Textile Structure
how cloth is put together
Setting and geometry

Crimp, and why cloth narrows when it is pulled

A thread in cloth is longer than the cloth it crosses. Pull the fabric one way and that extra length is taken out of one direction and put into the other, so the cloth gets narrower without a single fibre stretching.
14 min read 7 figures Measured, not claimedA mechanism, not a material

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.

A warp end in section — plainOne warp thread drawn through the cloth, with the weft threads it crosses shown end-on. The thread is longer than the cloth it spans, and the excess is the crimp — measured here from the drawn path rather than quoted beside it.the cloth this thread spansplainwarp crimp 22.3%8 interlacings per repeatso the crimp shown exceeds a real cloth'sthread thickness exaggerated for legibility3 face changes
Fig. 1 A warp end through a plain weave, with the wefts it crosses shown end-on. The thread travels up and down at every crossing, so the length of the path exceeds the width it spans — and the excess is the crimp, measured here off the drawn path. The thread thickness is exaggerated for legibility, so the figure overstates the effect.

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.

A warp end in section — 8-end satinOne warp thread drawn through the cloth, with the weft threads it crosses shown end-on. The thread is longer than the cloth it spans, and the excess is the crimp — measured here from the drawn path rather than quoted beside it.the cloth this thread spans8-end satinwarp crimp 3.2%32 interlacings per repeatso the crimp shown exceeds a real cloth'sthread thickness exaggerated for legibility1 face change
Fig. 2 The same measurement in an eight-end satin. Seven crossings in eight are travelled flat and only the eighth costs anything, so the crimp is a fraction of plain weave’s.

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.

Pull it lengthways and it narrowsThe same cloth before and after a small extension along the warp. No thread has stretched: the extension came out of the warp crimp, that crimp went into the weft, and the fabric is narrower for it.as wovenwarp crimp 8.0% · weft 4.0%pulled 3% along the warpwarp crimp 4.9% · weft 7.1%warp thread 108.0 and weft 104.0 — unchanged in bothboth thread lengths checked, not assumed3% pull
Fig. 3 The same cloth before and after a three per cent extension along the warp. Warp crimp falls, weft crimp rises, and the fabric is narrower for it. Both thread lengths are the same in both states, which the figure checks rather than assumes.

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+c1)L1(1 + c_1) L_1 and the weft is (1+c2)L2(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.

Pull it lengthways and it narrowsThe same cloth before and after a small extension along the warp. No thread has stretched: the extension came out of the warp crimp, that crimp went into the weft, and the fabric is narrower for it.as wovenwarp crimp 8.0% · weft 4.0%pulled 5% along the warpwarp crimp 2.9% · weft 9.1%warp thread 108.0 and weft 104.0 — unchanged in bothboth thread lengths checked, not assumed5% pull
Fig. 4 The same interchange at a larger extension. Read the figure right to left instead and it is relaxation shrinkage: a cloth held stretched along the warp, released, taking its crimp back and becoming shorter and wider.

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.

A warp end in section — 2/2 twillOne warp thread drawn through the cloth, with the weft threads it crosses shown end-on. The thread is longer than the cloth it spans, and the excess is the crimp — measured here from the drawn path rather than quoted beside it.the cloth this thread spans2/2 twillwarp crimp 12.7%16 interlacings per repeatso the crimp shown exceeds a real cloth'sthread thickness exaggerated for legibility4 face changes
Fig. 5 The quantity being measured, in a two-and-two twill: the length of the drawn path against the width it spans. A real measurement does this by taking the thread out and straightening it, which is why crimp is known to better precision than most structural numbers.

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.

A trellis sheared 20°The net at an angle, with every thread segment exactly the length it started at. The extension along the diagonal is the bias stretch, and it is a change of shape rather than a change of length.shear 20°bias +15.8%across -18.9%area 94%locks at 60°every segment checked against its own lengthno thread stretches
Fig. 6 The larger of the two mechanisms, for comparison. Crimp interchange gives a few per cent; shear gives tens of per cent, and it is available only at an angle to the threads.

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.

The plainThe plain on point paper, a filled square meaning the warp is on the face. Its longest float, its interlacing count and the number of separable cloths it describes were all counted from the matrix that drew it.plainlongest float 18 interlacings per repeat1 separable clothrepeat 2 × 2generated, then counted2×2
Fig. 7 A draft that is perfectly symmetric between its two directions. Everything the matrix knows about this cloth treats warp and weft alike, and the finished fabric need not — which is one of the clearer places where the structural account is incomplete.

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.

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.

Where this goes next

weaveinterlacingsdensest settingplain1.0020 per inch2/2 basket0.5027 per inch2/1 twill0.6724 per inch2/2 twill0.5027 per inch3/1 twill0.5027 per inch5-end satin0.4029 per inch8-end satin0.2532 per incha geometric jamming model, circular sections, yarn diameter 1/40 inch Interlacings and firmness Every time a thread changes face it has to bend, and a bend takes room. That one sentence decides how densely a cloth can be set, how firm it feels, and why the two run in opposite directions. weaveinterlacingsdensest settingplain1.0020 per inch2/2 basket0.5027 per inch2/1 twill0.6724 per inch2/2 twill0.5027 per inch3/1 twill0.5027 per inch5-end satin0.4029 per inch8-end satin0.2532 per incha geometric jamming model, circular sections, yarn diameter 1/40 inch How close can threads be set There is a maximum. Push more threads into a cloth than the geometry allows and they simply will not go, and the limit depends on the weave as much as on the yarn. shear 30°bias +22.5%across -29.3%area 87%locks at 60°every segment checked against its own lengthno thread stretches The bias is a mechanism Cloth cut at forty-five degrees stretches by a third and springs back, while the threads in it stretch by nothing at all. Almost every explanation given for this is wrong, and the right one is not about elasticity.