What a high-twist yarn costs a cloth

A spinner sets one number and five things follow from it. Four get worse as it rises and one gets better and then worse, and the twist factor a mill actually uses is where the five balance.

This collection has had three of the five for a long time and acquires the other two on this ladder, so they can be put side by side for the first time.

One: strength, which rises and then falls #

The oldest of the five and the one everybody knows.

More twist grips the fibres harder, so fewer of them slip out and the yarn holds together better. And more twist runs the fibres at a steeper angle to the yarn’s axis, so less of each fibre’s strength points the way the yarn is being pulled.

The two effects cross, and the crossing is the twist optimum. This collection computes it and finds it where the literature does, at a twist factor that depends on the fibre’s staple length and friction rather than on its strength.

Above the optimum, more twist costs strength. A crepe twist is well above it, so a crepe cloth is weaker than a cloth of the same count at ordinary twist — and the trade accepts that.

Two: liveliness, which rises as the square #

The cost this ladder adds, and it is steeper than any of the others.

A yarn’s residual torque goes as its twist, and the tension needed to keep it straight goes as the square of the torque over the bending rigidity. So doubling a yarn’s twist quadruples the tension it needs to be handled slack.

For a twenty tex cotton at eight hundred turns a metre that tension is about two metres of the yarn’s own weight; at fourteen hundred it is six.

That is why a crepe yarn cannot be handled slack at any stage — not on the creel, not in the shed, not between the reed and the fell — and why the whole crepe process is built around never letting go.

Three: diameter, which falls #

A twisted yarn is a compacted yarn: the twist presses its fibres together, raising the packing factor and shrinking the diameter.

This collection carries that as an explicit warning — a diameter quoted without its twist is a diameter quoted for an unknown yarn — and the effect is not small: a factor of two in twist moves a yarn’s diameter by several per cent.

A smaller diameter means less cover at the same sett, so a cloth of high-twist yarn is more open than one of soft-twist yarn at the same construction. That is a cost for a shirting and it is the point for a voile: an open, crisp, transparent cloth is what a high twist buys.

Four: bending rigidity, which rises #

A compacted yarn is a stiffer yarn, because its fibres are pressed together and slide less freely — which moves it away from the free end of the collection’s own stiffness bracket.

A stiffer yarn makes a stiffer cloth, so a high-twist cloth is crisper and drapes less. That is again a cost for some cloths and the point for others: crispness is what a voile, an organdie and a poplin are for.

The mechanism is worth naming because it is the same one four other results in this work depend on. Twist moves a yarn along its own bracket, from freely sliding towards coherent, and everything that depends on which end it is at moves with it.

Five: shrinkage, which rises #

A high-twist cloth shrinks more on relaxation, and this ladder says why in the crepe case: buckling takes up length.

Below the crepe threshold the same mechanism operates weakly. Every thread in a relaxed cloth is a little less straight than it was under tension, and a livelier yarn is a little less straight still.

So shrinkage rises with twist smoothly and then jumps once the buckling threshold is crossed, and the jump is the crepe effect.

Where the trade’s limits come from #

Putting the five together explains the numbers the trade uses rather than merely listing them.

A soft weft at a twist factor around thirty is chosen for bulk, cover and softness, and gives up strength to get them. It is below the optimum on purpose.

A warp yarn at forty to fifty sits near the optimum, because a warp is the system that has to survive weaving and strength is what it is for.

A voile or organdie yarn at sixty to seventy is above the optimum, chosen for the crispness and the openness, and pays in strength.

And a crepe yarn at eighty to a hundred is far above it, chosen for one effect and paying in everything else.

Four bands, four different quantities being optimised, and the same five costs traded differently in each.

Which of the five the trade actually watches #

Only two of the five are usually specified, and the other three are managed by experience.

The strength is measured, on every lot, because it is what stops the loom.

The twist itself is measured, because it is the setting.

The liveliness is measured in some mills, by the hanging-loop test, and is not usually a specification.

The diameter and the rigidity are almost never measured on a yarn at all, and are inferred from how the cloth turns out.

So three of the five costs are managed by looking at the finished cloth, which means a twist decision is corrected after the fact rather than made in advance. That is a fair description of how a mill actually works, and it is why the twist factor for a given cloth is a piece of house knowledge rather than a calculation.

Why the optimum is not where anybody works #

A detail about the first of the five that is easy to miss and matters to the other four.

The twist optimum maximises strength, and almost nothing in the trade is spun at it. Wefts are below it and warps are at or near it; everything decorative, crisp or open is above.

That is not carelessness. Strength is a constraint rather than an objective for most cloths: a yarn has to be strong enough to weave and strong enough to wear, and beyond that more strength buys nothing.

So the optimum is a ceiling on the useful range rather than a target, and the real decision is made among the other four costs, with strength watched to make sure it stays adequate.

That reframes the twist curve this collection computed several ladders ago. The other half of the twist curve — the falling half, past the optimum — is not a region to be avoided. It is where a good deal of the trade deliberately works, and the falling strength is the price of admission.

What was counted, and how #

Three of the five are this collection’s own from earlier ladders: the strength optimum, the diameter’s dependence on twist, and the rigidity’s.

Two are this ladder’s: the liveliness threshold, which is Greenhill’s criterion with this collection’s own numbers in it; and the buckling that produces the shrinkage jump, which is the same criterion applied to a thread in a cloth rather than a free one.

The four twist bands are trade practice and are quoted rather than derived. What is derived is the ordering of the costs and their rates: strength turns over, liveliness goes as the square, diameter and rigidity move gently, shrinkage jumps at a threshold.

The sixth cost, which is not the yarn’s #

There is a cost that belongs to the process rather than to the yarn and it is the largest of them all commercially.

Speed. A yarn is twisted by rotating it, and a spinning frame’s output is its spindle speed divided by the twist inserted per unit length. Double the twist and the frame produces half as much yarn in the same time.

So a crepe twist at a hundred against a warp twist at forty-five is not a little more expensive; it is less than half the output from the same machine and the same labour.

That is why high-twist yarns cost what they do, and it is the reason the twist factor is a commercial decision as much as a technical one. Everything else on this page is a property; this one is money.

It is also the reason the four bands exist as bands rather than as a continuum. A mill runs its frames at settings it knows, and moving a twist factor is a production decision rather than a design one.

Where the model stops #

Only the liveliness has a rate. The other four are directions rather than functions: this collection knows that a higher twist means a smaller diameter and cannot say by how much for a given fibre and process.

The rigidity’s dependence is qualitative. Saying that twist moves a yarn along its bracket is right and is not a number, and the bracket has no scale on it anyway.

The shrinkage account is a mechanism without an arithmetic. How much length a buckle takes up is a question about the buckle’s amplitude, which needs the cloth’s out-of-plane stiffness and is not computed.

And the five are not independent. A stiffer yarn has a higher snarling threshold, so raising the twist raises the liveliness through the torque and lowers it through the rigidity, and the net is the square law only if the rigidity is held. It is not.

That last is the most serious and it means the square law is an over-estimate of how fast liveliness rises. By how much is not known.

What a knitter chooses differently #

The five costs are weighted differently for a knitted fabric, and the difference is large enough to explain why knitting yarns look nothing like weaving yarns.

Liveliness matters far more. A knitted loop is free to rotate about its own axis in a way a woven thread under tension is not, so a residual torque leans the fabric. A weaving yarn’s liveliness is a handling problem; a knitting yarn’s is a product defect.

Strength matters far less. A knitted fabric shares load among many loops and is never loaded near its yarn’s breaking point in use, so the strength optimum is not a constraint at all.

Diameter and rigidity matter more, because a knitted fabric’s whole geometry is set by the ratio of its yarn’s diameter to its loop length, and its handle is set by the yarn’s bending.

So a knitting yarn is spun softer than a weaving yarn of the same count — typically at a twist factor two thirds of a warp’s — and the reason is not that it needs less strength. It is that liveliness is the binding constraint and softness is how it is avoided.

That is a conclusion this collection could not have drawn before this ladder, because it had no account of liveliness at all.

The generalisation #

The rung is an exercise in something this collection does rarely and should do more: putting a decision’s costs on one page.

Most of this site’s ladders follow one quantity deeply. That is the right way to find things and it is a poor way to describe a choice, because a choice is made against several quantities at once and the person making it does not have the luxury of considering them in sequence.

Five quantities, four of them monotone and one turning over, is a decision problem. It is also a place where the collection’s own gaps become visible in a useful way: three of the five have directions and no rates, and a designer who wanted to compute a twist factor rather than inherit one would need all five as functions.

That is a work list rather than a complaint, and it is the sort of thing that only appears when the quantities are written side by side.

The five, as a table a designer could use #

Set out plainly, with what this collection knows about each and what it does not.

Strength rises to an optimum and falls. The collection computes the optimum and the curve either side of it, from the fibre’s staple length, friction and the helix angle. Fully quantitative.

Liveliness rises as the square of the twist. The collection computes the threshold tension and the coil radius, both from Greenhill’s criterion, with the threshold carrying a factor of two from the shear modulus and the radius carrying none. Quantitative with a bracket.

Diameter falls. The collection knows the direction and the mechanism — compaction raising the packing factor — and has no function for it.

Rigidity rises. Direction and mechanism only.

Shrinkage rises smoothly and then jumps at the buckling threshold. The threshold is computable and the amount is not.

Two of five with functions, three with directions. That is an honest statement of where a collection eighteen phases into a subject stands on the most basic decision a spinner makes.

What it would take to finish the table #

The three missing functions are not equally hard and it is worth ranking them.

The diameter is the easiest. Yarn compaction against twist is a measured relation in the literature and could be brought in as a table rather than derived, in the same way this collection’s fibre moduli are.

The rigidity is harder and is the same problem as the stiffness bracket: it needs to know where along the bracket a yarn sits, which is exactly what the collection cannot compute. The snarl measurement proposed on this ladder would give it, which makes that measurement more valuable than it first appears.

The shrinkage is hardest, because it needs the buckle’s amplitude, which needs the cloth’s resistance to being deformed out of its own plane — a quantity this collection has for a knitted fabric and not for a woven one.

So one is a table, one is a measurement this ladder has already specified, and one is a piece of modelling. That is a tractable list and it would complete the most-used decision in the subject.

Who found it, and when #

The twist optimum is classical and has been measured since the nineteenth century; the modern account is Gégauff’s angle plus a slippage model.

The diameter’s dependence on twist and the compaction that produces it are standard and are why every yarn diameter measurement specifies a twist.

The liveliness criterion is Greenhill’s, from 1883, and is applied here with this collection’s own rigidities.

What is this collection’s own is the assembly: five costs, from four different ladders, put on one page with their rates where it has them and their directions where it does not.

Where the five interact, which is the part nobody has done #

The costs have been listed as though they were independent and two pairs of them are not, which is worth flagging because it is where a proper treatment would start.

Twist and rigidity. Raising the twist compacts the yarn, which raises its bending rigidity, which raises the tension it needs to buckle. So the liveliness rises with the torque and falls with the rigidity, and the square law quoted above holds the second fixed.

Twist and diameter. Raising the twist shrinks the diameter, which lowers both rigidities as the fourth power. That pushes the liveliness the other way again.

Those two corrections have opposite signs and neither is quantified. What can be said is that the true dependence of liveliness on twist is weaker than quadratic, and the observed practice — that a doubling of twist makes a yarn much harder rather than four times harder to handle — is consistent with that.

Sorting it out needs the diameter’s dependence on twist as a function, which is the first item on the work list above. One missing function blocks two of the five, which is a fair description of how this collection’s gaps usually behave: they are not independent either.

Where the ladder goes next #

A twist that has been suppressed comes back, and where it comes back is a fabric rather than a yarn. A cloth that lay flat in the shop and spirals after a wash is a torque that was set away and returned, and it is the commonest complaint about knitted cotton.

The twist a fabric gives back.