Ravel, fray and run

A snag in a woven shirt is a pulled thread. A snag in a knitted stocking is a ladder running from the ankle to the knee. Both fabrics were sound before, both were damaged in one place, and the outcomes are not remotely comparable.

The difference is structural and it can be stated exactly.

What holds a thread in place #

In a weave, every thread is held by the threads crossing it. A warp end passes over some picks and under others; to move, it must lift or depress every pick it is engaged with, against friction, all along its length. Remove a neighbouring end entirely and the rest are unaffected, because none of them was relying on it.

In a knit, every loop is held by exactly one thing: the loop below it, which it passes through. Remove that loop and nothing is holding it at all. It is free, and once free it releases the loop above it in turn.

That is the whole difference. A weave distributes the constraint on every thread across many other threads; a knit concentrates it in one.

The cascade, counted #

The consequence can be put as a number, which is what the figure does.

Break one loop in a wale $k$ courses from the top, and the loops above it are freed one after another: $k$ of them, all the way to the edge. Break one thread in a weave and one thread is freed, regardless of where the break is.

So the damage from a single break is proportional to the distance to the edge in a knit and constant in a weave. That is a difference in kind rather than degree, and it is why a small snag is a catastrophe in one structure and an annoyance in the other.

What the count establishes #

The figures on this page compute something exact, and it is worth saying precisely what.

For a break $k$ courses from the top of a knitted wale, the number of loops with nothing holding them is $k$ — each releases the next, all the way to the edge. For a break anywhere in a woven cloth, the number of threads with nothing holding them is one.

That is a topological statement about the structures and it is exact. What it does not establish is whether a given snag will actually run: that depends on friction, on how tight the loops are and on how much the fabric is handled afterwards, and nothing here computes any of them.

So the claim is that the potential damage differs by a factor that grows with the fabric, not that every knitted snag becomes a ladder. Plenty do not. The point is that in a woven cloth none can.

Why fraying is different #

A woven cloth’s failure at an edge is not a cascade and it is not driven by the same thing.

Fraying happens because at a cut edge the crossing threads run off the end, so the threads parallel to the edge are no longer held along their whole length — only up to where their partners stopped. Friction holds them for a while, and handling works them loose one at a time.

Two things follow. Fraying is a surface phenomenon: it stops when it reaches threads that are still fully engaged, so a frayed edge reaches a depth and then stalls. And it depends on friction rather than on topology, so it varies enormously with yarn and finish — a hairy woollen frays reluctantly and a smooth filament satin frays enthusiastically.

The rate also depends on the weave. Plain weave frays least, because a thread must disengage from a crossing at every intersection to escape. A satin frays most, because its threads are gripped rarely and can slide.

Cut edges, and why knits are handled differently #

The two failure modes lead to two completely different sets of workroom habits, and the habits are worth spelling out because they look arbitrary until the mechanism is clear.

A woven cut edge is unstable immediately and permanently. It frays with handling, and every seam allowance must be finished — overlocked, bound, pinked or turned — or the garment comes apart at the seams over its life. That is a fraying remedy: stop threads sliding out.

A knitted cut edge is stable in a different way. It does not fray, because there are no parallel threads to slide out; it may ladder, which needs no handling at all and can happen months later from a single snag. So knitted seams are made with stitches that both join and secure — an overlock, which trims and encases in one operation — and the encasing is a laddering remedy rather than a fraying one.

The asymmetry runs the other way too. A woven cloth can be cut in any direction and hemmed with a fold; a knitted one cannot easily be hemmed by folding, because the fold has no stability and the cut edge inside it can still ladder. Knitted garments are therefore finished with bands, ribs and bindings far more than woven ones, and the reason is structural rather than stylistic.

The two remedies are different #

Because the mechanisms differ, the fixes do not transfer.

For fraying, anything that prevents the parallel threads from sliding out will do: an overlocked edge, a bound edge, a fused edge, a hem, or a selvedge — which is simply an edge where the weft turns back rather than being cut, so no thread ends there at all. Fray-check liquids work by gluing the threads together, which is exactly the constraint that was lost.

For laddering, none of that helps in the middle of a fabric, because the failure does not start at an edge. What works is changing the structure so that a loop is held by more than one thing: interlock and rib ladder far less than jersey, because their loops are engaged with wales on both faces. Warp knits — tricot, raschel — barely ladder at all, because each wale is formed from its own thread which also travels sideways into its neighbours.

The historical case is stockings. Fully-fashioned silk stockings were plain jersey and laddered constantly; nylon did not fix it; what largely fixed it was moving to knitted structures with more constraint, and to fine gauges where a ladder is narrow enough to be less visible.

Ravelling, which is the third word #

The three words get used interchangeably and mean different things, which is worth sorting out.

Ravelling is a knit coming undone by pulling the free end of its thread — running the knitting backwards. It requires access to an end, and it undoes courses rather than wales. Pull the yarn from the cast-off edge of a jersey and the whole thing comes back as one continuous strand.

Laddering or running is a wale failing after a break, which needs no free end and no pulling.

Fraying is a woven edge losing threads to handling.

A weft knit does all of the first two. A warp knit does neither easily. A woven cloth does the third and neither of the others, since it cannot be pulled undone — a woven cloth has no single thread to pull, which is precisely what makes it two thread systems rather than one.

The connection to integrity #

There is a link here to the check this site is built around, and it is worth drawing carefully because the two things are related without being the same.

Cloth integrity asks whether a structure is topologically one piece. A weft knit passes trivially — it is literally one thread, so nothing can be separated from anything.

And yet the knit is the fabric that fails more easily. Being one connected object is not the same as being robust, because the connectivity in a knit is serial: every loop depends on one other loop, in a chain, and a chain is only as good as its worst link. A weave’s connectivity is redundant: every thread is held by many others, so removing one changes little.

That distinction — connected versus redundantly connected — is the real content of the difference, and it is a familiar one from anywhere else that networks are studied. A structure can be perfectly connected and extremely fragile if all its paths run through single points.

What decides how bad a ladder is #

Three factors, and only one is structural.

Loop length. A long, loose loop slips off its neighbour easily; a short tight one resists. Tightly knitted fabric ladders less, which is the main reason fine-gauge knitwear survives better than loose.

Friction. A hairy, high-twist or textured yarn grips itself and arrests a ladder; a smooth filament does not. This is why silk and early nylon stockings were notorious and why textured nylon was an improvement.

Structure. Interlock, rib, and warp knits ladder far less than plain jersey, for the reason above.

Only the third is a property the matrix-style analysis on this site can reach. The first two are yarn and finish, which is a reminder that the structural account is dominant rather than complete.

Where the two failures meet #

There is one structure where both failure modes are present, and it is the exception that clarifies the rule.

A cut edge of a weft-knitted fabric frays a little — the cut ends of the loops can work free — and ladders a great deal. A woven cloth with very long floats can do something that looks like laddering: pull a float and the thread runs, because it is not gripped along that length. A satin snags in a way that a plain weave cannot, and the snag can travel.

The common factor is free length between constraints, which is the same quantity behind float length in weaving and loop length in knitting. Failure travels along a thread exactly as far as the thread is unconstrained, and no further.

That gives a single sentence covering both structures. A break propagates as far as the structure leaves the thread free, which in a knit is up the whole wale, in a satin is along a float, and in a plain weave is nowhere at all.

Redundancy, counted #

The distinction between connected and redundantly connected is the essay’s sharpest observation and it is left qualitative. It can be counted, and the counting orders all three failure behaviours on one axis.

Ask, of one releasable element, how many independent constraints must be defeated before it comes out.

A woven pick in a metre-and-a-half cloth at twenty-four ends to the centimetre crosses 3,600 ends. In a plain weave every one of those crossings is an interlacing, so 3,600 constraints hold it. In an eight-end satin only one end in eight binds it, so 900.

A knitted loop is held by the loop below it. One.

Three and a half thousand, nine hundred, one. That is the whole of the difference between a cloth that cannot ladder, a cloth that snags, and a cloth that runs — and every one of the three numbers is read straight off the sett and the weave.

It also puts the fraying ordering on the same axis. Plain weave frays least and satin most, in the ratio of their redundancies, and the essay’s separate observation that fraying depends on the interlacing count is the same count divided by the same length.

The free length, in millimetres #

The closing unification — that a break travels as far as the structure leaves the thread free — takes numbers just as easily, and the three come out on a scale nobody would guess from the prose.

At twenty-four ends to the centimetre the thread pitch is 417 micrometres. So the unconstrained run is

One, seven, and fourteen hundred. A satin’s snag can travel three millimetres, which is exactly what a snagged satin looks like — a small pulled loop, not a ladder — and a jersey’s can travel the length of the garment.

And the two are not the same kind of number #

Putting the two counts side by side shows something the single sentence hides, and it is the reason the knit’s figure understates rather than overstates.

A satin’s free run is a single step. Pull a float and the thread travels its length and stops, because the next float along belongs to a different end and is held by its own crossings. Nothing has been released by the first float coming free.

A knit’s is a chain. Freeing one loop frees the one above it, which frees the one above that. The six hundred millimetres above is not a free length at all — it is the length of the chain that happens to be in the garment, and in a longer garment it is longer.

So the two failure modes differ in the same way the two redundancy counts do, and they differ twice over: the knit has one constraint per element rather than a thousand, and defeating that one constraint defeats the next one for free. A structure whose constraints are shared is robust; a structure whose constraints are serial is not merely fragile but self-propagating.

That is why no amount of yarn or gauge turns a jersey into a woven cloth in this respect, and why the only remedy that removes the failure mode rather than slowing it is the structural one. A rib or an interlock gives each loop a second thing to hold on to, which takes the count from one to two — and a chain whose links are doubled is not a chain.

What this account leaves out #

Two limits.

It counts rather than predicts. The figures here count how many loops a break frees, which is a topological fact. Whether a given snag actually initiates a ladder depends on friction and force, and nothing here computes either.

It is about weft knits. Warp knits share the loop and not the failure mode, and almost every generalisation on this page fails for them.

The first of those two is the one that matters and it should be stated as a boundary rather than as an apology. A count of freed loops is an upper bound on what a break can cost and nothing more: it says how much of the fabric is topologically unheld once a particular yarn is cut, and topology is indifferent to whether anything actually moves. What decides whether it does is the same friction this collection has declined to model everywhere else — a run propagates when the force pulling the next loop through exceeds what its crossings hold it with, and both sides of that comparison are outside the geometry.

That boundary is exactly where the trade’s own knowledge begins, which is worth noticing rather than regretting. Everything a knitter does about laddering — a tighter loop, a hairier yarn, a tuck stitch every few courses, a resin finish — acts on the friction side and none of it changes the count. So the count and the practice are complementary rather than rival accounts, and the count’s job is to say which structures have anything to be prevented in the first place.

The selvedge, and why it is not a hem #

One structural feature exists purely to solve the fraying problem, and it is worth understanding because it is not what most people assume.

A selvedge is the edge of the cloth as it comes off the loom, where the weft turns back rather than being cut. No thread ends there: the weft is continuous, going out and coming back, so the constraint that fraying needs to remove is never absent.

That is why a selvedge does not fray and needs no finishing at all, and it is a structural property rather than an applied one. Nothing was added — the edge simply never lost anything.

Modern shuttleless looms cut the weft at each pick and have to manufacture a selvedge afterwards, by tucking the ends back in or by binding them with a leno thread. Those work, and they are visibly different from a true shuttle selvedge, which is why selvedge denim is identifiable and is sold on the strength of it.

The knitted equivalent does not exist, because a knitted edge’s problem is not threads escaping sideways. A cast-off edge is a chain of loops each secured through its neighbour, which is a construction rather than an absence — and it is why a cast-off has to be worked and a selvedge does not.

What a designer can do about it #

Three levers, in decreasing order of how well they work.

Change the structure. Interlock, rib and warp knits ladder far less than jersey. This is the only remedy that removes the failure mode rather than making it less likely, and it is the reason most commercial knitwear is not plain jersey.

Change the yarn. Textured, high-twist or hairy yarns grip themselves and arrest a run; smooth filament does not. Textured nylon was a real improvement over flat, and it is why sheer hosiery moved to it.

Change the gauge. Tight knitting ladders less, because a short loop is harder to pull off its neighbour. It also costs yarn and stiffens the fabric.

For woven cloth the corresponding levers are the same in spirit. Fraying is reduced by a firmer weave, by a hairier yarn, or by a finish that binds the surface — structure, material, and treatment, in the order this site usually finds them.

The third failure mode #

Two structures were compared here and there is a third, made in enormous quantity, whose failure mode is neither.

A warp knit gives every wale its own thread running down the fabric, so the thread that made a loop in one wale made its next loop in a different one. Break it and the loops it made are scattered across several wales rather than stacked in one — and each of them is also held by the underlaps of neighbouring threads passing over it. The failure spreads sideways and dies out instead of climbing.

That is why tricot does not ladder, and why it is used for anything that must not fail conspicuously. It is not a stronger fabric than a weft knit; it has a better failure mode, for a reason that is entirely structural. Warp knitting works through the connectivity, including the condition that decides whether such a fabric holds together at all.

Where the ladder goes next #

The structure this all follows from is the loop, and the other consequence of its asymmetry is why stockinette curls.

The woven side of the comparison is plain, twill and satin, where fraying varies with the same interlacing count that decides everything else.

What the pictures here cannot show. The figures count freed threads, which is a statement about the structure. A real ladder is a dynamic event driven by friction and tension, and no static diagram shows why one snag runs and another does not.