Textile Structure
how cloth is put together
Cloth doing a job

A sewing thread is a different animal

It is folded, balanced, lubricated and finished, and every one of those is an answer to a requirement no weaving yarn has. The lubricant is the interesting one: it makes the thread sewable by lowering the friction that was holding its own fibres together.
14 min read 6 figures A mechanism, not a materialMeasured, not claimed

Worth reading first: What holds a thread in a seam · Folding is untwisting · What grips the end of a fibre.

This collection has priced two things about a seam. What holds a thread in one is a capstan grip counted crossing by crossing across the allowance, and the stitch itself weakens the cloth by removing threads at every puncture. Both take the sewing thread as given.

It should not be taken as given. A sewing thread is the most heavily specified yarn in ordinary use, it is made in a way no weaving yarn is made, and every one of its peculiarities is an answer to a requirement that only sewing imposes.

Folding, and what it takes out of the singles. Two 20 tex singles spun at 800 turns per metre and folded the other way at 460 — a ratio of 0.575, which is the trade's own and is a measurement rather than a derivation. A single held at its ends and wound round its neighbour turns about its own axis once for every turn of the fold, so it is left with 340 turns per metre of its own: its surface fibres lie at 10.1° to its axis rather than the 22.8° they were spun at. Folding untwists. The short strokes are drawn at that residual angle; the two long curves are centre lines and are not the yarn — each strand is itself a bundle of 118 fibres, and the residual angle is what holds them.
Fig. 1 A three-fold thread at the middle of its balance band. Three singles rather than two, folded at 0.575 of the singles’ twist, leaving each single at 340 turns a metre and a 10° surface angle. Every number here is a choice and each one answers a different requirement: three for roundness, folded for balance, and folded to that ratio because a thread that snarls stops a machine.

The claim

A sewing thread is folded, balanced, lubricated and finished, and each is an answer to a requirement no weaving yarn has — with the lubricant costing strength by an amount this collection can compute.

  • It passes through a needle eye and a cloth dozens of times per stitch that stays in the seam, so abrasion, not tensile strength, is what it is designed against.
  • It must be balanced, because a lively thread snarls at the needle and stops the machine, and a stopped machine is the dominant cost in a sewing room.
  • It is lubricated to survive the passage — and lubrication lowers the friction between its own fibres, which lengthens the critical length and lowers what the thread realises. Halving the friction costs about fifteen per cent of the thread’s strength.

The requirement that is not tensile

A seam’s strength is quoted as a force per unit length, and the natural assumption is that the thread has to be strong. It does, and that is not the demanding part.

Count the passages. In a lockstitch the needle thread is drawn down through the cloth, round the bobbin case, and back up, for every stitch — and the same length of thread makes that journey many times before it is finally laid into a stitch, because the take-up pulls thread back and forth as the stitch is formed. The usually quoted figure is that a given point on the thread passes through the needle eye between thirty and eighty times before it comes to rest.

At three to five thousand stitches a minute, that is a passage every few milliseconds, each one dragging the thread over a metal edge under tension and through a hole in cloth.

So the design criterion is abrasion, and abrasion is a surface property. That single fact reorganises everything about how the thread is made, because the surface of a spun yarn is the place where the pressure holding the fibres has fallen to zero and the fibres are least well held.

Where a 30 tex yarn breaks, against how much was clamped. A tensile test clamps a length of yarn and pulls until the thinnest section between the clamps gives. So a yarn's strength is a minimum, and a minimum depends on how many independent tries the sample contains. The tries are not sections — a plane can be taken anywhere — but staple lengths, because two planes closer together than one fibre share most of their fibres. At 28 mm staple a 100 mm specimen holds 3.6 independent tries and a 500 mm one holds 17.9, and the longer test reads 9% lower. The spread is not fitted either: it is the evenness floor at 176 fibres times an index of 1.35, which is 10.9%.
Fig. 2 Where a sewing thread breaks, against how much of it was clamped. A sewing thread is loaded over millimetres rather than over a gauge length, so the thin place that decides it is drawn from a much smaller sample — and it is stronger than a tensile test on the same yarn would suggest.

Why three-fold, and why balanced

Three rather than two, for two reasons this collection can state.

A three-fold yarn is rounder: the gap between its two diameters is 1.244 against a two-fold’s 1.414, because more circles pack a circle better. Roundness matters here in a way it does not in a cloth, because the thread must pass a hole of fixed size with clearance, and an oval thread presents a different width depending on how it happens to be rotated.

And a three-fold’s surface is smoother. Each single’s protruding fibres are trapped against two neighbours rather than one, so the hair layer — the thing abrasion works on — is smaller.

Balanced, because a lively thread snarls. A thread with residual torque forms a loop and the loop kinks back on itself, and at the moment of the take-up, when the thread is slack for a few milliseconds, a snarl is exactly what a slack lively thread does. A snarl at the needle is a thread break, a stopped machine and an operator’s attention.

The balance ratio for a three-fold is between 0.5 and 0.65 — lower than a two-fold’s, because the ply’s helix radius is larger when three singles sit round the axis — and it is a torque condition this collection declines to compute. What it can say is that the choice is nearly free in strength: a folded yarn’s realisation barely depends on its folding twist, because the grip the fold takes out of the singles it supplies from outside them.

That freedom is what makes a sewing thread possible. If folding hard enough to balance the thread cost a third of its strength, the trade would have to choose between a thread that snarls and a thread that breaks.

The lubricant, and what it costs

Now the part that is computable and is not usually put this way.

A sewing thread is finished with a lubricant — a wax, a silicone or a synthetic finish — at one to three per cent of its weight. Its purpose is to lower the friction between the thread and the needle, the needle plate and the cloth, so that the thread survives its dozens of passages and so that the needle does not heat enough to soften a synthetic thread.

The lubricant does not know which friction it is lowering. It lowers the friction between the thread’s own fibres too.

And the friction between a yarn’s own fibres is what holds them: the critical length is the fibre’s diameter over four times the friction times a function of the twist, so halving μ doubles the length of fibre that has to be gripped, and the cohesion factor falls.

Both halves of the twist curve, at 28 mm staple. The falling curve is obliquity and is exact — the affine end of the bracket, computed from the helix and nothing else. The rising curve is cohesion and is the half this collection had declined: a fibre end is gripped by friction under the twist's own radial pressure, the fibre's strength and the yarn's load cancel out of the comparison, and what is left is a critical length that depends on the twist through a pure function of the angle. Their product has a maximum at a twist factor of 3101 — 693 turns per metre at 20 tex, a surface angle of 20° — which is inside the range spinners use. The scale of the rising curve is fitted, through a contact efficiency of 0.05, and moving it moves the optimum; what it cannot move is the ordering between two staples or two fibres, which is what the two claims made from this figure are about.
Fig. 3 The strength curve at an ordinary μ of 0.3. The maximum is at a twist factor of 3,101 and realises 0.771 of the fibres.
The length of fibre a twist can hold. The critical length is the fibre diameter over four times the friction, times a pure function of the twist angle — the fibre's strength and the load on the yarn having cancelled. It falls steeply: below about five degrees it exceeds any staple anybody spins, so the fibres slide past one another and the yarn has no strength at all; by twenty degrees it is a small fraction of the staple. The three curves are three contact efficiencies spanning a factor of ten, which is the honest range for the one measured number in the argument. They are the same curve at three heights: the fitted number scales the length and does not change its shape, which is why every claim made from this is a claim about ordering. The horizontal rule is the cotton staple of 28 mm; a critical length above it means no fibre in the yarn is gripped over its whole length.
Fig. 4 And the quantity the lubricant moves. The critical length is inversely proportional to the friction, so a lubricant that halves μ has the same effect on this curve as dividing the contact efficiency by two: at 20° it moves the critical length from 7.1 mm to 14.2, which is half the staple rather than a quarter of it.

Running the arithmetic at both frictions:

μ optimum twist factor realisation at optimum realisation at 20°
0.30 3,100 0.771 0.771
0.20 3,440 0.722 0.715
0.15 3,790 0.682 0.659

Halving the friction costs about twelve per cent of the thread’s realisation at its own optimum, and fifteen per cent if the twist is left where it was. It also moves the optimum up: a lubricated thread wants more twist, because the grip has to be recovered from somewhere and the only place left is the angle.

That is a prediction with a check attached, and the check passes: sewing threads are twisted harder than weaving yarns of the same count. The trade’s explanation is usually abrasion resistance, which is also true. The arithmetic here supplies a second and independent reason.

The core-spun thread, which solves it structurally

There is a construction that attacks the same problem from the other end and it is now the ordinary one for industrial sewing.

A core-spun thread has a continuous filament core — polyester, usually — with staple fibres spun around it. The filament carries the load; the staple carries the surface.

Read against the arithmetic above, this is a way of separating the two requirements that the lubricant was trading against each other.

The strength is the filament’s, and a filament has no fibre ends, so the whole cohesion half of the twist curve does not apply to it: its realisation is the obliquity alone, and at the low twist a core sits at, that is nearly one. The lubricant cannot weaken it, because there is no fibre-to-fibre grip in the core to weaken.

The surface is the staple’s, and it is there to be abraded, to hold the lubricant, and to give the thread the handle and the sewability a bare filament does not have. Its own strength is beside the point.

So a core-spun thread breaks the trade this essay is about. The lubricant still lowers the friction in the sheath, and it no longer costs anything, because the sheath was not carrying the load.

What a packing factor decides. Every diameter on this site comes from a count through a packing factor of 0.6, and that number was obtained by inverting a rule published for cotton yarns at one particular twist. This is what moves if it is wrong by the width of the range real yarns occupy — 0.45 to 0.75, which is the whole of it. An areal weight does not move at all, because it is a count times a sett and never passed through a diameter; a cover factor moves by 15%; a bending rigidity moves by 78%, because it goes as the fourth power. The exponents are exact and are asserted, not read off the bars.
Fig. 5 What a packing factor decides, which is where a sewing thread differs most. It is folded and set to a packing an ordinary yarn never reaches, so its diameter for a given count is smaller — and a needle’s eye is sized on the diameter rather than the count.

The whole specification, read as a list of answers

Set out this way, a sewing thread’s oddities stop being a list and become a set of responses.

Folded, three or more. Roundness for the needle hole, a smoother surface for abrasion, and a load-bearing structure whose strength does not depend on the folding twist.

Balanced. Because a snarl stops a machine, and the balance is nearly free in strength.

Hard-twisted. For abrasion resistance directly, and to recover the grip the lubricant costs.

Lubricated. To survive the passages, at a computable cost in strength.

Dyed and finished as a thread rather than in the cloth, because a seam is sewn after the cloth is finished — which means a sewing thread cannot rely on any of the finishing operations that a woven yarn gets for free, and has to arrive complete.

And specified by a ticket number rather than by a count. The ticket system is a resultant count in disguise, and the reason it survives is that a sewing room’s question is “what fits this needle?” rather than “what does this weigh?” — which is a question about the diameter, and a folded yarn’s diameter is a bracket rather than a number.

Why the lubricant’s cost is affordable, and where it stops being so

The lubricant costs twelve to fifteen per cent of the thread’s realisation, and a thread designer accepts it. It is worth saying why that is a good trade rather than a reluctant one, because the arithmetic says the alternative is much worse than a fifteen per cent loss.

A thread that fails on its thirtieth passage instead of its eightieth does not deliver eighty per cent of a seam; it delivers a stopped machine. The abrasion requirement is a threshold and the strength requirement is a margin, and a threshold that is not met costs everything while a margin that is reduced costs proportionally.

So the two requirements are not comparable quantities being traded, and treating them as though they were is what makes the fifteen per cent look expensive. The correct reading is that the lubricant buys passage of a threshold with a fifteen per cent premium on a margin that had room in it — which is a cheap purchase, and is cheap for exactly the reason the seam section gives: the thread is not usually the thing that fails.

The trade stops being cheap when the margin runs out, and it does so in a predictable place. A fine thread on a heavy cloth is a thread whose breaking load is near what the seam will ask of it, and there the fifteen per cent is coming off a margin that was already thin. That is the case where core-spun construction is not a refinement but a necessity, and it is the case the industrial trade has moved to core-spun for.

And it says what a better lubricant would be worth. A finish that lowered thread-to-metal friction without touching fibre-to-fibre friction would deliver the threshold at no premium at all. Nothing in this arithmetic says such a finish is possible; what it does say is exactly how much it would be worth, which is the twelve to fifteen per cent, at every count and every construction, for as long as threads are spun from staple.

The qualification at the end of that sentence is the one a core-spun thread exploits: a filament core has no fibre-to-fibre grip to lose, so the premium is already nought, and no finish chemistry was needed to get there.

What the seam actually gets

It is worth closing the loop on the seam, because the thread’s properties reach it in a narrower way than one would expect.

A seam fails in one of three ways and this collection has priced two of them. The cloth’s threads slip out of the seam, which is a capstan grip over the allowance and depends on the cloth’s friction and construction rather than on the thread at all. The cloth tears along the stitch line, which is the removal of threads at every puncture and again does not involve the sewing thread’s strength. Or the thread breaks, which is the only one of the three where any of this essay’s arithmetic enters.

So the elaborate construction described above is aimed at a failure mode that a well-made seam does not have. That is not a criticism: a thread strong enough to be the last thing to fail is the design target, and hitting it is what all the folding and twisting is for. But it does mean that the difference between a good sewing thread and an excellent one shows up in the sewing room rather than in the seam, as breaks per thousand stitches rather than as a stronger garment.

A stitched seam is one of the few structures in this collection where the component that is most carefully specified is the one whose properties matter least to the finished object, and where the reason is entirely about the process that assembles it.

The finest yarn each fibre can make. A spun yarn needs enough fibres in its cross-section for twist to hold them — the ring frame's floor is put at about 35 for cotton — and below that the yarn breaks at its thin places faster than it can be wound. The floor is a count of fibres, so the finest yarn is that count times the fibre's own linear density and the limit belongs to the fibre rather than to the spinner. Cotton at 0.17 tex a fibre reaches 5.9 tex, which is Ne 99; wool at 0.50 tex a fibre cannot get below 17.5 tex however it is spun. The ratio between the two is the ratio of their finenesses and nothing else.
Fig. 6 And the floor a sewing thread sits well above. It is not spun to the finest count its fibre allows, because everything about it is chosen for the load over a short length rather than for fineness — which is the sense in which it is a different animal.

What was counted, and how

The lubricant’s cost is the same strength curve run at two frictions, with the friction being an argument to the critical length rather than a separate model. The comparison is a ratio between two points on curves that share the fitted contact efficiency, so most of the fit cancels.

The direction of the optimum’s move is asserted rather than read off. A lower friction must move the optimum twist up, at every contact efficiency, because both enter the critical length as a product — which makes the claim a statement about a group rather than about either quantity.

And the balance freedom is the folded-yarn result, which is checked as a claim that a quantity is flat: a folded yarn’s realisation must vary by under twelve points across the whole span of folding ratios.

One more asymmetry is worth recording. A weaving yarn is consumed by the cloth it becomes: every metre of warp ends up in the fabric and is protected there for the rest of its life. A sewing thread is consumed by the machine — most of the abrasion it will ever suffer happens in the seconds before it is laid into the seam, after which it is held between two layers of cloth and rarely touched again. So the thread that arrives in the finished garment is not the thread that was bought; it is that thread minus eighty passages through a needle eye, and nobody measures what is left.

Where the model stops

Abrasion is not modelled at all, and it is the thread’s actual design criterion. This collection has nothing that predicts how many passages a thread survives, and the essay is careful to say that its computable part — the strength cost of the lubricant — is a secondary consideration in the design.

The lubricant is treated as a change to one number. In reality it changes the thread-to-metal friction, the thread-to-cloth friction and the fibre-to-fibre friction by different amounts, and only the last of the three is in the arithmetic. A lubricant that lowered the first two and left the third alone would be free, and formulating one is presumably what a finish supplier is trying to do.

The passage count is quoted from practice and is not derived. It depends on the stitch type, the take-up geometry and the machine, and the range given is wide.

The needle’s heat is absent. A needle in a fast machine reaches temperatures at which a polyester thread softens, and that is a large part of why lubrication matters — a mechanism this collection has no way to price.

And the ticket systems are a mess that is not tidied here. Several coexist, they are not simply convertible, and the one thing they have in common is that they are about a diameter rather than about a mass.

Where the ladder goes next

Back into the seam, where the thread now has properties rather than being a given. A seam slips before it breaks when the cloth’s grip on its own threads is weaker than the sewing thread — and knowing what the sewing thread actually realises makes that comparison a computation rather than an assumption.

And sideways into the other place where a thread is asked to survive an operation rather than a load. A warp end is abraded a hundred thousand times by heddles and reed before it is ever pulled hard, which is why a warp is twisted past its strength optimum — the same trade as this one, made by the same reasoning, in a trade that does not describe it that way either.

Where this goes next

What holds a thread in a seam. A cloth thread inside a seam allowance, drawn past the crossings that grip it, with the capstan's factor at each. The tension falls by that factor at every crossing, so the grip is exponential in the crossing count and the count is what the weave decides. Beyond the thread's own strength the thread breaks rather than slides, and the rest of the allowance holds nothing. What holds a thread in a seam A seam fails in two quite different ways, and the one the trade worries about is not the stitches breaking. It is the cloth's own threads sliding out of the weave beside the seam — and what resists that is friction at the crossings, accumulating multiplicatively, so a satin gives a seam a thousandth of the grip a plain weave gives it. The stitch density that makes the strongest seam. Seam strength against stitch density, as the two limits that decide it: the sewing thread crossing the seam, which rises with the stitches, and the fabric the needle perforates, which falls. The seam is the lower of the two, so the optimum is where they cross — and whether the fabric line falls at all is decided by the clear gap between threads against the width of the needle. The stitch that weakens the seam More stitches per centimetre put more sewing thread across a seam and more holes through the cloth beside it, so seam strength rises, crosses and falls. Whether the fabric line falls at all is decided by the clear gap between two threads against the width of the needle — the same arithmetic a filter cloth is specified by, doing a different job. The pressure a 23° twist puts on its own fibres. A twisted yarn squeezes itself. Every fibre under tension at a radius pulls inward with sin²θ of its tension per unit length, and integrating outward to the surface — where the pressure is zero by definition, because there is nothing outside to push against — gives p(r) = ½σ(cos²θ(r) − cos²α) in closed form. At a surface angle of 23° the pressure on the axis is 7.6 per cent of the core fibre's own axial stress and the mean over the section is 3.61 per cent of it. The shading is that closed form and the curve is the same function plotted; the shape is what matters, and its one uncompromising feature is the zero at the edge. The outermost fibres are held by nothing, which is why a yarn is hairy, why a surface fibre is the one that comes away on a finger, and why singeing changes a yarn's behaviour out of all proportion to the mass it removes. What grips the end of a fibre A twisted yarn squeezes itself, and the squeeze holds the fibre ends in. Write the slip and the break out side by side and the fibre's own strength cancels — and so does the load on the yarn — leaving a gripped length that depends on fineness, friction and the twist and on nothing else.

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.

AbrasionContact efficiencyCritical lengthFolding twistFrictionPlySeamSpecification