Crimp, and why cloth narrows when it is pulled

Cut a warp thread out of a piece of cloth and straighten it, and it is longer than the cloth it came from. It has to be: it went over and under, and the path over and under is longer than the straight line.

That excess has a name and a number.

The definition #

Crimp is the fractional excess of thread length over cloth length. A crimp of eight per cent means a thread eight per cent longer than the fabric it crosses.

It is a fraction, so it is dimensionless and comparable across cloths of any size. A mill quotes it as a percentage and uses it constantly, because it is the number that turns a warping calculation into a weaving calculation: to weave a hundred metres of cloth with eight per cent warp crimp, a hundred and eight metres of warp have to be put on the beam.

Getting that wrong is expensive in an immediately visible way, which is why crimp is one of the better-measured numbers in the trade.

Where it comes from #

Crimp is bought entirely by interlacings. A thread only deviates from straight where it changes face; along a float it runs flat and costs nothing.

So the ordering follows the interlacing count exactly: plain weave crimps most, twill less, satin least. It is the same trade appearing for the fourth or fifth time on this site, which is what happens when a subject has one dominant variable.

There is a second contributor that a draft cannot see. The two thread systems compete: whichever is under more tension during weaving stays straighter and forces the other to do more of the bending. A warp woven tight and a weft beaten lightly gives a cloth with low warp crimp and high weft crimp, from the same draft. Crimp is therefore partly a structural quantity and partly a processing one, which is why it is measured rather than only computed.

The interchange #

Now the consequence that surprises people.

Pull a woven fabric along the warp. The threads do not stretch — a cotton yarn breaks at a few per cent and the fabric extends more than that without damage — so the extension has to come from somewhere else. It comes from the warp crimp: the warp straightens.

But the warp straightening means it no longer pushes the weft out of line as far, so the weft has to take up more of the bending. Weft crimp rises. And a weft with more crimp spans less distance, so the cloth narrows.

That is crimp interchange, and it is the mechanism behind a great many everyday observations: why a bandage narrows as it is stretched, why a woven tape pulls in, why cloth wound on a roll under tension is narrower than the same cloth relaxed, and why fabric measurements taken under any tension at all are not measurements of the fabric.

What is conserved #

The figure above asserts something rather than merely drawing it, and the assertion is the point.

Both thread lengths are computed before and after. The warp is $(1 + c_1) L_1$ and the weft is $(1 + c_2) L_2$, and both must be identical in the two states to arithmetic precision. A figure in which a thread had changed length would throw and the build would stop.

That is a small check and it earns its place, because “the yarn does not stretch” is the entire content of the argument. An account of crimp interchange in which the thread lengths quietly drifted would be describing something else — a fabric of elastic yarn, which behaves quite differently and is a genuinely separate subject.

Shrinkage is the same fact #

A fabric that has been kept under tension and is then released does the interchange in reverse, and the trade calls the result shrinkage.

Cloth is woven with the warp under considerable tension and is wound onto a roll still under it. The warp is therefore straighter in the roll than it wants to be, and the weft is correspondingly less crimped. Wash the fabric, relax it, and the warp takes back its crimp — so the cloth gets shorter along the warp, and wider across it.

That is relaxation shrinkage, and it is a rearrangement rather than a change in any fibre. It is completely reversible in principle: stretch the cloth again and the length comes back. It is distinct from fibre shrinkage, where the material itself changes dimension on wetting, which is not reversible and which affects wool and viscose far more than cotton.

Mills deal with the first by compacting the fabric before it is sold — mechanically over-feeding it so that the warp is pushed into more crimp than it will settle at, so that washing lets it out rather than takes it up. Sanforizing is the best-known version and the name is a trademark from the 1930s.

The moral is the one that keeps recurring here: when a fabric appears to do something a material could not, the explanation is usually that a length has been moved rather than changed.

Why the extension is bounded #

A material that stretches has no natural limit short of breaking. A mechanism does, and crimp interchange is a mechanism.

The extension available along the warp is exactly the warp crimp: once the warp is straight, there is nothing left to take out, and any further extension has to come from stretching fibres. So a plain weave with eight per cent warp crimp gives about eight per cent and then becomes very stiff indeed.

That is why woven fabric has the characteristic feel it does — easy at first and then abruptly firm. The knee in the curve is where crimp runs out, and it is the reason woven cloth holds its shape while a knit does not.

It also explains why a satin gives so little. Its crimp is small, so its available extension is small, and a satin lining feels dead in the thread directions where a plain-weave shirting gives a little.

Two directions, one budget #

Crimp is not distributed symmetrically, and the asymmetry is designed for.

A cloth woven with high warp tension has low warp crimp and high weft crimp; woven with low warp tension, the reverse. The total is roughly fixed by the geometry — the threads have to get past each other somehow — but how it is split between the two systems is a processing choice.

The consequence is that a fabric can be made to extend more in one direction than the other from the same draft, which matters for anything cut on the straight grain. Shirting is usually woven with more crimp in the weft, so it gives across the body rather than along it.

Because the split is set on the loom and not by the weave, it is one of the places where the weave matrix genuinely cannot help. The draft is symmetric between warp and weft in a balanced weave, and the finished cloth need not be.

Measuring it #

Crimp is one of the few numbers in this subject that is properly measured rather than computed, and the procedure is worth knowing because it explains why the figures on this page are illustration.

Take a marked length of cloth — say ten centimetres along the warp. Unravel a thread from it. Straighten that thread under a small standard tension, just enough to remove the waviness without stretching the fibre, and measure it. The crimp is the excess over ten centimetres, as a fraction.

The standard tension is where the difficulty lives. Too little and residual waviness inflates the answer; too much and the fibre extends and deflates it. Standards specify it in terms of the yarn’s linear density, and results are quoted with the tension used.

Typical values are smaller than the figures here suggest. A shirting might have four to eight per cent in the warp and a little more in the weft; a heavy plain-weave canvas rather more; a satin two or three. The site’s sections exaggerate the thread thickness so that the interlacing is visible at all, which inflates the measurement several-fold, and every one of them says so.

Why a cut edge behaves oddly #

One practical consequence of the interchange that anybody who has sewn has met.

A strip cut from a piece of cloth along the warp will narrow as it is handled, more than seems reasonable for its width. The reason is that the strip is free to interchange: nothing holds its width, so any lengthways tension immediately converts warp crimp into weft crimp and pulls the edges in.

The same strip cut on the bias does something far more dramatic, because there a second and much larger mechanism is available. A bias strip narrows enormously, and the narrowing is shear rather than interchange. Anyone who has cut bias binding has watched a two-inch strip become an inch and a half in the hand.

The remedy in both cases is the same and it is old: stabilise the edge before handling it. Fusible tape along a cut edge, a line of stay-stitching, or simply not letting the piece hang under its own weight. Every one of those is preventing a rearrangement rather than resisting a force, which is why very light stabilisation works.

Which model, and why it matters #

Every crimp number depends on a model of what a thread does at a crossing, and there are several.

Peirce’s geometry, published in 1937, is the reference. It treats the yarn as a circular cylinder of fixed diameter and the thread path as circular arcs at the crossings joined by straight lines between them, and derives exact relations between crimp, thread spacing, yarn diameter and cloth thickness. It is the model this site’s figures use, and it is the one the trade quotes.

The racetrack model replaces the circular section with a rectangle capped by semicircles, which is closer to what a gripped yarn actually looks like. The elliptical model uses an ellipse. Both allow the yarn to flatten, both give lower crimp for the same cloth than Peirce does, and they disagree with each other by ten or twenty per cent.

The disagreement is not a scandal; it is what happens when a model has to choose an idealisation. What matters is that a number is quoted with the model that produced it, because two sources giving different crimps for the same cloth are usually not disagreeing about the cloth.

Where the figures overstate #

An honesty note about this site’s own drawings.

The section figures here draw the yarn thick relative to the thread spacing, because a section drawn to a realistic ratio is nearly a straight line and shows nothing. That exaggeration inflates the crimp the figure measures: the numbers printed are several times larger than a real fabric’s, and every such figure says so in its own caption.

What survives the exaggeration is the ordering — plain, then twill, then satin — because the exaggeration applies equally to all of them. That is the claim the figures are making, and the absolute numbers are illustration rather than measurement.

Why the two systems do not crimp equally #

One more asymmetry, and it is the reason crimp has to be measured rather than only computed.

The two thread systems compete for the same space. Whichever is under more tension during weaving stays straighter and forces the other to do more of the bending. A warp held tight and a weft beaten lightly gives a cloth with low warp crimp and high weft crimp; slacken the warp and the balance reverses.

So the split between the two is a processing variable, not a structural one. The same draft on the same yarn can be woven to give a fabric that extends more along the warp or more across it, and neither is more correct.

Mills exploit it. Shirting is usually woven with more crimp in the weft, so it gives across the body rather than along it, which is where a shirt needs to move. That choice is made at the loom and is invisible in the draft.

The total is roughly fixed by the geometry — the threads have to get past one another somehow — so what is being chosen is a split rather than an amount. That makes crimp one of the few numbers in this subject where the structure sets a budget and the process spends it.

What the interchange is worth, as an exchange rate #

The interchange is drawn above at one extension and described as a rearrangement. It has a rate, and the rate is the quantity a garment engineer actually meets.

Because both thread lengths are conserved, the states a cloth can reach form a one-dimensional curve, and moving along it the ratio of the two fractional changes is a single number — how much width the cloth gives up per unit of length it gains. For an ordinary shirting that is about 0.73 per cent of width for every one per cent of length, and it is not a constant: it drifts by a fifth of itself for every percentage point of extension, so it is a reading at a state rather than a property.

What is worth having here is the sign and the size rather than the value, because they explain a family of complaints the trade treats separately.

A woven tape narrows as it is pulled, and it narrows by nearly as much as it lengthens. A bandage, a webbing, a seam binding: each loses close to one per cent of its width for each per cent of extension, which on a fifty-millimetre tape at five per cent is two and a half millimetres. That is a visible and often a functional loss.

A cloth wound under tension loses width, for the same reason and by the same rate, which is why a roll measured on the machine and the same cloth measured relaxed disagree — and why the disagreement is largest for the fabric that was wound hardest.

And a shirting gives across the body rather than along it because the trade puts the greater crimp in the weft, which is the direction with the greater budget to spend. That is a choice made at the loom and it decides which of the two directions has the useful give and which has the awkward narrowing.

Which is why the two directions have to be quoted together #

A crimp quoted for one direction is not half of the information; it is a number whose meaning depends on the other one, and quoting it alone is closer to quoting nothing.

The reason is that the two crimps are not independent quantities. A cloth’s two thread systems occupy the same thickness, so the amplitude one system’s crimp needs is supplied by the other system’s diameter — and a cloth with eight per cent in the warp and one in the weft is a different construction from one with eight and four, not a coarser measurement of it. The first has almost all its interchange budget in one direction and a weft that is effectively straight; the second is nearer balanced and will behave differently in both. A specification naming only the warp cannot tell them apart.

And the sum of the two is very nearly fixed by the yarns and the sett. Whatever thickness the cloth has to accommodate has to be accommodated, so raising one crimp lowers the other rather than adding to it. That is what makes the pair a budget and a single figure a share of an unstated total: a warp crimp of eight per cent means one thing in a cloth whose total is nine and another in a cloth whose total is fourteen, and nothing on the ticket says which.

The practical form of this is the one a finisher meets. Every wet process moves crimp from one system to the other without changing the sum, so a cloth can be finished to a stated warp crimp by taking it out of the weft — and it will then shrink in the weft, in wear, by exactly what was taken. A specification that gates on one direction is a specification that can be met by moving the problem into the other, which is precisely what happens.

The rate is bounded above and below by two events #

The exchange rate is not free to be anything, and the two things that bound it are the two ways a locus can end.

At one end the warp goes straight. There is no crimp left in it to give, so further extension has to stretch the yarn, and the cloth has stopped narrowing because the weft has stopped taking anything up. The rate goes to zero there: length without width.

At the other end the weft jams. Its threads are touching and can accept no more crimp, so the cloth has stopped shortening in the warp direction while the width is still moving. The rate runs away there: width without length.

So a cloth’s exchange rate sweeps from nothing to unbounded across its own locus, and the value anybody quotes is a point somewhere in the middle of that sweep. Which end a given cloth is nearer decides how it behaves in the hand: a cloth near the straight-warp end gives length cheaply and holds its width, and one near the jammed-weft end narrows dramatically for very little extension.

That is the shape a designer can use, because the two ends are set by the construction rather than by the yarn. An open cloth sits far from both ends and has a long, gentle exchange; a close one sits near the jam and narrows violently. The trade’s own preference for shirtings at sixty or seventy per cent of their jamming sett is a preference for the middle of that curve, arrived at by feel and explained here as a distance from two boundaries.

And it says which fabrics should never be cut on the straight for anything that will be pulled. A closely set cloth pulled along its length loses width faster than it gains length, which is a tape that necks, a strap that cuts, and a seam that draws in — every one of them a consequence of being near a jam rather than of anything about the fibre.

The exchange rate is one number describing a trade between two dimensions, so quoting the extension of a fabric in one direction without the contraction in the other reports half of what happened.

That is not a fastidiousness. A fabric that extends five per cent along the warp has narrowed by three or four per cent across it, and a garment panel cut to a measured length has arrived at a width nobody measured. Where the two panels are seamed together the mismatch is a pucker, and the usual diagnosis is a sewing fault.

The rule that follows is short. Measure a fabric’s extension and its contraction at the same time and at the same extension, because they are one measurement of one mechanism and separating them loses the only thing the pair says: that no length was created or destroyed, and every millimetre the cloth gained one way it gave up the other.

Where the ladder goes next #

The geometry underneath all of this is how close threads can be set, which is the same models applied to a different question.

The measurement crimp interferes with is thread count, since a fabric under tension has a different count from the same fabric relaxed.

And the other place a fabric moves without anything stretching is the bias, where the mechanism is shear rather than crimp and the extension available is far larger.

What the pictures here cannot show. Every section on this page is a geometric idealisation with a fixed circular yarn. A real thread flattens where it is gripped, is hairy, and is under a tension that varies along its length — and the crimp of a real fabric is measured by unravelling it and straightening the thread, which no drawing can do.