Rib and interlock

The cuff of a jumper stretches enormously and springs back. So does the neck of a T-shirt, the top of a sock, and the waistband of anything knitted. None of them has elastic in it, and the yarn in them is the same yarn as in the body of the garment, where it does nothing of the kind.

The difference is a rib, and a rib is a very simple change: alternate wales are drawn to the back instead of the front.

That is all. And what falls out of it is a fabric with roughly twice the widthwise extension of a plain knit, which does not curl at its edges, and which is thicker and warmer for the same amount of yarn.

The face alternation #

The quantity that decides everything is the same one stockinette’s curl turned on, seen along the other axis.

A knitted loop is not symmetrical front to back: its legs lie on one face and its head on the other. In a plain knit every loop is worked the same way, so every asymmetry points the same way. In a rib, alternate wales are worked the other way — a knit stitch then a purl stitch, repeating.

Count the face changes across the wales and the pattern is immediate. A plain fabric has none. A one-by-one rib has one at every wale boundary. A two-by-two rib has one at every second boundary.

Each face change is a place where the fabric has to turn over, and turning over costs plan-view width. That is the whole mechanism.

The extension is a cosine #

Make the geometry explicit, because the number that comes out is checkable and the model it comes from is worth naming.

Treat the relaxed rib as a section folded through an angle: the face wales lie in one plane, the back wales in another, and the fold angle between them is $\alpha$. The plan-view width of a wale is then its true width times $\cos\alpha$, so the whole fabric’s relaxed width is

$$w_{\text{relaxed}} = w_{\text{flat}} \cos\alpha$$

and pulling it flat gives an extension of $\sec\alpha - 1$.

At a fold of sixty-two degrees — which is roughly where a well-relaxed one-by-one rib in a soft yarn sits — that is about 113 per cent. The fabric can be pulled to a little over twice its relaxed width, and every bit of that is section unfolding.

The model is deliberately crude and it is worth saying so. It has one angle, a rigid fold, and no account of the loops changing shape as the fabric opens; a real rib does both, and the loops flatten as the fold opens. What the model gets right is the form of the answer — that the extension is a secant of a fold angle, so it rises very steeply as the fold approaches a right angle — and the order of magnitude. What it does not get right is any particular fabric’s number.

Which is the second thing worth taking from it: rib is a mechanism, not a material, in exactly the sense that the bias is. The extension is a shape change, it is recoverable because shapes do not yield, and it has a hard limit where the shape runs out — the fabric pulled flat cannot be pulled further without stretching yarn, and past that point it goes suddenly stiff.

Anyone who has pulled a cuff too far has felt exactly that transition, and it is the same transition as the locking angle in a woven cloth: a kinematic mechanism running out of travel.

Why a rib does not curl #

The curl argument transfers directly and gives the answer in one line.

Stockinette curls because every course’s asymmetry points the same way and they add up along the edges. A garter fabric does not curl because alternate courses are worked oppositely and the asymmetries cancel.

A rib does the same thing across the wales rather than down the courses. Alternate wales point opposite ways, so at a side edge the asymmetries cancel and the fabric lies flat.

The asymmetry is worth stating carefully. A one-by-one rib does not curl at the side edges, because the wales alternate. It still curls at the top and bottom edges, because the courses do not — which is why a ribbed cuff has a tidy vertical edge and a rolled cast-on edge unless something else is done about it.

That prediction is a genuine one: the structure says the two edges should behave differently, and they do.

Two-by-two, and what the ratio buys #

A two-by-two rib alternates in pairs. It has half as many face changes as a one-by-one, so half as many folds, so less extension — and correspondingly it is flatter, less bulky, and more stable.

The trade-off is monotone and the numbers are the point rather than the direction. Going from one-by-one to two-by-two roughly halves the extension available; going to four-by-four halves it again. A designer choosing a rib for a cuff wants the most extension and takes one-by-one; a designer choosing it for a sweater body wants texture without a fabric that will not hold its shape and takes two-by-two or wider.

There is a second thing the ratio buys, which is coverage. A one-by-one rib in its relaxed state is nearly twice as thick as the plain knit it is made from, because two layers of wale are stacked. That is why ribbed cuffs are warm out of proportion to the yarn in them.

Interlock, and what it adds #

Interlock is two ribs, knitted together so that the back wales of one lie in the front wales of the other. It requires a machine with two needle beds arranged to interlock rather than to alternate, and it makes a quite different fabric.

Three properties, all of which follow from the construction rather than from the yarn.

Two identical faces. Each side of an interlock shows only face loops, because the other fabric’s purl loops are hidden inside. That is why interlock is used for anything reversible, and why it is the standard fabric for a good T-shirt where single jersey would show its wrong side at a hem.

No curl in either direction. The two fabrics’ curling tendencies oppose each other exactly, so an interlock edge lies flat whichever way it is cut. Single jersey curls at every edge; rib curls at two; interlock at none.

Much less extension. The interlocking is what removes it: the two fabrics cannot fold independently, so the concertina mechanism is largely locked out. An interlock stretches perhaps a third as much as a rib in the same yarn, and it is dimensionally stable in a way rib is not.

Which is the general trade in knitted structure. Extension comes from a mechanism, and every mechanism can be taken away by connecting something to something.

The machine the alternation needs #

A rib cannot be made on a single bed of needles, and the reason is worth one paragraph because it explains why rib is a machine-age fabric in industry and an ancient one by hand.

A loop drawn to the front and a loop drawn to the back are made by needles pointing opposite ways. A machine with one needle bed can only draw loops one way, so it makes plain knitting and nothing else. A rib needs a second bed, set at an angle to the first, with its needles interleaved between the first bed’s — and every rib machine, from a hand flat-bed to an industrial circular rib machine, is that arrangement.

The needle spacing is where rib and interlock diverge. In a rib machine the two beds’ needles sit in the gaps between each other, so a needle on one bed is opposite a gap on the other; that is what allows the two sets of wales to fold past one another. In an interlock machine the needles are opposite each other and work alternately, so two complete rib fabrics are made at once in the same space, each using half the needles of each bed.

By hand it is trivial: knit and purl are the two directions, and alternating them is what every ribbed cuff in every hand-knitting pattern is. The hand knitter’s needle can be entered from either side, which is a second needle bed at no cost. That is why rib is prehistoric as a handcraft and nineteenth-century as an industry.

Cardigan, and the alternations that are not ribs #

Alternating the face direction across the wales gives a rib. Alternating it in more complicated patterns gives a family of fabrics that share the mechanism and use it differently.

Half-cardigan knits one bed normally and tucks on the other, so that some loops are held for two courses instead of one. The held loops make the fabric bulkier and less extensible in one direction than the other. Full cardigan, or fisherman’s rib, tucks on both beds alternately and produces a very thick, very soft fabric with the wales pushed far apart.

Both are ribs by the face-alternation count and neither behaves like a one-by-one rib, because tucking adds a second mechanism: a held loop is a loop with extra yarn in it, and that yarn is available as extension quite separately from the fold.

The general point is that the face-alternation count is necessary and not sufficient. It says how much folding is available. It says nothing about tucking, about float stitches, or about any of the other ways a knitting machine can put slack into a fabric — and a full description of a knitted structure needs all of them.

The rib that grows #

Recovery is where the model in this essay stops and the fibre begins, and the failure is common enough to be worth naming.

The geometry says a rib pulled wide will spring back, because the fold is a shape and shapes do not yield. That is true of the structure. It is not true of the yarn, and a rib in a fibre with poor elastic recovery — cotton, linen, viscose — comes back a little short of where it started every time it is stretched. Repeat that a few hundred times and the cuff no longer fits the wrist.

Wool recovers well, which is why a wool rib holds its shape for years and a cotton one does not. Synthetic elastane is added to cotton ribs for exactly this reason: not to provide the extension, which the structure already has in abundance, but to provide the return.

That is a useful separation to hold on to. The structure supplies the extension; the fibre supplies the recovery. Confusing the two is the reason people are surprised that a cotton rib and a wool rib, identical on the machine, behave completely differently after a month.

The yarn a rib costs is one plus the extension it gives #

The essay ends by noting that a rib’s extension and its thickness are the same figure seen twice. There is a third reading of it, and it is the one a costing sheet wants.

Within the rigid-fold model the relaxed width is the flat width times cos α, so the wales per unit of relaxed width are the flat fabric’s times sec α — and the yarn consumed per unit of relaxed area rises in exactly the same proportion. Since the extension available is sec α − 1,

yarn per unit relaxed area ÷ a plain knit’s = 1 + (extension available).

A rib that stretches by 113 per cent costs 2.13 times the yarn per unit of relaxed width, and the two numbers are not merely correlated: they are the same number, offset by one.

That identity is worth having because it prices a decision that is usually made on handle.

Going from a one-by-one rib to a two-by-two saves a quarter of the yarn and half the extension. For a cuff, where the extension is the whole point, that is a bad trade; for a sweater body worked in rib for its texture, where the extension is incidental, it is a good one. The identity says the exchange rate exactly, and it says it without any measurement of a fabric.

Two consequences follow that the extension figure alone does not give.

A rib cannot be made cheaper without being made less stretchy, within the fold mechanism. Every route to a narrower relaxed fabric is a route to a deeper fold, and a deeper fold is more yarn in the same relaxed width. A designer wanting a cuff that stretches and costs a plain knit’s yarn is asking for a mechanism a rib does not have — which is what elastane is for, and why it is added: it supplies extension without a fold, so it breaks the identity.

And the identity is a check on a costing. A knitted goods costing that shows a one-by-one rib trim at less than twice the body fabric’s yarn per unit area has either measured the rib stretched or has mis-stated its structure. That is a cheap arithmetic check on a document nobody usually checks, and it needs no fabric.

The caution is the model’s own. The fold is treated as rigid, the loops do not change shape as it opens, and a real rib’s loops flatten — so the true relation carries a correction in the direction of less yarn than the identity says. What survives the correction is the coupling: the yarn and the extension are one decision, and a rib cannot be given one without the other.

What the model does not have #

Four things, and the first is the one that limits every number above.

No loop mechanics. The fold angle is an input, not an output. What decides it in a real fabric is the balance between the yarn’s bending stiffness, the tightness of the knitting, and how much the fabric has relaxed — and none of that is in the model. The extension formula converts a fold to a width and stops.

No yarn. Two ribs in the same structure and different yarns behave very differently: a wool rib recovers, a cotton one grows. Recovery is a fibre property and nothing here touches it.

No loop distortion. The model folds a section rigidly. A real rib’s loops change shape as it opens, which means the extension is larger than a rigid fold would allow and the force needed is not constant.

And the sections drawn here are schematic. The loops in the figures are drawn as smooth arches at a uniform size, which is a diagram of the topology rather than a picture of a fabric. Real loops are irregular, the fabric is compressed, and the fold is not a crease but a gradual turn.

The stretched rib is a plain knit #

One last observation, because it makes the mechanism unmistakable.

Take a one-by-one rib and pull it as wide as it will go. What is on the face is the face wales, spread out, with the back wales lying flat between them — and every loop visible is a face loop, exactly as in a plain knit. The fully extended rib has the same plan-view structure as the plain knit it was made from, at the same wale spacing.

That is not a coincidence and it is not an approximation. The rib is the plain knit, folded. The folding is the only difference, and pulling the fold out returns the original.

Which explains something that otherwise looks like machine trivia: a one-by-one rib and a plain knit made on the same gauge with the same yarn have the same number of loops per unit area. The rib has more wales per centimetre in its relaxed state, and it has them because they are stacked in two planes rather than one. The yarn consumption per unit of relaxed fabric is roughly doubled, which is why a ribbed cuff costs about twice what its area suggests — and why the calculation matters commercially even though it is entirely geometric.

It also explains why the extension figure and the thickness figure are the same figure seen twice. A rib is twice as thick and twice as extensible as a plain knit for the same reason: half its wales are somewhere else.

Where the ladder goes next #

The next rung asks the question this essay has been circling: why a knit recovers and a woven does not, which puts the four extension mechanisms in this site side by side and computes what each of them is worth.

The rungs below are the curl, which is this argument along the other axis, and the loop itself. The nearest thing in another field is the bias, where a woven cloth gets its extension from a mechanism as well — and gets rather more of it.