Textile Structure
how cloth is put together
Setting and geometry

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.
14 min read 7 figures Measured, not claimedStructure before fibre

Ask how many threads go into an inch of cloth and there are two answers. One is a choice, and the other is a ceiling that no amount of choosing can exceed.

What an interlacing costsEach weave's interlacing count beside the closest it can be set in the same yarn. The two run opposite ways, because a thread that changes face often has to bend often and a bend takes room.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
Fig. 1 The ceiling, for several weaves in one yarn. Plain weave jams at about twenty threads to the inch and an eight-end satin at about thirty-two, which is the same yarn and sixty per cent more threads.

The ceiling is geometric. At some spacing the threads are touching, and there is nowhere for another one to go.

What jamming means

Take a woven cloth and push the picks closer together. At first they move. Then the warp, which has to bend round each pick, runs out of room to make its bends in, and the cloth resists absolutely rather than stiffly. That state is jamming, and it is where every geometric setting theory tries to locate the maximum.

Two things are jammed at once and they are worth separating. Warp jamming is the ends touching each other; weft jamming is the picks touching. A cloth can be jammed in one direction and open in the other, which is exactly what a warp-faced cloth like denim is.

The condition is that the space taken by the threads themselves plus the space their crossings demand fills the available width. Both terms depend on yarn diameter, and the second depends on how often the thread changes face — which is why the weave enters at all.

Why an interlacing costs room

The mechanism was set out in the essay on firmness and it bears restating in one sentence: a thread that changes face has to travel from one side of the crossing plane to the other, and that travel needs horizontal distance.

Crowd the threads and the distance available for each transition shrinks. Eventually the thread is running vertically between crossings, the bend is as sharp as the geometry permits, and the neighbouring threads are in contact. Nothing more will go in.

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. 2 The transitions that consume the room, in the weave that has the most of them. Every crossing is a face change and every face change needs horizontal distance to happen in — which is why plain weave jams at a lower thread count than anything else.

A weave with fewer interlacings has fewer transitions to accommodate, so more threads fit. That is the whole of the weave’s contribution, and it is a large contribution.

Ashenhurst, and what a Victorian rule is for

The first usable version of this calculation is Thomas Ashenhurst’s, from Bradford in the 1880s, and it is still quoted in mill practice.

Ashenhurst’s insight was to count the crossings. The width a repeat must occupy is the threads in it, each taking one diameter, plus one further diameter for each place a crossing thread has to pass through. Divide the number of threads in the repeat by that width and the maximum sett falls out.

The result is crude. It treats yarn as an incompressible circle, ignores that a gripped thread flattens, and takes no account of how the crossings are arranged rather than merely how many there are. It gives maxima below what a mill can actually weave.

What makes it good engineering rather than bad physics is that it is wrong by a consistent margin in a known direction for a comprehensible reason. A practitioner applies a correction factor and gets a usable number for a cloth nobody has made — which is exactly what a mill needs and what experience alone cannot supply.

Peirce, and what a careful model buys

Frederick Peirce’s 1937 geometry is the serious treatment, and it changed the subject from rules to relations.

Peirce modelled the thread path properly: circular yarn cross-sections still, but the path taken as circular arcs where a thread wraps a crossing, joined by straight lines where it does not. From that he derived a set of relations connecting thread spacing, yarn diameter, crimp, weave angle and cloth thickness — so that given any few of them the rest follow.

The jammed state falls out as a limiting case rather than as a separate rule, which is the mark of a model that is doing real work. And because the relations are exact within the model, they can be inverted: a mill can ask what sett gives a required cover, or what crimp a required sett implies.

The circular assumption is where it is vulnerable, and everybody has known that since it was published. A yarn in cloth is squashed at the crossings and rounder along the floats, so its effective width varies along its own length.

The two directions are set separately

A cloth has two setts and they are chosen independently, which the single word “sett” obscures.

Ends per inch is fixed at warping and threading: the warp is wound, threaded through the heddles and the reed, and its spacing is settled before a single pick is thrown. Changing it means rebuilding the warp.

Picks per inch is fixed during weaving, by how hard each pick is beaten up against the cloth already made. It can be changed on the fly, and it is the variable a weaver actually controls.

That asymmetry has consequences. A mill running one warp can produce several cloths from it by varying the picks — heavier and lighter versions of the same fabric — and it is a cheap way to extend a range. It is also why warp-dense cloths are common and weft-dense ones less so: crowding the warp is a decision made once, and crowding the weft costs loom time on every pick.

The 3/1 twillThe 3/1 twill 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.3/1 twilllongest float 316 interlacings per repeat1 separable clothrepeat 4 × 4generated, then counted4×4
Fig. 3 A warp-faced twill, the structure that goes with a warp-dense sett. The face is three quarters warp, the warp is crowded, and the weft is comparatively open — a combination chosen together rather than arrived at separately.

The two constraints also interact. Crowding the warp leaves less room for the weft to be beaten in, so a very warp-dense cloth has a lower maximum in the weft than the same weave loosely warped — which is why the jamming condition has to be evaluated for the cloth rather than for each direction alone.

Racetrack, ellipse, and the ten per cent

Two later families relax the circle in different ways.

The racetrack section is a rectangle with semicircular ends: a yarn free to flatten to a chosen ratio and no further. The elliptical section is what it says. Both allow a gripped thread to spread, which means it takes less vertical room and more horizontal room, which means the cloth jams at a higher thread count than Peirce predicts.

The three models disagree by ten or twenty per cent on the same cloth, and the disagreement is not resolvable by being cleverer — it is a disagreement about which idealisation to make. Real yarn flattens by an amount that depends on its twist, its fibre, the tension it was woven under and how the cloth was finished, and none of that is in any of the models.

So the honest position is the one this site takes everywhere: the model that produced a number is named. The ordering across weaves is robust and every model agrees on it; the absolute values are not, and quoting one without its provenance is how two internally consistent sources come to disagree permanently.

Nobody weaves at the maximum

The ceiling is a reference point rather than a target, and cloths woven at it are usually bad.

A jammed cloth has no room for the threads to move. It cannot shear, so it has no bias and drapes badly. It is stiff. It uses a great deal of yarn. And it is hard to weave, because the reed has to force each pick into a space that barely accepts it, which strains the warp and slows the loom.

A trellis sheared 25°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 25°bias +19.3%across -24.0%area 91%locks at 46°every segment checked against its own lengthno thread stretches
Fig. 4 Why a dense cloth has little bias. Shearing closes the space between parallel threads, so a cloth already near its jamming point locks almost immediately — the mechanism is still there and there is nowhere for it to go.

So setts are quoted as a percentage of the maximum: perhaps sixty to eighty per cent for clothing, higher for a cloth that must be windproof, lower for something meant to fall in folds. That percentage is comparable across weaves and yarns in a way a raw thread count is not, which is one more reason to prefer it to the number on the packet.

Where a cloth actually sits

Real cloths occupy a fairly narrow band below the ceiling, and knowing the band is more useful than knowing the ceiling.

A shirting runs at perhaps sixty to seventy per cent of maximum: firm enough to hold its shape, open enough to drape and to breathe. A windproof or waterproof cloth runs at ninety per cent or above, which is where the air permeability falls off sharply. A voile or a georgette runs at thirty or forty, and is deliberately open.

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 A moderately set twill in section — a two-and-two structure at the sort of density most clothing uses. The threads have room to move at their crossings, which is what gives the cloth its drape and its bias.

The band is narrow because both ends are bad. Above about ninety per cent the cloth is stiff, expensive in yarn and hard to weave; below about thirty it is not really a fabric. Almost the entire useful world of woven cloth lives in a factor of three, and where a fabric sits in it predicts more about how it will behave than its fibre does.

That is the fourth or fifth time on this site that a single geometric ratio has turned out to organise a whole family of properties, and it is the same trade every time: compliance against firmness, bought with space.

What the ceiling is used for

Three practical jobs, and they are the reason a Victorian rule survives.

Designing a cloth that does not exist yet. Given a yarn and an intended weave, the maximum sett says whether the specification is possible before anything is warped. A specification above the ceiling is not ambitious; it is impossible, and finding that out on the loom is expensive.

Comparing across weaves. A percentage of maximum is comparable where a raw count is not. Two cloths at seventy per cent of their respective maxima are similarly set, whatever their thread counts say.

Predicting behaviour. Where a cloth sits relative to its ceiling predicts its handle, its drape, its air permeability and how much bias it has, and it does so across yarns and weaves. A cloth at ninety-five per cent is stiff and windproof whatever it is made of; one at fifty is soft and open.

The same thread count, twiceTwo cloths with identical thread counts and different yarn. The count is the same number in both; the fraction of the surface the threads actually occupy is not, and that fraction is what thread count is usually taken to mean.100 ends and 100 picks per inch in bothfine yarncover 78%coarser yarncover 97%cover from diameter and spacing, circular sections
Fig. 6 The quantity a setting calculation is usually reaching for. Cover is what a mill wants to hit; the maximum sett is the constraint it has to hit it within, and the two are different numbers that get conflated constantly.

The general shape is familiar from any engineering constraint. The ceiling is rarely the design point, and knowing where it is turns a set of intuitions into a design space that can be reasoned about. That was Ashenhurst’s contribution, and it is why a crude model that is honest about being crude has outlived several more accurate ones.

The two limits that are not this one

Two other ceilings get confused with jamming and are different.

Cover reaching one hundred per cent means the threads leave no visible gap. That happens before jamming in most weaves, because a cloth can be optically solid while the threads still have room to move — which is why a cloth can look dense and still drape.

Locking is the shear limit rather than the setting limit. It is the angle at which threads jam against their parallel neighbours when the cloth is sheared, and it is a different geometry with a different formula. Its own essay takes it up, and the two are related — a densely set cloth locks at a smaller shear — without being the same quantity.

Where the model stops

Three limits, and the first is the largest.

It is geometry, not mechanics. The calculation says when threads touch. It says nothing about the force required to get them there, and a cloth can be beaten up harder at the cost of straining the warp. Practical maxima are a matter of what the loom and the yarn will tolerate as much as of what the geometry permits.

Yarn is compressible. Real threads flatten and their fibres migrate, so a jammed cloth is not a rigid packing of circles. Every model that takes this seriously gets a different answer.

Finishing moves the sett. Cloth relaxes, shrinks and is often deliberately compacted after weaving, so the sett in the loom and the sett in the hand are different numbers — sometimes by ten per cent, occasionally by more. A quoted sett should say which.

Why the ceiling is a weave property at all

It is worth closing on the thing that makes this calculation interesting rather than merely useful.

A naive account would say the maximum thread count is a property of the yarn: threads have a diameter, an inch is an inch, and the answer is one divided by the other. That would give the same maximum for every weave, and it is wrong by a factor approaching two.

The extra factor is entirely structural. It comes from the crossings, and its size is set by how many of them there are — which is the interlacing count, the same number behind firmness, crimp, drape and lustre.

The 8-end satinThe 8-end satin 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.8-end satinlongest float 732 interlacings per repeat1 separable clothrepeat 8 × 8generated, then counted8×8
Fig. 7 The extreme case. One interlacing per end per repeat, so almost no room is spent on transitions and almost all of it on thread — which is why this structure carries more threads per inch than any other in the same yarn.

So the sett ceiling is not a yarn fact with a weave correction. It is a weave fact scaled by the yarn, and that ordering matters: change the yarn and every weave’s ceiling moves together, but change the weave and the ceilings move relative to one another. The structure decides the shape of the answer and the yarn decides its size, which is the site’s organising claim turning up once more.

Where the ladder goes next

The other geometric ceiling is the locking angle, which limits shear rather than setting and matters wherever cloth has to go round a curve.

The measurement this one is confused with is thread count, and the structural variable behind both is the interlacing count.

What the pictures here cannot show. Every setting figure on this page assumes a circular yarn of one fixed diameter, which is Peirce’s assumption and not a fact about thread. Flattening, twist, hairiness and the tension history of the cloth are all absent, and they are between them the reason a mill’s numbers differ from a geometric model’s.

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. 100 ends and 100 picks per inch in bothfine yarncover 78%coarser yarncover 97%cover from diameter and spacing, circular sections Thread count is not quality It counts threads. It says nothing about how much of the cloth they cover, it can be inflated by counting plies, and it ranks fabrics in nearly the wrong order. The quantity it is mistaken for is cover factor, and that one is computable. 0%10%20%30%40%0°15°30°45°60°cover 40%locks at 66°, +38%cover 60%locks at 53°, +34%cover 80%locks at 37°, +26%extension along the biasshear anglethe yarns never stretch; the net changes shape The locking angle The bias runs out at an angle that yarn diameter and thread spacing decide between them. It is the number behind whether a cloth will go round a curve, and it has nothing to do with how strong the fabric is.