Why a knit shows a thick place

A woven cloth beats down its yarn’s irregularity by a square root: a patch three millimetres across holds fourteen independent threads, and the averaging reduces a thirteen per cent yarn to a three and a half per cent cloth.

A knitted fabric is made from the same yarn on the same day and does not look the same. Knitters spend more of their time on yarn appearance than weavers do, machines are equipped with elaborate arrangements for mixing packages, and the characteristic complaint about a jersey is a faint horizontal banding that no weaver has ever met.

The reason is not that knitting is more demanding. It is that the averaging argument requires independent threads, and a weft-knitted fabric does not have any.

The claim #

A weft knit turns a difference between yarn packages into a periodic band whose spacing is set by the machine, and the averaging that saves a woven cloth does not apply.

• A woven cloth has a warp of hundreds of separate ends drawn from hundreds of packages, and it averages them.
• A weft knit is one thread, taken from F packages at F feeders, laid in strict rotation. The band spacing is F ÷ courses per centimetre and is a property of the machine.
• A periodic variation is not averaged. It beats a random one of the same size by √(2n/π) at its own frequency, which over a few hundred courses is a factor of ten or more.

So a knit’s appearance problem is a correlation problem, not an evenness problem, and the remedies are all about breaking the correlation rather than about improving the yarn.

Where the independence goes #

Take the woven argument apart and see which of its premises fails.

It said: a patch contains sett × L threads from each system, they are independent because they came from different places on the spinning frame, and independent errors add in quadrature.

In a weft knit the first premise still holds in a sense — a patch contains several courses and several wales — but the second does not, and it fails in two different ways at two different scales.

Along a course, the yarn is one continuous thread. Two loops a centimetre apart in the same course are a few centimetres apart along the yarn, which is longer than a staple, so those are independent. This is the scale at which the knit behaves like the woven cloth.

Between courses laid by the same feeder, the yarn is one package. Two such courses are separated along the thread by F course-lengths, which for an ordinary machine is a kilometre — so they are independent as samples of yarn and identical as samples of package. Anything that differs between packages rather than within them is perfectly correlated between them.

That is the failure. A woven warp averages over packages; a knit rotates through them. Averaging destroys a package-to-package difference and rotation preserves it, at a period the machine sets.

The arithmetic of the band #

The band spacing is a division:

$$\text{band} = \frac{F}{\text{courses per centimetre}}.$$

For the ordinary large-diameter single-jersey machine — ninety-six feeders on a thirty-inch cylinder, twenty courses per centimetre — that is forty-eight millimetres. For a small twelve-feeder machine at the same course density it is six.

Both numbers are the machine’s and neither is the yarn’s. The same packages on the two machines produce a band five centimetres apart in one fabric and half a centimetre apart in the other, and the second is far less objectionable — not because the fabric is better but because a half-centimetre period is nearer the scale the eye averages well.

That is the whole design tension of a multi-feeder machine. More feeders means more production, because more courses are laid per revolution; and more feeders means a coarser band from the same yarn. The trade’s answer is to make the packages as alike as possible, and the arithmetic says why that is the only answer available: nothing else in the expression can be changed without giving up the production.

Why the eye is so good at finding it #

The band lands where human vision is most sensitive and it lands there parallel to itself, which is the worst combination.

Contrast sensitivity peaks at a few cycles per degree — at reading distance, a period of two to five millimetres, and at arm’s length nearer a centimetre. A forty-eight-millimetre band on fabric held at arm’s length is a little coarser than the peak and is still well inside the range; and because it is a stripe rather than a patch, the eye integrates along it, which is exactly the direction in which integration helps detection rather than hurting it.

This also explains a fact that surprises people coming from weaving: a knitted fabric can be made from a worse yarn than a woven one and look better, provided the packages are alike. The random part of the yarn’s irregularity is averaged by the knit as effectively as by the weave; it is only the correlated part that survives, and the correlated part has nothing to do with the yarn’s coefficient of variation.

What a thick place actually does to a knit #

There is a second difference, smaller and worth stating, because it decides what the band looks like rather than where it is.

A knit’s dimensions come from its loop length, and loop length is set by the yarn fed rather than by the yarn’s mass. A knitting machine feeds a length; a thick place going through the feeder makes the same loop, with more mass in it.

So a thick place in a knit changes the fabric’s mass and not its dimensions. A course of heavy yarn is the same width, the same number of wales, the same course spacing, and heavier — which shows as a shade band, since a denser course reflects and absorbs differently.

In a woven cloth the reed sets the spacing, so a thick end changes the local cover rather than the mass alone, and shows as a change in the cloth’s opacity as well as its shade.

The band is not the only period the machine imposes #

A feeder rotation is the largest of the machine’s periods and it is not the only one, and the others are worth naming because they are diagnosed by their spacing rather than by their appearance.

The cylinder’s own revolution is a period of F courses divided by nothing — one turn lays F courses, so anything that varies once per revolution repeats at exactly the same spacing as the feeder band. A worn cam track, a single damaged needle’s neighbour, a take-up that pulls harder on one side: all of them produce a mark at the revolution period, which is indistinguishable in spacing from a package difference.

One needle produces a wale-way mark rather than a course-way one, at the wale spacing, and is the easiest of all to identify because it runs the length of the fabric rather than across it.

And a yarn feed device — a positive feed wheel, a storage feeder — has its own circumference, so a fault in one puts a period on the yarn rather than on the fabric, at a spacing of the wheel’s circumference divided by the loop length in courses. That period is generally not a whole number of courses, so it beats against the feeder rotation and produces a slow drift rather than a stripe.

The diagnostic is arithmetic rather than visual. Measure the spacing, divide by the course density, and compare the result against the feeder count, against one, and against the feed wheel’s circumference in loops. Each fault has its own number, the numbers are not close, and a band whose spacing does not match any of them is a yarn fault rather than a machine one.

That is a more useful procedure than looking at the fabric, and it is available only because the period is set by the machine and is therefore known in advance. A knitted fabric’s faults are labelled by their spacing, and a woven cloth’s mostly are not, because a woven cloth has no equivalent rotation to stamp a period onto everything that goes wrong.

The exception on the woven side proves the same point from the other direction: the one woven fault that does carry a machine’s period is the reed mark, and it is diagnosed exactly this way, by counting threads rather than by looking.

What the remedies are, and why they are what they are #

Every remedy in the trade is an attack on the correlation, and each corresponds to a term in the arithmetic.

Plating and package mixing. Feed each feeder from more than one package, or rotate packages between feeders. This makes each feeder’s yarn a mixture, so the difference between feeders falls. It is the direct attack and it is why creels are arranged to draw from many lots.

Alternate feeders from alternate lots. If two lots have to be used, alternating them halves the period — a difference every two courses rather than every ninety-six — and moves the band from the eye’s sensitive range down into texture.

Buy the yarn as one lot. The bluntest and most effective, and the reason knitters specify lot sizes that weavers do not need.

And run fewer feeders, which is never done, because the production loss is the whole economics of the machine.

The ordering is worth noticing: three of the four are about the packages, and none is about the spinning. The index of irregularity, which is the only measure of how well the yarn was spun, does not appear in any of them.

The measurement that does not predict the complaint #

Put the two halves together and something uncomfortable follows for the way knitting yarn is bought.

A knitting yarn is specified and paid for on its count and its evenness, exactly as a weaving yarn is. The evenness figure is a coefficient of variation measured along a length of yarn from one package — which is a measurement of the random part, the part the knit averages as effectively as the weave does.

The complaint is about the correlated part: the difference from package to package, which that measurement is not taking and which no amount of care within a package affects.

There is a neat way to see that the two are genuinely different quantities. Take a knitted fabric showing bands and measure the yarn unravelled from it: the coefficient of variation comes out at the yarn’s usual figure, because the measurement runs along the thread and crosses every feeder’s contribution in turn, averaging exactly what the fabric is failing to average. The instrument and the fabric are looking at the same yarn from perpendicular directions, and only one of them sees the fault.

The weft bar, which is the woven version #

The argument has a smaller counterpart in weaving and it is worth setting beside this one, because the comparison locates precisely what is special about the knit.

A woven weft is also one thread, laid pick by pick from one package. So a woven cloth averages its warp over hundreds of ends and does not average its weft at all: a difference between weft packages shows as a bar across the piece, and the trade calls it exactly that.

The difference is the period. A weaver changes weft packages every few thousand picks, so a weft bar appears once, at the change, as an isolated defect that can be cut out. A knitter’s machine changes package every course, ninety-six times a revolution, so the difference appears as a repeating stripe through the whole roll and cannot be cut out anywhere.

One thread system and a rotation is what makes it periodic, and a woven cloth has one of those two.

Two more places the one-thread fact decides something #

The banding is the visible consequence, and there are two others that follow from exactly the same premise and are usually filed elsewhere.

Twist liveliness has nowhere to go. In a woven cloth a lively yarn is held by its crossings and almost nothing happens. In a knit the loop is free to rotate and the fabric leans — and because every loop in the fabric comes from the same thread with the same twist, the lean is in the same direction everywhere and adds up across the width instead of cancelling.

A fault has no neighbours to hide behind. A thin place bad enough to break stops the machine and drops a stitch, and a dropped stitch runs. In a woven cloth a missing end is a fault the length of the piece and the cloth still hangs together; in a knit a single failure propagates, because the thread that failed was holding the loops on either side of it.

Both are the same structural statement as the banding: a knit has one thread, so everything that is true of the thread is true everywhere at once, while a woven cloth has hundreds and can average, hide and localise.

What was counted, and how #

The band spacing is asserted proportional to the feeder count — not merely rising with it — at twelve decimal places across a range from one feeder to a hundred and forty-four. The claim is about the form of the relation, because the practical conclusion is that halving the feeders halves the band.

The one-feeder case is computed rather than argued. It has to give a band of the fabric’s own course spacing, which is to say no band at all, and it is the control on the whole claim.

And the along-thread separation is computed to check that it is irrelevant. Two courses laid by the same feeder are about a kilometre apart along the yarn, against a staple of a few tens of millimetres, so nothing in the correlation being described can come from the yarn’s own structure. It has to come from the packages.

Where the model stops #

The machine is idealised as a strict rotation and it is. But it is a helix rather than a set of rings: a circular machine lays courses continuously as the cylinder turns, so a course is a spiral and the “band” is a very shallow spiral too. Over a fabric width this is invisible; over a whole garment it means a band drifts, and the drift is the same beat arithmetic that decides what a periodic weft fault looks like in a woven cloth.

Nothing here says how big the difference between packages is. The arithmetic gives the period and the visibility; the amplitude is a yarn and dyeing question and is not in reach.

The eye’s sensitivity is quoted rather than derived, as it was in the woven case, and the range is wide.

And the argument is about weft knitting only. A warp knit has a thread per wale and a beam of hundreds of ends, so it averages packages the way a woven warp does — which is a prediction worth stating: warp-knitted fabrics should not show feeder banding, and they do not.

Where the ladder goes next #

Sideways, into the other consequences of a knit being one thread. A knit has no hole to lose and a run travels because the loop is a single thread, and both are the same structural fact seen through a different question.

And back to the woven case, where the exception this essay is about also exists in a smaller form. A woven weft is also one thread, laid pick by pick from one package, so a weft-way bar is the woven equivalent of a feeder band — and its period is set by the package change rather than by a feeder count, which is why it appears as an isolated bar rather than as a repeating stripe.