Whether a straightened jersey’s courses drift back towards the machine’s helix in laundering has not been measured here, and the arithmetic says which way they would go if they do.

A barré’s period is one turn’s climb #

The machine’s helix and a problem every jersey knitter already knows are the same number.

A knit shows a thick place because a difference between packages repeats every F courses, one band per feeder cycle, and a course is one thread where a warp is many, so the band has no averaging to hide in. That band spacing is F course spacings — 48 millimetres on the large machine. The course helix climbs F course spacings in one turn — 48 millimetres. They are the same length, because they are the same fact about the machine: F courses are laid in every turn.

So a barré band on a multi-feeder machine is not a ring round the tube. It is a helix at exactly the course angle, and one band’s end meets the next band’s start after one turn. A band that reads as a horizontal stripe on a garment is lying on the machine’s helix, and a tube with a single faulty package shows its fault as one continuous spiral rather than as a stack of rings.

A slow machine is nearly square #

The helix is the price of feeders, and a machine that does not pay for many feeders does not pay much helix.

The twelve-feeder machine climbs at 0.43 degrees. Its courses are nearly rings, and a yarn knitted on it reads almost exactly its torque lean — at a twist factor of 3.2, 7.63 or 6.77 degrees for the two directions of rotation, against 8.90 or 5.50 on the 96-feeder machine.

That bears on a comparison mills make often. A sample knitted on a small machine and production knitted on a large one should not agree about spirality even from one yarn: they should differ by the helix of the production machine, which the small machine barely has.

Feeders, needles and two counts #

The helix angle’s tangent is the feeder count over the needle count, times the fabric’s wales per centimetre over its courses per centimetre: equivalently the rise per turn, F course spacings, over the relaxed round of the tube, N wale spacings. Needle counts come from each machine’s diameter and gauge. The torque lean is the fitted relation the first spirality essay used, nine degrees per unit of twist factor above 2.4, multiplied by each structure’s counted imbalance, and a spirality reading is that lean plus the helix for the cylinder turning with it and minus it for the cylinder turning against.

The tangent was confirmed to equal the rise over the round exactly for all three machines, and to be unchanged by halving a machine’s diameter at the same feeders and needles per unit; reversing the cylinder was confirmed to move the reading by exactly twice the helix, with the torque lean midway, at four twist factors; and a set yarn, S and Z alternated, and a rib were each confirmed to leave exactly the helix.

What the helix leaves out #

The torque lean is fitted. Every angle attributed to the yarn inherits the first spirality essay’s working figure of nine degrees per unit of twist factor, and the knitted model here has no writhe to derive it from. The machine’s helix is derived; the comparison between them is between a derivation and a fit.

Which rotation is “with” the lean is not given. It depends on the yarn’s twist direction, on which face the loops are knitted towards, and on how the lean is measured; the arithmetic says the two add for one rotation and subtract for the other, and does not say which is which on a particular machine.

The counts are the relaxed fabric’s. On the needles a jersey is stretched and its counts are different, so the helix angle on the machine is not the angle in the finished tube; the finished angle is the one a garment carries and is the one computed. A finish that compacts the fabric lengthwise or stretches it widthwise changes the ratio of counts and moves the angle with it.

And the machines are illustrative. Their feeder and needle counts are round figures for common builds, not a survey, and the angle depends on nothing else about them.

Still open: whether a mill ever pairs a machine with a twist #

The arithmetic says a mill running singles yarns of one twist direction could halve the difference between its best and worst spirality simply by running them on machines that turn against their lean. A mill that runs most of its singles in one twist direction on machines that all turn one way has a pairing it did not choose, and whether that pairing is the favourable one or the unfavourable one is a matter of which way its machines and yarns happen to go — a survey of machine rotations against yarn twist, and a measured spirality on each combination, that has not been made here. It would also show whether the helix is already quietly inside the fitted nine degrees per unit of twist.