Textile Structure
how cloth is put together
Cloth doing a job

A run cannot cross a bed

A dropped stitch unroves because its neighbour above can pull it out along a path that costs almost nothing. In a rib the neighbour above is on the other bed, and the path goes through the gap — so a run in a two-bed fabric has to pay for a climb before it can take a single loop.
14 min read 6 figures Does it hang togetherA mechanism, not a materialStructure before fibre

Worth reading first: A run is a race between two energies · Ravel, fray and run · A rib climbs a gap.

Drop a stitch in a jersey and it runs. The loop above it, no longer held, is pulled through by the tension in its own course, and it takes the loop above that with it, and the ladder walks up the fabric until something stops it.

Drop a stitch in a rib and it does not — or not far, and not easily. That is one of the oldest pieces of practical knowledge in the trade and it has never been given a mechanism here beyond “the structure is different”.

The structure is different in a way this ladder can now say precisely.

A rib crosses a gap where a jersey crosses a diameter. A one-by-one rib in section across 5 wales, drawn at a bed gap of 3 yarn diameters — 0.501 mm — because the relaxed gap of a rib is a measurement this collection does not hold and every figure of one says what it was drawn at. Alternate wales sit on opposite beds, so every sinker loop between them travels the whole gap. In a jersey the same yarn climbs one diameter, 0.167 mm. That single difference takes the contact force from 38.30 mN at 11.7° out of the fabric to 72.51 mN at 16.2°, and the through-thickness part from 7.81 mN to 20.17 mN.
Fig. 1 Why a run has somewhere to go in one fabric and not the other. In a rib, the wale above a dropped stitch sits on the opposite bed, so unroving it means dragging yarn through the whole gap between the beds rather than along the fabric.

What a run is, mechanically

A run is a race between two energies. Unroving a loop releases the bending energy stored in it; dragging the yarn through the interlacing above costs friction. If the release exceeds the cost the ladder propagates, and if it does not the fabric holds.

This collection computes both sides. The hold on a dropped stitch runs from 35.1 millinewtons for a tight jersey at a 2.8 mm loop to 14.7 for a loose one at 4.5 — so a tighter fabric holds a dropped stitch harder, which is the only lever a knitter has on a single-bed fabric.

The lever is not a big one: a factor of 2.4 across the whole range one machine can knit, and the direction is the one that also makes the fabric harsher and less extensible.

What a second bed adds

In a jersey, the loop above a dropped stitch is in the same wale, on the same bed, in the same plane. The yarn being pulled through travels along the fabric.

In a one-by-one rib, the wale above is on the same bed — but the loops on either side of the ladder are on the other bed, and the sinker loops joining them cross the gap. Every loop the run wants to take is joined to its neighbours by yarn that has to be dragged through the whole bed separation.

So the run’s path is not along the fabric any more. It is through it.

What that costs

The crossing yarn’s climb is the bed gap, and a climb has to be paid for twice over.

In length. The straight line a crossing spans is longer than a jersey’s — at a three-diameter gap, 0.993 millimetres against 0.916, out of the same 1.750 millimetres of yarn — so more of the yarn’s length is committed to going somewhere and less of it is spare to be pulled.

In direction. The contact force at a crossing is turned much further out of the fabric than a jersey’s: nearly a third of it acts through the thickness at a three-diameter gap, against a fifth in a jersey. A force acting through the fabric is a force the run is not helped by, because the run is trying to move yarn along it.

Both push the same way. A rib’s crossings hold their yarn against a pull along the fabric better than a jersey’s interlacings do, and they do it by geometry rather than by friction.

A rib is quietest at a gap of two diameters. The through-thickness force of a one-by-one rib against the bed gap it is knitted at, in units of the yarn's own diameter. It does not rise from the bottom, and the dip is geometry rather than noise: a crossing is shared between the two half periods either side of its sinker loop, and each of those also carries the interlacing's own diameter — one climbing with it and one against. At a gap of two diameters the second half period climbs nothing at all, and the fabric is at its quietest through its own thickness. Above that both halves climb the same way and everything rises together, which is the regime a real rib is knitted in: 14.8 mN at 5 diameters against 7.0 mN at two.
Fig. 2 The quantity that grows with the gap. A wider bed setting turns more of the contact force through the fabric, where a run pulling along the fabric is not helped by it — so the same setting that makes a rib thicker makes it harder to ladder.

And the topology does the rest

The energetic argument is the smaller half. The larger one is that in a two-bed fabric there is often nowhere for the ladder to go at all.

A run walks up a wale. In a jersey every wale runs the full height of the fabric on one bed, so a ladder started anywhere can reach the top. In a one-by-one rib the wales alternate beds, and a wale on the front bed is flanked by wales on the back — so a ladder walking up a front wale is walking through a fabric whose adjacent columns are held from the other side.

In interlock it is worse for the ladder and better for the fabric: the two interknitted rib fabrics each hold the other, and a loop dropped from one of them is still surrounded by the other’s loops.

That is why interlock is used where stability matters and why a rib does not ladder in practice. The mechanism is that a wale is not an independent column any more.

The force at an interlacing, which no longer lies in the fabric. A crossing of a relaxed jersey in section on the left, with the thickness expanded 3×, and on the right the contact force drawn at the angle the solve gives it — which is a true angle, unlike anything in the section beside it. The head of one course and the feet of the next lie one yarn diameter apart through the fabric, 0.167 mm, so the interlacing is not a point in a plane and the force at it is not in one either. It comes out at 38.30 mN a stitch, turned 11.75° out of the fabric: 37.50 mN along the wales, which is what friction has to hold, and 7.81 mN through the thickness, which is what holds the two faces apart. Divided by the area a stitch occupies the second is 15.1 kPa, or 113 mmHg — a pressure, and the quantity a compression measurement reports.
Fig. 3 Where the sign of the dependence comes from. A loop is held by the loop below it on the same bed and by nothing on the other, so a run climbs a wale and has nowhere to go sideways — the section is the whole of the argument.

Which is a connectivity statement

There is a way of putting this that connects it to the oldest argument in the collection, and the connection is worth drawing.

A knitted structure hangs together if it cannot be cut in two along a line no yarn crosses. That test is about the fabric surviving a cut. A run is the same question asked about a wale: can a column of loops be removed from the fabric along a path that costs nothing?

In a jersey it can, and the path is the wale itself. In a rib it cannot, because the wale’s neighbours are threaded through it from the other bed and removing the column means dragging yarn across the gap at every course.

A fabric that does not ladder is a fabric whose wales are not separable. That is the same shape of argument as the one that decides whether a double jersey is one fabric, asked one dimension down.

Where a course of yarn sits through the thickness. The through-thickness position of one course of yarn, half period by half period, for 3 structures at a bed gap of 3 yarn diameters — 0.501 mm — on a 20 tex yarn whose diameter is 0.167 mm. Single jersey never leaves the bed it started on: it oscillates by 0.167 mm and comes straight back, because a loop's feet were drawn through the head below and are on the far side of it, and that is the whole of its third dimension. A one-by-one rib crosses between the beds 4 times a course, travelling 0.501 mm through the thickness. A two-by-two rib crosses between the beds twice a course, travelling 0.668 mm through the thickness. The horizontal is a count of half periods rather than a length, because the repeats are not the same width and the comparison is not about their widths.
Fig. 4 The path a run would have to take. A jersey’s course sits in one plane and oscillates by a diameter; a rib’s crosses the whole gap at every sinker loop, and a ladder walking up a wale has to unpick a crossing at every course.

What the single-bed lever is worth, for comparison

It is worth putting the structural change beside the dimensional one, because the contrast is the argument.

On a jersey the only lever is the loop length, and this collection computes the hold on a dropped stitch across the range: 35.1 millinewtons at a 2.8 mm loop down to 14.7 at 4.5. A factor of 2.4, bought at the cost of a fabric that is harsher, less extensible and stiffer through its thickness by a factor of twenty.

On a two-bed fabric the lever is which structure is knitted, and the result is not a factor at all — it is a fabric that ladders and one that does not. A cuff in one-by-one rib does not need to be knitted tight to hold a dropped stitch, which is why cuffs are ribbed rather than merely dense.

What the crossing share predicts

If the resistance comes from crossings, it ought to scale with how many of them there are — and the crossing share is exactly that quantity, counted from each structure’s own grid.

A one-by-one rib is at one: every sinker loop crosses. A two-by-two is at a half. A half-milano is at two thirds; a fabric with three front wales to every back wale is at four sevenths.

So the ordering this account predicts is: a one-by-one rib holds best, a two-by-two next, a three-by-one after that, and single jersey not at all. That is the trade’s own ordering, and a knitter asked which rib is most run-resistant would give the same list.

Getting a known ordering right is not a strong test. It is the minimum a mechanism has to pass before its quantitative claims are worth anything.

Where a course of yarn sits through the thickness. The through-thickness position of one course of yarn, half period by half period, for 3 structures at a bed gap of 3 yarn diameters — 0.501 mm — on a 20 tex yarn whose diameter is 0.167 mm. Single jersey never leaves the bed it started on: it oscillates by 0.167 mm and comes straight back, because a loop's feet were drawn through the head below and are on the far side of it, and that is the whole of its third dimension. A one-by-one rib crosses between the beds 4 times a course, travelling 0.501 mm through the thickness. A tubular fabric never leaves the bed it started on: it oscillates by 0.167 mm and comes straight back, because a loop's feet were drawn through the head below and are on the far side of it, and that is the whole of its third dimension. The horizontal is a count of half periods rather than a length, because the repeats are not the same width and the comparison is not about their widths.
Fig. 5 Three structures’ traverses, which is where the crossing count is read off. A run travels along a wale and a wale belongs to one bed, so a structure whose yarn crosses often has more wales for a run to fail to enter and no more ways for it to cross.

What this account does not compute

The honest position is that the ordering is predicted and the magnitude is not.

Working out how much harder a rib’s crossing is to unrove than a jersey’s interlacing needs the yarn to be dragged along a path, with friction accumulating over a wrap angle, in a geometry where the two threads are not parallel. This collection has a capstan argument for a woven thread being pulled from a cloth and nothing equivalent for a knitted loop crossing a gap.

What is available is the two ingredients above — a longer chord and a force turned further out of the fabric — and their directions. Both make the run harder. Neither is a number.

Why the practical lever is different on the two fabrics

On a single-bed fabric the only thing a knitter can do about laddering is to knit tighter, and the gain is a factor of 2.4 across the whole practical range.

On a two-bed fabric the lever is the structure, and it is not a factor of 2.4 — it is the difference between a fabric that ladders and one that does not. That is why the practical advice has always been structural rather than dimensional: put a rib at the cuff, an interlock in the body, a garter border at the hem.

The general shape is one this collection meets repeatedly. A structural change usually beats a dimensional one, because a dimension moves a quantity by a factor and a structure changes which quantity is being asked about.

What a float does, which is the opposite

There is a case that runs the other way and it belongs here as a caution.

A float — a length of yarn passing needles that missed — is the least supported piece of yarn in any weft-knitted fabric, and a fabric with long floats is more vulnerable to snagging rather than less. A float does not cross beds and does not climb, so nothing in this account distinguishes it from the fabric around it.

So the same second bed that makes a rib run-resistant makes a rib-float fabric no more resistant along its floats than a jersey would be. The crossing share for that structure is two thirds rather than one, and the third that is missing is where the floats are.

What would test it

Two experiments, and the first is a swatch and a pin.

Drop a stitch in each of four structures — jersey, three-by-one rib, two-by-two rib, one-by-one rib — knitted from one yarn at one loop length, and count how many courses each ladder walks under a stated tension. The prediction is a monotone ordering in the crossing share.

And do it again with the bed gap changed. The account here says a wider gap holds harder, because the crossing is longer and its force is turned further out of the fabric. That is a prediction about a machine setting rather than about a structure, and it is the sharper of the two because nothing else in the fabric changes.

Neither has been run here.

The other half of the ladder’s race

The energetic side of a run is a race between what unroving releases and what it costs, and only the cost has been discussed above. The release is worth a paragraph because a crossing changes it too.

Unroving a loop releases its stored bending energy, and a crossing half period holds less of it than an ordinary one — 23,086 nanojoules a stitch in a one-by-one rib against a jersey’s 24,395, because a longer climb spends slack that would otherwise be spent on curvature.

So a crossing lowers the release as well as raising the cost, and both push the same way. That is a small effect against the topological one and it is worth having because it is the piece the energy account supplies directly, without any assumption about friction.

Why a garter border works and a rib border works better

The practical remedies for a curling, laddering jersey edge are the same two remedies, and this account separates them.

A garter border alternates the facing of successive courses, which balances the curl. It does nothing whatever about laddering: every wale still runs the full height of the fabric on one bed, so a dropped stitch still has a free path. Garter is a cure for one problem and not the other.

A ribbed band balances the curl and interleaves the wales, so it does both. That is why almost every knitted garment begins at a rib rather than at a garter border, even though garter is easier to work by hand.

Two remedies, two mechanisms, and the fact that one of them happens to fix both is the reason it has become the convention. Which knitted fabrics lie flat is the curl half of that; this rung is the ladder half.

What a dropped stitch has to be dropped from

There is a step before the run that the account above assumes and that is worth making explicit, because it is where a real fabric usually fails.

A stitch does not drop on its own. It is dropped by a needle failing to hold it, by a snag pulling it clear, by an abrasion breaking the yarn, or by a cut edge being left unsecured. So a fabric’s practical run resistance is the product of two things: how likely a loop is to be freed, and how far the ladder goes once one is.

This rung is entirely about the second. The first belongs with abrasion and with a fabric’s floats, and a fabric with long floats is more likely to be snagged even if its structure is one a ladder cannot walk.

So a rib with long floats is a fabric that is hard to ladder and easy to start a ladder in, which is a combination nobody would design deliberately and which the crossing census puts a number on.

What is genuinely new here

Two things, neither of them a number.

A mechanism for run resistance in two-bed fabrics, in terms this collection already computes: a crossing’s longer chord and its more steeply turned contact force, both of which make the yarn harder to drag along the fabric.

And the ordering, predicted from a count. The crossing share is read off a structure’s grid in a tenth of a second and it puts the named fabrics in the order the trade puts them in — including the composites nobody has an opinion about.

What the pictures cannot show

Neither figure shows a run. A ladder is a sequence of events, and both drawings are of a fabric at rest.

What they show is the path a run would have to take, which is the part of the argument that is geometric. The part that is not — how much friction accumulates as a thread is dragged round a crossing it is being pulled out of — is not drawn because it is not computed.

What is left as a shortfall

Three things, and the first is the one that would make this rung quantitative.

No capstan for a knitted crossing. The friction a thread accumulates as it is dragged round something is a wrap angle and a coefficient, and this collection has that arithmetic for a thread being pulled out of a woven cloth. A knitted crossing is two threads at a shallow angle rather than a right angle, and nothing here has been written for it.

No account of what happens at the top of the ladder. A run in practice stops somewhere, and where it stops is a fabric-scale question about tension redistribution rather than a per-loop one.

And nothing about a cut edge. Every practical run starts at an edge or a hole, and this collection’s account of how far a cut edge frays is a woven one.

A knitted loop is a plane curve in a plane that is not the fabric's. A relaxed 20 tex jersey at a 3.5 mm loop, seen from the end of a course. Each course is a straight line because it is one: a half period leaves and arrives along the course direction, so the plane it bends in contains that direction, and a plane curve seen along a line in its own plane projects to a segment. The upper panel expands the thickness 3× so the arrangement can be seen and no angle may be measured off it; the lower panel is the same fabric at one scale, where the tilt is what it really is. The angle is 11.75°: a climb of one yarn diameter, 0.167 mm, against a drop of a course spacing and a diameter, 0.803 mm. Successive courses overlap by exactly one diameter, which is the interlacing, and the fabric is therefore 0.334 mm thick — two yarn diameters, with nothing fitted.
Fig. 6 The jersey a run walks up. Every course lies in one plane tilted a dozen degrees out of the fabric, and every wale runs the full height of the piece on one bed — so a ladder started anywhere has a clear path to the top.

Where the two beds’ resistances differ from one another

The account so far treats every crossing alike, and the two-bed family does not.

A one-by-one rib interleaves its wales at every position, so a ladder in it is surrounded on both sides at every course. Interlock does the same and adds a second fabric occupying the same space. A two-by-two rib interleaves in pairs, so a ladder walking up the middle of a pair has a neighbour of its own bed on one side.

That last case is the interesting one, because it says a two-by-two rib should ladder in a way a one-by-one does not: not far, and only within a pair. Whether it does is a swatch-and-pin question, and a positive answer would separate the topological half of this account from the energetic half — the crossing share puts a two-by-two at a half either way, and only the interleaving pattern distinguishes where the ladder can go.

Where the ladder goes next

A fabric held together by its crossings is a fabric whose crossings are load-bearing in more ways than one, and the same crossings decide how much the fabric weighs per unit of its own bulk: how dense a knitted fabric is.

Where this goes next

What a run has to overcome. The friction holding one loop in the loop below it, against how tightly the fabric is knitted. It is the coefficient of friction times the contact force times the two interlacings a stitch makes, and it runs from 14.7 to 35.1 millinewtons across the knittable range — a factor of 2.4 for a factor of under two in tightness factor, because the contact force and the tightness move together. That is the arithmetic behind a rule every knitter has: a slack fabric runs and a tight one does not, and tightening it is the only lever that works. The figures are upper bounds, since a set yarn presses less. A run is a race between two energies A dropped stitch travels when a loop can be pulled out of the loop below it, and there are two candidate drivers: the energy the loop releases by unravelling, and the load the garment is under. One of them turns out to be negligible, and knowing which changes what a knitter can do about it. One break, two outcomes. The same single break in a knit and in a weave. In the knit nothing holds the loop above the break, so the failure climbs the wale; in the weave every other thread is still held by the threads crossing it, and one thread comes loose. Ravel, fray and run Cut a woven cloth and one thread comes loose. Break one loop in a knit and every loop above it follows. The two structures fail in opposite ways, and the reason is topology rather than strength. A rib crosses a gap where a jersey crosses a diameter. A one-by-one rib in section across 5 wales, drawn at a bed gap of 3 yarn diameters — 0.501 mm — because the relaxed gap of a rib is a measurement this collection does not hold and every figure of one says what it was drawn at. Alternate wales sit on opposite beds, so every sinker loop between them travels the whole gap. In a jersey the same yarn climbs one diameter, 0.167 mm. That single difference takes the contact force from 38.30 mN at 11.7° out of the fabric to 72.51 mN at 16.2°, and the through-thickness part from 7.81 mN to 20.17 mN. A rib climbs a gap A jersey's yarn crosses one diameter between interlacings because that is what a crossing of two threads is. A rib's crosses the whole distance between the two beds. Nothing else in the model changes, and that one length is the whole mechanical difference between the fabrics.

What links here

Computed from the collection rather than written here: the essays that point at this one.

Shares its objects with

Essays naming at least two of the same things, that neither author linked.

Named objects

A flat tag is an object no other essay names yet.

ConnectivityContact forceFrictionInterlockLoopNeedle bedRibRunTwo-bed