A fancy yarn has its crimp in the wrong thread

A bouclé is three threads. A core runs straight; an effect thread is delivered faster than the core and has nowhere to put the surplus but into loops standing off the surface; a binder goes over the top and holds them down.

The overfeed is a length ratio — extra thread per unit of finished yarn — and that is exactly this collection’s definition of crimp. So a fancy yarn is a yarn with crimp built into it, at a value the spinner chooses rather than at one the geometry forces.

The analogy is worth pushing because it fails, and where it fails is the whole essay.

The loop size is not a design choice #

Before the failure, the part of the analogy that works, because it makes the construction computable.

The surplus has to be consumed by the loops, and a semicircular loop of radius r uses up πr of thread across a base of 2r — so each loop consumes r(π − 2) of surplus. At one loop every s millimetres the overfeed v is r(π − 2)/s, and therefore

r/s = v / (π − 2) = v / 1.142.

At eighty per cent overfeed and a three-millimetre loop spacing that is a radius of 2.1 mm — loops seven tenths as large as their own spacing, which is a bouclé that reads as loops rather than as a texture. At thirty per cent it is 0.79 mm, a quarter of the spacing, which is a gimp — or would be, if the loop were a semicircle. Solved as the elastica it is, a loop held along its core rises as the square root of its surplus, and the thirty-per-cent loop stands 1.10 mm, over a third of its spacing; the eighty-per-cent loop stands 1.95.

So the two things a designer names — how big the loops are and how often they come — are not independent of the overfeed. Any two of the three fix the third, and a specification quoting all three is either redundant or wrong.

Where the crimp analogy fails #

A woven cloth’s crimp is in the threads that carry the load. Pull a cloth warpwise and the warp’s crimp comes out first, because straightening a bent thread costs far less than stretching a straight one — which is why a cloth extends by moving its crimp and why its stress–strain curve has two regimes with a knee between them.

A bouclé’s surplus is in the effect thread, and the effect thread is not the load path.

The core and the binder are at the yarn’s own length. The effect thread is longer than the yarn by its overfeed, so at any extension below eighty per cent it is slack — it has no tension in it at all and contributes nothing to the yarn’s resistance. Pulling the yarn pulls the core, immediately, with no compliant first regime whatever.

So the built-in crimp buys no extension. It is the right quantity in the wrong member, and the difference between a crimped cloth and an overfed yarn is entirely a question of which thread the surplus is in.

That is a sharper statement than it looks, because the fix is obvious and is not done: overfeed the core instead and the yarn would have a genuine compliant regime. Nobody does, because a slack core makes a yarn that stretches under its own weight on the bobbin.

Which prices the decoration #

Put numbers on the load path and the picture is stark.

A bouclé of 20 tex core, 30 tex effect at eighty per cent overfeed and 15 tex binder has a resultant count of 89 tex, of which the core and the binder are 35. So thirty-nine per cent of the yarn’s mass is on the load path and the remaining sixty-one per cent is decoration that carries nothing.

Raise the overfeed and it gets worse in the way that matters: at 160 per cent the yarn is 113 tex and thirty-one per cent of it is load-bearing. Every gram of the effect a designer adds is a gram off the load path, so a strongly looped bouclé is not a stronger yarn made decorative, it is a weak yarn made heavy.

That is the honest account of why bouclé is a weft yarn. It is not that the loops abrade in the warp, though they do; it is that the count on the ticket is nearly three times the count that would break.

And the count on the ticket is wrong twice over #

The resultant count is not the sum of the components’ counts, and the reason is the overfeed again.

A yarn of core c, effect e and binder b at overfeed v has a linear density of c + e(1 + v) + b. The naive sum is c + e + b, and the two differ by e·v. For the yarn above that is 89 against 65 tex — thirty-seven per cent heavier than the sum of what went into it.

A designer computing a cloth’s weight from the component counts is therefore out by thirty-seven per cent, in the direction of a much heavier cloth than expected. What a fabric weighs is threads per centimetre times count times length, and putting the wrong count in it is the commonest way that arithmetic goes wrong.

The useful inversion is that the overfeed is recoverable. Given the four numbers a specification usually carries — three components and a resultant — the overfeed is (resultant − sum)/effect, exactly. So a mill that has the ticket has the overfeed whether or not it was told, and can compute the loop geometry from it.

That is worth having, because the overfeed is the parameter that decides everything here and is the one least often written down. The trade names the yarn — bouclé, gimp, loop, snarl — where a number would do.

What the effect thread does instead of carrying load #

A thread that carries no load is not doing nothing, and what it is doing is worth separating into three because they behave differently.

It occupies space. That is the bulk below, and it is the intended effect.

It abrades first. A loop stands proud of the yarn, so it meets everything the cloth rubs against before the core does — and it is the member with no tension in it, which means it can be pulled out rather than broken. A bouclé fails by snagging: a loop catches, the effect thread runs, and a length of the yarn loses its decoration while remaining perfectly sound. That is a failure mode with no analogue in an ordinary yarn, and it is the reason the binder exists at all.

And it decides the surface, not the structure. Every property a fancy yarn is bought for lives on the effect thread and every property that decides whether the cloth survives lives on the core. So the two halves of a specification are about two different threads and neither is about the yarn.

That separation is unusually clean and it is worth stating as a general form: an overfed construction splits a thread’s jobs between two members, and the member doing the visible job is the one under no tension. The same split appears in a chenille, whose pile is held by a ground that carries all the load — which is this ladder’s first rung and is the same architecture one level up, a fabric instead of a yarn.

Two ways to read an eighty per cent overfeed #

The number is a delivery ratio at the machine and it can be read three ways, which is a small trap worth marking because the three differ by enough to matter.

As a ratio of speeds: the effect thread is delivered at 1.8 times the core’s speed. That is what is set on the machine.

As a fraction of the yarn: the yarn contains 1.8 metres of effect thread per metre of length, so the surplus is 0.8 metres — eighty per cent of the yarn’s length and forty-four per cent of the effect thread in it.

As a crimp: the effect thread’s crimp, by this collection’s own definition of extra length over cloth length, is exactly 0.8 — the same number, which is the one respect in which the analogy is free of trouble.

The confusion to avoid is between the second and third readings. Eighty per cent overfeed does not mean eighty per cent of the effect thread is surplus; it means the surplus is eighty per cent of the core’s length. A yarn described as having “eighty per cent effect” would be a different and much lighter yarn.

And the resultant count arithmetic uses the third reading, which is why the effect enters as e(1 + v) rather than as e/(1 − v). Those two differ by twenty-five per cent at v = 0.8, which is the size of the error a designer would make by taking the wrong one — larger than most of the effects anybody is trying to compute.

The bulk, which is the reason for the whole construction #

Everything above has been about what the overfeed costs. What it buys is not strength and not extension, and it is worth naming: bulk.

A yarn’s count is a mass per length and its diameter is not. Ordinary yarns have a nearly fixed relation between the two, because a yarn is a twisted bundle at a packing factor that varies over a narrow range — which is what makes count systems useful as a proxy for thickness at all.

A looped yarn breaks that relation on purpose. Its effective diameter is set by the loops, which stand a radius off the core, so an 89 tex bouclé occupies the space of a yarn several times its count. The cloth it makes is thick, open and light for its bulk — and every one of those is a property nothing about the count predicts.

So the fancy yarn’s real specification is a diameter and its recorded specification is a mass, and the two have been deliberately decoupled. That is the same complaint the rung below makes about the coefficient of variation, arriving from the other direction: a number that summarises a family stops summarising anything the moment somebody builds an object outside the family on purpose.

The other overfed constructions, and where each puts its surplus #

A bouclé is one member of a family and the family is organised by exactly the question this essay asks: where the extra length goes.

A gimp overfeeds gently — a third or less — so the surplus makes a wavy outline rather than closed loops. Its load path is the same core and binder, and its share of load-bearing mass is much higher because there is less surplus to carry: at thirty per cent overfeed the yarn is 74 tex against a component sum of 65, and forty-seven per cent of it is on the load path against a bouclé’s thirty-nine.

A snarl or spiral yarn overfeeds past the point at which the loops can stand clear, so they twist on themselves. That happens when the loop radius approaches its own spacing, which by the expression above is an overfeed near 1.14 — and above it the drawn loops overlap, which is a picture of a construction rather than of a yarn.

A chenille is the extreme and is a different object entirely: it is a woven gauze cut into strips, so its “effect” is a cut pile held by twist rather than a thread held by a binder, and the surplus is not a length ratio at all.

And a slub is the family’s other axis: it changes the thread’s thickness and leaves its length alone, which is why its consequences are about strength and this one’s are about bulk.

The organising statement is a short one. A fancy yarn changes a thread’s thickness or its length, and the two families have almost no consequences in common — one moves the minimum and the other moves the load path, one is measured by a coefficient of variation that cannot see it and the other by a count that is wrong by a third.

What was counted, and how #

The loop radius is solved and not fitted. A semicircular loop of radius r on a base of 2r has arc length πr, so the surplus per loop is r(π − 2) exactly. Everything about the loop geometry follows from that one line and the loop spacing, with no shape parameter chosen.

The resultant count is arithmetic, and the assertion on it is a relation. That the resultant exceeds the component sum is required at every overfeed tried; the amount is not asserted, because it is a fact about one yarn’s three counts.

The load-bearing share is a share of mass and not a share of strength. What is computed is which threads are at the yarn’s own length and what fraction of the linear density they are; converting that to a breaking load needs the fibres, the twist and the migration, which are not here.

The trend is asserted over three overfeeds rather than at the one the figures draw: the load-bearing share must fall as the overfeed rises and the loop radius must rise, both strictly. A single-point check would have been consistent with either quantity being constant.

And the guards are fed what they must refuse: a yarn with no core, an effect thread of negative count, an effect thread not overfed at all, and loops with no spacing.

Where the model stops #

The loops are semicircles and they are not. A semicircle meets the core at a right angle where the binder holds the thread along it, and its base is not the binder spacing. A loop is an elastica on its two binder points, and it is taller than the semicircle below an overfeed of 66 per cent and shorter above it — so the radius computed here understates a small loop and overstates a large one, by an amount a binder pulling the loop’s feet together changes further. The loop also lies at an angle to the yarn’s axis, which is not modelled at all.

The three threads are treated as separate and the twist is ignored. A bouclé is twisted, the binder is wound helically, and helix angle takes length out of every member. The overfeed is measured as a delivery ratio at the machine, so it is right; the core’s length in the finished yarn is slightly less than the yarn’s length, and the count arithmetic here does not include it.

“Slack until the overfeed is consumed” is the geometry and not the mechanics. A slack thread bound down at intervals is not free: the binder pins it, and a loop being pulled straight has to drag through its own bindings. So the effect thread does take some load before the yarn extends by eighty per cent, by an amount the capstan equation would give if the wrap angles were known.

And nothing here is about the cloth. A bouclé weft in a plain ground behaves as a much thicker yarn than its count, sets far more openly than the count would allow, and abrades at the loops. How openly is a bracket twelve times wide, between the loops touching and the count touching; the abrasion is not computed.

Who found it, and when #

Fancy-yarn spinning is a mature craft with a substantial technical literature: the machines are described, the delivery ratios are tabulated, and the relation between overfeed and loop size is known to everybody who sets one up.

The framing as crimp in the wrong member does not appear, and it is not merely a rephrasing. It says which quantity to reach for — the load path’s share of the mass — and it predicts the thing the trade knows without explaining: that a looped yarn is weak out of proportion to its count.

The count arithmetic is elementary and appears to be genuinely absent from the design side rather than from the spinning side. A spinner knows the resultant count because the yarn is weighed; a designer computing a cloth weight from components has no reason to suspect a thirty-seven per cent error, and the recoverability of the overfeed from the four numbers is the useful half of noticing.

Where the ladder goes next #

Three rungs of this anchor have taken the fancy yarns apart by what they do to a thread: a chenille makes it a fabric, a slub changes its thickness, an overfed effect changes its length. What none of them has asked is what a cloth does with one — how a yarn whose diameter and count have been decoupled sets, how a loop abrades, and whether the cloth’s own averaging touches a variation this large at all.