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Most of what is said about fabric is a slogan that quotes a mechanism and forgets its stop. Bias-cut cloth stretches half as much again is the standing example: the mechanism is real, the ceiling is 41.4 per cent at any shear whatever, and a real cloth jams well short of that. A claim of that shape survives because it sounds like a measurement.
There are 89 of them below. Each carries the verdict, what was found instead, and — the column that matters — the quantity that settles it, computed while this page is built from the same libraries the figures are drawn from. None of these numbers is typed in. If one of them stopped agreeing with the essay it points at, the build would stop rather than serve the page.
The verdicts are not all wrong, and the interesting ones are not. Almost nothing in this subject is simply false; the common failure is a true mechanism quoted past its own domain, which is why several rows below say right about one quantity, wrong about another. Distinguishing the two is most of the work.
A higher thread count means a better cloth.
Wrong. Thread count counts threads. What a person judging a sheet by holding it to the light is actually seeing is the open fraction, which is (1 − K)² and moves as the square of the cover. Two 200-count cloths in yarns a factor of two apart in diameter cover 56% and 89% of their surface — a ratio of 1.6, and unimpressive — while the gap between the threads goes from 44% to 11%, which is exactly a factor of four.
What settles it: open fraction 44.4% against 11.1% — a factor of 4.0 at the same thread count. Argued in Thread count is not quality.
Cloth cut on the bias stretches half as much again.
Outside the mechanism. The trellis cell is a rhombus, so the extension along its long diagonal is √2·cos(45° − γ/2) − 1, largest when the net has closed flat. That ceiling is √2 − 1 at any shear whatever, so half as much again is not an optimistic reading of the mechanism — it is outside it. Real cloth stops far short because the threads jam first.
What settles it: a ceiling of 41.4% at any shear whatever; 38.4% at a cover of 0.4 and 26.5% at 0.8. Argued in Why a knit recovers and a woven does not.
A satin can be woven on any number of shafts.
Wrong. A regular satin steps by a move coprime with its order, so the moves available are Euler's totient less the two that give a twill. On four ends and on six there are none at all, and no ingenuity supplies one: the arithmetic decided it before anybody wove anything.
What settles it: satin moves on 4, 5, 6, 8 ends: 4→0, 5→2, 6→0, 8→2. Argued in There is no satin on six ends.
A twill's diagonal is a thread running diagonally.
Wrong. No thread in a woven cloth runs diagonally. Every warp end runs warpwise and every pick runs weftwise; what runs diagonally is the pattern of which of them is on top, which is a different kind of object and belongs to the matrix rather than to the yarn.
What settles it: every float in a 2/2 twill runs along a thread — 2 warpwise, 2 weftwise — and none runs diagonally, because no thread does. Argued in The diagonal is not a thread.
A twill line runs at forty-five degrees.
Only in a square-set cloth. The line climbs one pick for every step ends, so its angle is the arctangent of the warp sett over the weft sett times the step. Forty-five degrees is what a balanced sett gives, and most cloths are not balanced. A shirting at 120 × 80 puts its twill at 56°.
What settles it: 45° at 100 × 100, 56° at 120 × 80. Argued in Twill direction, and how it is named.
A draft in which every thread interlaces describes a cloth.
Wrong. Interlacing everywhere is necessary and not sufficient. A draft is one cloth exactly when the above-and-below relation on its threads is strongly connected, and 144 of the 22,874 four-by-four drafts that interlace everywhere fail it — they describe two fabrics lying on one another, and nothing about the drawing betrays it.
What settles it: 144 of 22,874 interlacing four-by-four drafts are not one cloth. Argued in Does it hang together.
All seventeen plane groups occur in weaving.
Wrong. Twelve occur. The five missing ones all require a three-fold rotation, and a draft's symmetries must permute the intersections of warp and weft — so the linear part lies in the symmetries of the square, among which there is no element of order three. It holds at every repeat size, not only at four.
What settles it: 12 groups occur among the census; 5 are unreachable at any repeat size. Argued in The seventeen groups a draft can have.
A colour-and-weave effect tells you what the weave is.
Wrong. Where the two threads crossing are the same colour the intersection looks identical whichever is on top, so the weave leaves no trace there. On a one-and-one order half the intersections are blind, and the whole census collapses onto a few hundred surfaces with dozens of drafts apiece that no eye can separate.
What settles it: 8 of 16 intersections blind; 22,874 drafts collapse onto 256 surfaces, 89 apiece. Argued in Colour and weave as a two-colour problem.
A double cloth stitched here and there is still two cloths.
Depends where, and half the places are fatal. Exactly half of a double cloth's intersections are load-bearing in the sense that reversing one of them merges the two layers into one. One mistake at one of those is enough to destroy the construction, and the fabric that results looks entirely reasonable.
What settles it: 8 of 16 single stitches make the two cloths one — 50.0%. Argued in Backed and stitched constructions.
Peirce's 1/(28√Ne) is a rule of thumb with no derivation.
Right about the rule, wrong about the arithmetic. Setting the 1937 diameter equal to the one conservation of volume gives leaves the packing factor as the only unknown, and inverting it returns 0.601 — the accepted figure for a ring-spun cotton yarn, which is not a number anybody chose for the convenience of the constant.
What settles it: the constant implies a packing factor of 0.601. Argued in The yarn count systems, and why there are several.
Which yarn cross-section model you pick hardly matters.
Right about the sett, wrong about the thickness. Peirce's circle and Kemp's racetrack, given the same yarn and the same closure condition, predict jammed setts within an eighth of each other and cloth thicknesses a third apart. Anyone comparing them on the quantity they were introduced to argue about would conclude the choice was academic.
What settles it: the two models are 4.4% apart on the jammed sett and 33.7% apart on the thickness of the same cloth. Argued in Peirce against the racetrack, measured.
The same thread count means the same density whatever the weave.
Wrong. A thread that changes face has to bend, and a bend takes room, so the closest a cloth can be set falls with the number of interlacings. A plain weave and an eight-end satin in the same yarn differ by more than half again in the sett they will accept, which is why the same count on the label means different cloths.
What settles it: 20 per inch in plain against 32 in an eight-end satin, same yarn. Argued in Interlacings and firmness.
Reversing a twill is free.
Wrong for the reversal everybody draws. A point reversal duplicates exactly two ends per repeat at every width and lengthens the longest float from two to four — the cracked line a weaver curses. The clean reversal duplicates none and lengthens it to three. Nothing on the point paper announces which one has been drawn.
What settles it: at width 4: the point reversal duplicates 2 ends and runs a float of 4; the clean one duplicates 0 and runs 3. Argued in Broken and herringbone twills.
A knit stretches because the yarn in it is elastic.
Wrong. Four mechanisms make a fabric longer with no yarn stretching at all — warp crimp, weft crimp, the bias, and a rib's fold opening out — and they are worth wildly different amounts. The rib's is the largest by a wide margin and none of them is elasticity.
What settles it: the bias contributes at most 41.4%, and it is the ceiling of a mechanism rather than a property of the fibre. Argued in Why a knit recovers and a woven does not.
A nonwoven holds together by entanglement, so there is nothing to compute.
Wrong. A random web has no repeat, so the exact integrity criterion has nothing to work on — and what replaces it is sharp rather than vague. Coherence appears at a percolation threshold, and the site's measurement brackets the published constant rather than reproducing it, which the essay says plainly.
What settles it: a threshold, bracketed between 5.4 and 5.8 against a published 5.637. Argued in Nonwovens, and what holds them together instead.
A woven cloth and a knitted one fail in the same way.
Wrong, and oppositely. Cut a woven cloth and one thread comes loose; break one loop in a knit and every loop above it follows. The difference is topology rather than strength: a woven thread's neighbours do not depend on it, and a knitted loop's does.
What settles it: removing any one of a plain weave's 6 ends leaves it one cloth — 6 of 6 — while one broken loop frees an entire knitted wale. Argued in Ravel, fray and run.
A loom with n shafts can weave a repeat of n ends.
Outside the mechanism. True of a straight draw and of nothing else. A shaft holds every end that behaves identically, so the bound is on the number of distinct columns in the matrix and not on its width. A reversed twill on ninety-six ends weaves on the four shafts its base twill needs, and the ratio grows without bound.
What settles it: a 192-end repeat on 4 shafts — 48 ends per shaft, against 1 for a straight draw. Argued in The harness does not grow.
There are 22,874 four-by-four weaves.
Wrong. That is a count of notations. Shifting the repeat's origin, turning the cloth end for end and turning it over all change the matrix and not the fabric, and quotienting by the operations that carry a piece of cloth to itself leaves 426. An earlier essay here recorded this as safe to skip on the grounds that no fraction would move; one did.
What settles it: 22,874 drafts are 426 cloths, and the separable share rises 0.63% to 1.41%. Argued in How many cloths are there.
W-fastened pile is held better than V-fastened.
Right, and not by a constant. Correct, and the reason is the capstan on the wrap angle: one half-turn against three. But how much better is decided by a friction coefficient that is measured rather than known, and across the range anyone reports for cotton the advantage runs from under three to over twelve. Quoting a single multiple as a property of the construction is the error.
What settles it: 6.6× at μ = 0.3, but 2.6× to 12.3× across μ = 0.15–0.4, for a third less pile density. Argued in How a tuft is held.
A leno holds its weft better than an openly-set plain weave.
Right, and exactly. The rare case where the friction coefficient cancels. A plain weave wraps its pick through twice the weave angle, which Peirce's geometry cannot take to a right angle at any spacing; a leno crossing is half a turn by construction and does not know the sett. So the plain weave never reaches the leno — at any sett, in any yarn, at any friction.
What settles it: closest approach 57% of the leno's grip, at the tightest sett the geometry solves — and the integrity criterion returns one cloth for both. Argued in What holds a pick in.
Damask's figure and ground are different weaves.
Wrong. They are one weave and its complement. Figure and ground need the same shafts on the same threading, carry the same longest float and the same interlacing count, and differ only in which thread system is on the surface — which is why a damask, alone among figured cloths, has no weak half.
What settles it: both on 8 shafts, both with a longest float of 7, differing by 0 in float length and by 75% of the surface. Argued in A damask is its own complement.
Corduroy and terry are two versions of the same pile fabric.
Wrong. Their pile heights share no quantity whatever. A corduroy's is half a cut weft float, so it comes from a float count and a warp sett; a terry's is half the surplus fed in by a second beam, so it comes from a let-off ratio, a group size and a pick spacing. Neither construction contains the other's parameter anywhere.
What settles it: 1.27 mm from a six-end float against 3.81 mm from a 5:1 let-off — and doubling the sett halves only the first. Argued in Terry needs two beams.
If the integrity check says one cloth, the fabric holds together.
Outside the mechanism. The criterion is topological: it asks whether a separation exists, and a separation exists or it does not. A tuft bound under one pick and a tuft bound under three are both connected; a leno gauze and the open plain weave that comes apart in the hand are both one cloth. The verdict is correct and it is not an answer about durability.
What settles it: V and W fastenings both return 1 separable cloth, and a leno and its uncrossed control both return 1 — while the capstan puts W and V 6.6× apart in holding force. Argued in The criterion cannot see friction.
The crimp in a woven reinforcement costs fibre content.
Wrong, and the sign is backwards. At a given thickness a woven fabric holds slightly MORE fibre than two flat plies of the same tows, because a crimped tow is a longer tow. What the crimp costs is stiffness, through the local off-axis angle of the path, and the two calculations are separate — which is why the trade sells non-crimp fabrics on a stiffness argument rather than a fibre-content one.
What settles it: the crimp is worth +0.46% of fibre and −6.3% of stiffness, and across four weaves the fibre content moves 0.43% against the stiffness's 6.3%. Argued in The crimp is the price of being cloth.
A woven filter can be set close enough to retain any soil.
Wrong. Retention wants a small hole and flow wants a large one, and both are functions of the sett in opposite directions. Everything cancels but a ratio: at the usual two criteria the finest soil a woven cloth can hold is 1.25 times its yarn's diameter, whatever the diameter, and below that line the answer is a nonwoven rather than a sett.
What settles it: 188 µm from a 150 µm yarn and 375 µm from a 300 µm one — 1.25 times the diameter in both cases. Argued in A filter cloth has two jobs.
A hole weakens a cloth the way it weakens a sheet.
Wrong, by a factor of thirty. A film is a continuum and concentrates stress at the hole's edge, so any hole at all costs it about two thirds of its strength. A cloth's threads carry their own load, so a hole costs exactly the threads it removes — linear in the hole, independent of the sett, and nothing at all for a slit along the load.
What settles it: a 1 mm hole in a 50 mm strip leaves 98% of the cloth and 33% of the film, and a 40 mm slit along the load leaves 100%. Argued in A cloth does not mind a hole.
More stitches make a stronger seam.
Right, then wrong. More stitches put more sewing thread across the joint and more holes through the cloth beside it, so the seam rises to a crossing and falls after it. Whether the fabric line falls at all is decided by the clear gap between two threads against the width of the needle — the same arithmetic a filter cloth is specified by.
What settles it: strongest at 16 stitches/cm at 30 threads/cm, where a needle severs a thread 80% of the time — and at 20 threads/cm the needle finds room and nothing is severed. Argued in The stitch that weakens the seam.
A pressurised braided hose keeps its length.
Wrong unless it was braided at one angle. Inflation drives the braid angle towards the one that encloses the most volume, and the hose's length is its yarn length times the cosine of that angle. So below 54.74° a hose shortens and fattens, above it lengthens and narrows, and only at arctan √2 does it do neither — an angle with no material constant in it, arrived at twice by arguments sharing no algebra.
What settles it: 54.74° from the volume maximum and 54.74° from the 2:1 stress balance, with 4 of 8 drawn angles shortening and the rest lengthening. Argued in The angle a hose wants.
A balanced cloth is the safe choice for a pressure fabric.
Wrong, and by a quarter. A closed cylinder carries exactly twice the stress around its circumference as along its axis, because that is the ratio of the two areas the pressure acts on. A cloth with equal strength both ways therefore reaches its limit in the hoop direction with the axial system at half capacity, and the utilisation is (1 + 1/R)/2.
What settles it: 25% of the fibre wasted at 2:1 and 38% at 4:1 — the field wants 20:10 rather than a balanced cloth. Argued in An inflated cylinder wants an unbalanced cloth.
Three-dimensional weaving escapes the binary matrix.
Wrong. The integrity criterion consumes contacts and a direction at each, not a matrix, so it decides a five-level orthogonal preform unchanged. What the third dimension takes away is periodicity: a thickness has a top and a bottom, and the binder's job is defined by those boundaries rather than by a repeat.
What settles it: 27 of 243 binder paths on five levels make one piece — exactly a ninth, at every thickness — and an unbound stack returns five. Argued in The third index is not a repeat.
A bigger dome needs bigger darts.
Wrong. The total angle a pattern must remove is the surface's total curvature, which is a pure number: a hemisphere costs one full turn whatever its radius. Scaling a pattern lengthens its darts and leaves their angles alone — and how much of the total the cloth can supply by shearing instead is a property of its sett.
What settles it: 360° at a radius of 3 mm and 360° at 3 km, while the areas differ by a factor of 1e+12. Argued in A hemisphere costs one full turn.
Bias cutting wastes half the cloth.
Wrong about the mechanism. For one panel in a bounding box the figure is at least a half and usually more — exactly twice its area for a square, worse for any other shape. But identical panels at one angle tile the plane, so a marker loses nothing in the interior and everything at the two selvedges. The penalty therefore falls as the bolt gets wider, which no account in terms of the diagonal can produce.
What settles it: 2.00× the panel's area in a box, but the marker penalty falls from 49 points on a 1.1 m bolt to 28 on a 3.2 m one. Argued in The bias cut and the selvedge.
A loose weave tears better because its yarns group.
Right, and it needed a friction to say so. An earlier essay here found that geometry alone cannot settle it: the slack in each gap contains no weave, so two drafts at one sett give one number. With the capstan in hand the question resolves into a mode — the threads at a tear's tip slide and bundle below a computable sett and break above it — and the crossover moves with the friction coefficient, so it is a claim at a stated μ.
What settles it: threads slide up to 32/cm and break at 36/cm at μ = 0.3, while at μ = 0.15 every weavable sett slides — no crossover at all. Argued in A tear stops where the grip is.
Compensation is the crimp redistributing under prestress.
Not at a fixed thickness. Peirce's closure condition holds the two crimp heights to a constant sum, so at a fixed cloth thickness a prestress can only interchange crimp — one direction grows and the other shrinks. A membrane grows both ways, so the growth has to come from the crossings flattening, which needs a transverse stiffness this site does not have and states as a calibration.
What settles it: at a fixed thickness the interchange is 2.6% and -5.7%, of opposite sign; with the crossings flattened 12% both grow, 1.65% and 2.80%. Argued in A membrane is cut smaller than it is.
The extension a woven cloth has along the warp is its warp crimp.
Outside the mechanism. The crimp is a true ceiling and it is not the stop. All the crimp the warp gives up has to be taken by the weft, whose straight runs shorten as it takes it, and when they vanish the weft has jammed and the cloth stops — whatever the warp still had in hand. Six of eight ordinary plain weaves stop that way, and the changeover happens at a warp cover of 0.3374, which is a ratio of spacing to diameter and therefore the same for every yarn count.
What settles it: 6 of 8 stop at the weft's jam; the sheeting reaches 4.03% of the 14.61% it is credited with. Argued in A cloth extends by moving its crimp.
A fabric's Poisson ratio is a number that can be quoted for the fabric.
Wrong. It is above one half on every cloth measured here, which an isotropic continuum cannot be; it roughly doubles across a four per cent span of extension, so it is not a constant; and the two directions measured at equal extension are not reciprocals, which an elastic sheet's would have to be. All three follow from the deformation being a mechanism at constant thread length rather than a material straining.
What settles it: 1.10 at the measured state, 0.80-1.63 over the band, and the two directions multiply to 1.45 rather than to one. Argued in A cloth's Poisson ratio is not a material's.
A tube is a double cloth joined at one selvedge and a double width is joined at both.
Wrong, and the other way round. A tube's weft has to encircle the cloth, so it crosses into the other layer at both selvedges; a double width folds at one and turns back in its own layer at the other. This site had it reversed in two essays for a long time. The draft is identical in both cases and in the case of two entirely separate cloths, so nothing about the point paper could have caught it — what separates the three is the number of free edges, which is 0, 2 and 4.
What settles it: two-cloths: 4 free edges · stitched: 4 free edges · double-width: 2 free edges · tube: 0 free edges. Argued in A tube and two cloths are the same draft.
A triple cloth needs at least two stitching points to be one cloth.
Wrong. One stitch is enough, provided it reaches from the outermost layer to the outermost layer — found by exhaustive search over stitching sets rather than argued. Two are needed only when a stitch may reach no further than the next layer down, which is a restriction on the construction and not a property of the cloth.
What settles it: 1 unrestricted, 2 when a stitch may only reach the next layer. Argued in How many layers a draft can have.
A satin hides a stitching point better because its floats are longer.
Outside the mechanism. The float is not what decides it. Two satins on seven ends have the same order, the same longest float, the same interlacings and the same shaft count, and differ by a factor of two in how many positions will hide a stitch — because what covers a stitch is how far apart in the picks the neighbouring interlacings sit, which the move number decides and the float length does not.
What settles it: move 3 gives 14 strict positions and move 2 gives 7, at an identical float. Argued in Where a stitch can hide.
A double jersey is one fabric, because it is knitted from one continuous yarn.
Wrong. One yarn is not one fabric. A tubular structure is knitted from a single yarn and is two fabrics joined nowhere but at the selvedges the enumeration does not contain; the criterion is connectivity of the wales through the courses that feed them, and the enumeration finds fifty two-fabric arrays at the smallest two-bed repeat.
What settles it: 50 of 1135 arrays are two fabrics, 28 of them splitting across the beds rather than along them. Argued in Does a double jersey hang together.
Two beds make one fabric as soon as some course knits on both of them.
Wrong. That is the criterion anybody would state standing at the machine and it is wrong in both directions — it joins structures the connectivity separates, and separates structures the connectivity joins. The enumeration disagrees with it on sixty-two arrays, and the criterion the census actually produces is about which wales share a course rather than which beds do.
What settles it: 62 arrays disagree — 28 joined that separate, 34 separated that are one. Argued in Does a double jersey hang together.
A long float in a knit shines, snags and wears before anything else does.
True of one bed, void on two. Five rungs of the float ladder take a float to be a length of thread on the surface with nothing holding it down. Add a second bed and the wale opposite lies across the float, which is then in the gap between two fabrics, on no surface at all — and almost every float in the enumeration is of that kind. The yarn arithmetic is untouched; lustre, abrasion, snagging and raising are void.
What settles it: 1248 of 1272 floats — 98.1% — are on no surface at all. Argued in A second bed changes what a float is.
A striped cloth needs as many shafts as its two weaves put together.
Outside the mechanism. The cost is the union of the two column sets, not their sum, and the overlap is never partial — two shift-rule weaves share every column or none, because each set is the rotations of one column. Three of the forty-five standard pairs share, and in all three the stripe costs what the wider weave costs alone. The pair a reader expects to share, the 2/2 and the 3/1 twill, shares nothing.
What settles it: 3 of 45 pairs share a column, and all 3 of those stripes are free. Argued in A stripe is a partition of the warp.
A tartan is symmetric about its diagonal.
Outside the mechanism. Exact diagonal symmetry is impossible for every weave there is: the condition has to hold where the two colour indices are equal, and there no matrix disagrees with its own transpose. The ceiling is (n-1)/n and only a matrix that is a tournament off the diagonal reaches it. A 2/2 twill reflects exactly half of its mixture intersections; a plain weave and a hopsack reflect none at all. What the eye reads is the balance of each mixture, which is a different property.
What settles it: 50.0% of a 2/2 twill's mixtures survive reflection, against a ceiling of 75.0% no weave reaches. Argued in A check is two stripes and a tartan is one.
How often the threads interlace is what decides how a cloth behaves.
Outside the mechanism. A 2/2 hopsack and a 2/2 twill interlace equally often, have the same longest float, the same balance, the same layer count and the same densest setting in both directions — six of the nine measures this site takes off a matrix agree — and they are not the same cloth to handle. The three measures that separate them are the shaft count, the fundamental domain and the largest thread group, and no mill quotes any of the three.
What settles it: 6 of 9 measures agree; the 3 that do not are shafts, fundamental domain, largest thread group. Argued in A cord is a stripe with no colour in it.
A fabric's wicking height is what a thirty-minute strip test measures.
Past its domain. A strip test reports a Washburn number and the specification reads it as a Jurin one, and the two describe different pore systems of the same cloth. The holes between the threads reach their own ceiling within seconds and stop; the spaces between the fibres are still climbing at thirty minutes and are days away from an equilibrium metres higher.
What settles it: the coarse system stops at 137 mm after 4.8 s; the fine one's ceiling is 6.37 m. Argued in How high a cloth wicks.
A closely set fabric wicks higher.
Wrong. The sett decides the holes between the threads and touches the spaces inside a yarn not at all, and it is the second system that lifts. Over the whole weavable range of one yarn the maximum rise is identical to twelve decimal places while the permeability falls by nearly two orders. The sett decides how much a cloth carries and the yarn decides how high.
What settles it: 6.375 m at every one of 11 setts, while the flux spread is 86. Argued in The sett decides how much, not how high.
Directional wicking shows that the warp and weft yarns differ.
Wrong. A cloth woven from one yarn in both directions still wicks faster one way, because a front travelling a thread travels the thread's path and the two systems are crimped differently. The apparent coefficient is the yarn's own divided by exactly the square of the path length, so the anisotropy is two crimps and nothing else — and stretching the cloth interchanges the crimp and reverses which way is faster.
What settles it: 11.9% faster weftwise in a cloth of one yarn, from the crimps alone. Argued in Wicking is slower along a crimped thread.
There are three basic weaves and everything else is derived from them.
Wrong. Taken as a generating claim it is checkable, because the catalogue of the smallest interesting repeat is complete. Start from plain weave, every twill and every satin a repeat admits, apply every derivation the manuals name — reversing, breaking, pointing, doubling, counterchanging, turning — close under everything that leaves a cloth the same cloth, and nine of the 426 four-by-four cloths are reached. The 417 missed are ordinary sound cloth with the same range of float lengths.
What settles it: 9 of 426 cloths reached — 2.1%. Argued in The three basic weaves do not generate the rest.
A weave's name says which weave it is.
Wrong. The fraction notation writes exactly the weaves whose every column is a rotation of one column, which is five of the 426 four-by-four cloths — and it does not identify even those, because the step is nowhere in the name. Three of its four names cover two cloths apiece, which is why the trade has to add a letter for the twill's handedness.
What settles it: 5 of 426 cloths have a fraction name, under 4 names. Argued in Four ways to write a weave down.
A jacquard's resolution is its hook count.
Outside the mechanism. The hook count is the resolution of the machine. What a designer can place is a block, and a block is at least one repeat of the ground weave — so the cloth's own step is the repeat divided by the sett, and on an eight-end satin at 24 by 22 threads per centimetre that is 3.33 mm across against a hook pitch of 1.17. The machine resolves nearly three times finer than the fabric can hold, and a finer machine buys nothing.
What settles it: 3.33 mm of cloth against 1.17 mm of machine — 2.86×. Argued in A woven outline is a staircase.
Two sound weaves put together make sound cloth.
Sometimes. For a stripe it is a theorem, proved earlier here. For a figure it is false, and whether it is false depends on a quantity that appears nowhere in either draft — where the two weaves start relative to each other. Eight of the sixteen relative origins of one ordinary pair are safe at every one of 65,536 profiles, and the other eight break on more than a third of them.
What settles it: 8 of 16 relative origins safe at every figure; the worst breaks 36.7% of them. Argued in A figure is not a stripe.
The reed sett is the cloth's sett.
Wrong. A pick's thread length is fixed at the reed and the cloth then takes up its weft crimp, so the cloth is narrower than the reed by exactly the crimp over one plus itself. It is 1.87 per cent on an open scrim and 12.75 on a close balanced sheeting — a factor of 6.8 across ordinary cloth — so a single allowance is wrong at both ends of the range.
What settles it: 1.87% on a cheesecloth to 12.75% on a sheeting. Argued in The reed is not the sett.
Warp and weft are interchangeable.
Sometimes. In the matrix they are: transposing a draft gives a draft, and a loom of three shafts and four treadles reaches exactly as many cloths as one of four and three. In the machine they are not. The warp sett is a reed and a whole number of ends per dent; the pick density is a pair of change wheels — so over the range ordinary cloth is woven in the loom can choose one of the two roughly a hundred times more finely than the other, and cannot change the coarser one at all once the warp is drawn in.
What settles it: 49 warp setts against 4,825 pick densities over the same range — 99×. Argued in The setts a loom can reach.
A loom's shaft count is set by its shedding mechanism.
Outside the mechanism. Warp strain grows without bound towards the back rest, so a tolerance on it is a distance from the fell and a distance is a whole number of shafts. The tangent of the shed enters squared, which means the limit moves with the *insertion* mechanism rather than the shedding one: a shuttle's 30 mm opening buys thirteen shafts at a one per cent budget and a rapier's 16 mm buys thirty-six.
What settles it: 1 shaft at a 44 mm shed and 43 at 12 mm, on one strain budget. Argued in The harness has a depth.
A knitted panel can be shaped to any angle.
Wrong. A fashioned edge steps by whole wales at whole courses, so its angle is the arctangent of a fraction times the loop's own aspect — and that aspect is a constant of the relaxed structure, independent of yarn, gauge and loop length. Eighteen angles exist up to two wales a course, the widest gap between them is 16.67 degrees, and nothing at all reaches within twenty-one degrees of the horizontal.
What settles it: 18 angles, widest gap 16.67°, and a horizontal neck out of reach by 21.4°. Argued in A fashioned edge has a quantised angle.
A coated fabric is specified by its coating weight.
Wrong. A film is unsupported only over the holes, and the hole is the cloth's. Two cloths under an identical coating differ in what the film will hold by exactly the inverse ratio of their openings — the thickness, the strength and the polymer all cancel — so the same coating weight covers a factor of seven across the weavable range of one yarn.
What settles it: 3.47× between 24 and 12 threads per centimetre, at one coating weight. Argued in A coated cloth fails at its holes.
A finer mean pore makes a better substrate for a coating.
Wrong. A membrane fails at the largest hole it meets, not at the mean one. A woven cloth's holes are all one size because a repeat is a repeat; a nonwoven's are a distribution. So a nonwoven whose mean pore is finer than the woven cloth's opening still bursts first, and by a factor — the quantity that decides is the spread rather than the size.
What settles it: 136 bar against 381 — the finer fabric loses by 2.8×. Argued in A coated cloth fails at its holes.
How much of a stretch a fabric gives back is a property of what it is made of.
Wrong, and the corner has no fibre in it. A woven cloth extends first by moving its crimp, which costs its threads nothing and comes back in full, and only afterwards by stretching them. So its recovery curve has a corner in it, and the corner is where the interchange runs out — a number about the sett, the two counts and the balance. Substituting a different fibre's recovery table moves the falling part of the curve and does not move the corner by a hair.
What settles it: one 20 tex cotton yarn returns 61% of a 5% strain at 8 ends per centimetre and 100% at 20. Argued in A cloth gives back less than it took.
Setting a cloth closer gives it more free extension, because there is more crimp to take out.
Wrong past a cover of 0.41. Interchange is a trade and it needs both sides. An open cloth has no crimp to give and a close one has nowhere to put what the warp gives up, so the budget rises to a maximum and falls away. The maximum is at a cover factor rather than at a sett, so the count divides out exactly — the best sett moves fourfold across a twentyfold range of yarn count and the answer does not move at all.
What settles it: 7.2857% at a cover of 0.407782, at setts from 10.9 to 48.8 ends per centimetre. Argued in The most a cloth can give back.
A fabric's free extension is a property of the fabric, so it is the same whether the cloth is slack or already tensioned.
Wrong, and the same shock is permanent in one and not the other. There is one locus and one position on it, so a cloth held stretched has moved along its own curve and its two budgets are the two distances from where it now stands. Two per cent of extra strain applied to a relaxed poplin is wholly inside its budget and leaves nothing behind; the same two per cent applied to one already held at three per cent finds nine hundredths of a point of budget and hands the rest to the threads.
What settles it: nothing kept from rest, against up to 0.286% kept when held at 3%. Argued in A cloth has one budget for two directions.
A fibre recovers well because its stress–strain curve bends over, giving a strain somewhere to go.
Wrong — there is no signal at all. Wool and cotton tell the story loudly: wool's measured breaking extension is nearly six times the strain a linear fibre of its strength would break at, and it recovers well; cotton's is barely above its own prediction, and it does not. Rank six fibres by both quantities and the correlation vanishes. Nylon is the second most spring-like fibre in the table and recovers best of all; viscose is the least and recovers worst.
What settles it: Kendall's tau -0.20 over 6 fibres, with cotton displaced by 4 ranks. Argued in Recovery is measured and nothing predicts it.
A tensioned fabric that has gone slack should be pulled tighter next time.
Wrong, and pulling harder keeps proportionally less. A cloth clamped at a fixed length loses load without losing length: its crossings rearrange locally until the load has fallen to what friction alone can hold. That level is a property of the cloth and not of the tension applied, so the fraction retained is the floor divided by whatever was applied, and it falls. Below the resting band's own edge nothing is lost at all.
What settles it: 96% kept at 3.74% strain and 29% at 4.94%. Argued in A tensioned cloth loses its load.
A cloth shrinks over several washes because relaxation is slow.
Wrong — it is a distribution and not a rate. A domestic cycle agitates a fabric tens of thousands of times in half an hour. If every crossing had the same frictional barrier, all the shrinkage there was going to be would happen in the first cycle. A second wash that shrinks the cloth again is direct evidence that the barriers are spread, and the ratio between successive washes measures how far — which comes out far wider than any reported friction range gives.
What settles it: a spread of 37× fitted to two washes predicts the next three to within 11%, against 1.34× from the friction table. Argued in A cloth shrinks most the first time.
The fibres in a yarn are held together well enough to bend as one.
Wrong, and a creased shirt proves it. A fold cannot be tighter than the yarn it is made of, because two crowns on the inside cannot pass through one another. At that radius a yarn bending as a solid rod would strain its outermost fibres by exactly one hundred per cent, which no fibre in the table survives or comes within a factor of two of surviving. A creased cloth does not fall to pieces, so the fibres slide.
What settles it: 100% demanded against breaking extensions of 3 to 40%, worst margin nylon at 2.5×. Argued in A crease is a fold the crimp cannot supply.
Fibres that crease badly are the ones whose fibres are weakest at a fold.
Right for two of them and wrong for the third. Flax and cotton are strained past their own breaking extension at the sharpest fold their yarn can make, and both are among the three worst by a crease recovery test. The third is viscose, which survives the fold with a factor of two to spare and returns a third of what it was given. Two mechanisms end in the same complaint, and a treatment that fixes one does nothing for the other.
What settles it: breaking: cotton 7.1% against 6.0%–10.0%; flax 9.5% against 1.5%–3.0%. Surviving and not returning: viscose at 7.1% with a factor of 2.1 in hand and 32.0% returned. Worst three by measurement: flax, viscose, cotton, with 1 fibre misplaced.. Argued in Which fibres crease, and why there are two answers.
How much crimp a fold can spend is the weave's average crimp.
Wrong, and a satin has places with none. Crimp is made where a thread turns and nowhere else, so what a fold has to spend is whatever is inside the few picks it crosses. A plain weave turns at every pick and is uniform; an eight-end satin turns twice in eight and bunches the two turns together, leaving a clear run of six. Half of its end-and-place pairs cross a three-pick fold with no turn in them at all.
What settles it: plain 0%, 2/2 twill 0%, 3/1 twill 0%, 2/2 basket 0%, 5-end satin, move 2 20%, 4/4 twill 25%, 8-end satin, move 3 50%. Argued in How sharply a weave lets a cloth fold.
A specification can name the ends and the picks per centimetre of the finished cloth.
Wrong — one of the two is free. A cloth relaxes to the least-energy state of its own locus, which is a state at a different sett in both directions and in opposite senses. The locus is one-dimensional, so the finished construction is a point on a curve rather than a pair of independent choices, and a pair chosen by a customer has no reason to lie on it. What is left over comes out in the wash.
What settles it: the poplin moves -6.8% in the warp and +10.6% in the weft. Argued in The construction a loom must be set to.
A crushed carpet stays flat because its fibres have been bent past what they return.
Wrong by an order of magnitude. A tuft pressed flat turns through a right angle over its own length, so it bends to a radius of 2h/π and its fibres are strained π·d/4h — under two tenths of a per cent for a five-millimetre pile, an order of magnitude below the smallest strain anybody has measured a recovery at. What holds a pile down is the tufts leaning on one another. Below about half a millimetre the fibre does enter its measured range, which is the difference between a carpet and a velvet.
What settles it: 0.094% at 10 mm against a measured floor of 2%, crossing at 0.469 mm. Argued in A crushed pile is not held down by its fibres.
Spirality is a property of the yarn, so a lower twist is the cure.
Incomplete — a rib is exempt at any twist. A loop on the front bed and one on the back are mirror images, so their torques oppose and a fabric knitting equally on both nets to zero whatever the yarn is doing. The count has to be made per fabric rather than per structure: an interlock and a tube both knit equally on the two beds and are opposite cases, because an interlock's two components each straddle the beds and a tube's are each wholly on one.
What settles it: flat: 1x1-rib, 2x2-rib, interlock; leaning: plain, half-cardigan, tubular. Argued in A jersey leans because its yarn still turns.
A woven filter cloth passes what its opening size says it passes.
Right for a plain weave and for no other. The opening a cloth shows is its projection — what a straight line of sight can use — and the passage it has is the narrowest cross-section anywhere along the channel between four threads. Those are the same number only where the four threads round every hole are level in pairs, which happens when every thread transits at every gap, which is the plain weave and nothing else. Every other weave passes a particle larger than its rating, by up to 15.2 per cent, with no change to its cover or its open area.
What settles it: plain 249.6 µm against a 249.6 µm opening; 2/2 basket 287.4 µm, +15.2%. Ceiling over all 22874 drafts at this repeat: 15.2%, reached by the basket.. Argued in A hole is a channel, not an opening.
Fabric air permeability goes as the fourth power of the gap between the threads.
True at the jam and nowhere near it before. That is Poiseuille's result and it is about the viscous part of the pressure drop. A channel through a cloth is about as long as it is wide and the air in it moves at metres per second, so most of the pressure is spent accelerating the air rather than shearing it — and the inertial term does not depend on the hole's size at all. The viscous share is one per cent in a scrim and reaches half only where the yarn jams.
What settles it: viscous share 1.0% at a cover of 0.115 and 61.6% at 0.571; the fourth power alone overstates the flow 98-fold at the open end. Argued in The fourth power is a close cloth's rule.
Close a cloth up far enough and it stops passing air.
Wrong — there is a floor and the yarn sets it. The channels between the threads close and the pores inside the threads do not, because a spun yarn is sixty per cent fibre and forty per cent air whatever is done to the construction. The two are paths in parallel between the same two pressures, so they add, and the second has no sett in it. Every route that actually closes a cloth — flattening, swelling, coating — closes the channel and leaves the floor exactly where it was.
What settles it: 8.1 mm/s at 100 Pa with every channel shut, against 3505 as woven — a factor of 434, and no weavable sett reaches it. Argued in A cloth stops having holes before it stops passing air.
Some fibres are warmer than others.
Not decidable — the model's own bracket is wider than the effect. A fabric is a two-phase mixture of fibre and air, and Wiener's bounds say its conductivity lies between the volume average and the harmonic one. At a cloth's solid fraction — about a fifth — both bounds sit within a fifth of air's own conductivity, and the band each fibre carries is wider than the gap between any two fibres. What does change the answer is thickness, exactly and proportionally, and a garment's resistance is mostly the still-air layer outside the cloth.
What settles it: 0 separated pairs out of 56 across 8 fibres; the fabric is 8.3% of what a person wearing it has. Argued in Warmth is a thickness of air.
A cloth's openness is one minus its cover factor.
True along the normal and nowhere else. A hole is a rectangle at the top of the cloth and the same rectangle one thickness below, so a line of sight arriving at an angle must clear both. The openness falls with the angle and reaches nothing at atan(g/t), which for an ordinary shirting is under forty degrees. Averaged over the whole sky with Lambert's cosine weighting, a muslin is a seventh as open as the covering rule says, and the ratio worsens as the cloth closes.
What settles it: muslin 5.4% to the whole sky against 37.9% by the rule; sheeting 1.6% against 24.5%. Argued in One minus the cover is a cloth with no thickness.
Two layers of a cloth pass the product of their open areas.
Exactly right as an average and right at no particular registration. The open fraction of two stacked cloths is a triangular function of how they happen to lie: in register the pair is as open as one cloth, and a fraction of a thread out it is much less. Integrating that over every offset gives the product exactly — not approximately — so the familiar rule is a statement about an expectation being used as a statement about an object. A pair that was assembled in register stays there.
What settles it: 37.9% in register against a product of 14.3%, mean 14.3% over offsets. Argued in Two layers are the product on average and nowhere.
A fabric can be chosen to wick well and to resist water.
Not by its geometry — the two are one expression with a sign in it. Both are 2γcos θ / r. Read at a wetting angle it lifts liquid up a pore and read past a right angle it holds liquid out of one, so every geometric change that improves the head improves the rise by the same factor and the whole design freedom is in the contact angle, which is a finish rather than a structure. The two also read opposite ends of the pore distribution: a rise is set by the finest pore and a leak by the coarsest.
What settles it: a muslin holds back 56 mm of water at its coarsest pore (134 µm) and would hold 2,975 mm at the pores inside its own threads — a factor of 53. Argued in The pore that wicks is the pore that leaks.
A percent-open-area measurement tells you whether a filter cloth still meets its rating.
Wrong — the one thing it cannot see is the one thing that moves. Push one end sideways and the gap on one side falls by exactly what the gap on the other side gains. The sum is unchanged, so the open area is unchanged to twelve decimal places, and the largest hole — which is the whole of what a filtration rating means — has grown by the displacement with no factor between them. What holds the end in place is friction at its crossings, which falls smoothly to nothing as a cloth opens.
What settles it: 1.000000000 µm of rating per µm of drift, at an open area constant to 12 decimal places; 364 µm against a 264 µm specification after 0.1 mm. Argued in A filter is rated by the hole it does not show.
A knit's air permeability can be computed from the holes between its loops.
Wrong at any commercial tightness — there are none. A loop's occupancy is its diameter times Munden's stitch-density constant over its loop length, with no gauge, no count and no fabric dimension in it. Past an occupancy of one there is no hole: the loops overlap in projection and the planar model has been handed a fabric it cannot describe. The threshold lands inside the tightness range the trade knits at, so a jersey closes its own holes as it relaxes.
What settles it: occupancy 0.955, 1.037, 1.129 in the three relaxed states of a 20 tex cotton at a 3.5 mm loop; the threshold is at a tightness factor of 13.4–12.3–11.3 and the trade knits at 13 to 17. Argued in A knit has no hole to lose.
A thickness gauge measures a fabric's thickness.
Right about the fabric, wrong about the gauge — the draft is in the reading. A presser foot does not stop at the top of a cloth. It sinks until the area it is touching can carry the standard's kilopascal, and how far that is depends on the shape of the bearing curve near the top — which is a property of the interlacement. Six drafts of one sheeting, identical in yarn, sett and geometric thickness, report readings 4.7 micrometres apart. That is systematic rather than scattered, so it survives any number of repeats and biases every comparison between weaves.
What settles it: plain 377.7 µm, 1/3 twill 376.0 µm, 2/2 twill 379.8 µm, satin 8 380.7 µm against a geometric 381.6 µm for all of them; the foot sinks 3.93–0.87 µm. Argued in A thickness gauge reads the draft.
Setting a cloth closer makes its surface smoother.
Wrong — it makes it finer-grained and slightly steeper. Peirce's closure condition says the two crimp heights add to the two diameters whatever the spacings are, so the height a woven surface swings through is pinned by the yarn before any sett has been chosen. Doubling the sett halves the spacing of the crowns and leaves their height exactly where it was, so the relief occupies twice the fraction of its own wavelength. A close-set cloth is steeper than an open one, not flatter.
What settles it: 14 to 29 ends/cm moves the crown spacing 714 → 345 µm and the peak-to-valley height 381 → 381 µm. Argued in The sett owns the pitch and the yarn owns the height.
An abrasion mass loss says how much of a fabric's life has gone.
Wrong by a factor between three and eight, and the factor is the draft's. Rubbing takes material off the whole surface and takes it off every thread at the same place. A thread breaks at its thinnest place, so the strength lost is set by the depth reached and the mass lost by an integral down to it — two different quantities that move at different rates. At one per cent of a cloth's solid volume removed, the section of every thread is already several per cent smaller, and how much depends on how much crown line the weave carries.
What settles it: plain ×8.3, 2/2 twill ×5.4, 3/1 twill ×3.8, satin 8 ×2.6 of section lost per unit of mass lost, at one per cent removed. Argued in A cloth loses its strength before its mass.
A calender adds lustre by smoothing the cloth's surface.
Wrong about the mechanism — the crowns are where they were and are wider. Specular area factors exactly into a length of crown line and a width of section within the tolerance. Pressing a two-and-two twill at 0.8 newtons per crossing multiplies the specular area by 23.6, and the arithmetic refuses to put the gain in the wrong factor: the width moves by 24.4 times and the length by 6 per cent. A flattened section has a plane on top of it, and a plane has one normal rather than a fan of them.
What settles it: ×24.4 in width against ×1.06 in length, for ×23.6 overall, at 42 per cent thinning. Argued in A calender buys the width.
A damask's figure shows because it stands proud of its ground.
Wrong — a step returns no light, and the contrast reverses. A figured cloth's regions do differ in height, by about fifty micrometres, and a height difference is invisible to a reflection: the two regions have the same slopes and return the same fraction of a diffuse illumination. What differs is direction. The figure is a satin and the ground its complement, so their crowns run at right angles, and the contrast between them reverses exactly when the cloth is turned a quarter turn — which no step can do.
What settles it: 1.38% and 1.29% of specular area — within 8 per cent of one another — with their crown lines at right angles. Argued in A figure shows by its shine, not its step.
A friction coefficient measured against a plate describes how a fabric slides on another fabric.
Wrong by more than an order of magnitude, and the error is geometric. A gap between two rough surfaces is the sum of two depths, so the pair's contact is the convolution of two height distributions and requires both surfaces to be near their own maxima at the same place. Friction is proportional to real contact area, and the pair's is between seven and twenty-five times smaller than either surface against a flat, with the worst suppression in the middle of the range a hand explores.
What settles it: ×14, ×21, ×25, ×13, ×7 at approaches of 0.7, 1.9, 3.7, 7.5, 18.7 µm; median gap 160 µm. Argued in Friction is two surfaces, not one.
A relaxed knitted fabric sits where its own elasticity puts it.
Wrong, and the sign is wrong rather than the size. Solved as an elastica, a loop's bending energy falls away from the relaxed fabric in both directions and has no interior minimum at all — it goes on falling until the yarn runs straight between its interlacings. Worse, the three relaxation states everybody measures get smaller in both directions, so each further stage of relaxation leaves the loop holding more bending energy than the last. A fabric relaxing towards its own energy minimum would do the opposite.
What settles it: 4.98 mN across the courses and 39.0 mN along the wales, per stitch, both downhill — and 22351 → 23944 → 25074 nJ across the three relaxation states, a 12 per cent rise. Argued in The relaxed knit is not at a minimum.
A knit stops stretching when its loop runs out of yarn.
Wrong by a factor of three, and the gap names what actually stops it. The yarn between two interlacings is fixed, so the straight line between them cannot exceed it, and that ceiling is computable from four lengths with nothing elastic in it. It sits three times beyond where a jersey jams. What stops a real fabric first is the loops of adjacent courses meeting sideways in the fabric's own plane — a contact the yarn-length bound knows nothing about.
What settles it: 322 per cent course-wise and 148 wale-wise, against a jersey that jams near a hundred, and the ceiling moves by 2 per cent across the whole knittable range. Argued in How far a knit could go if its yarn were the limit.
A knitted seam fails because its sewing thread is not strong enough.
Wrong by three orders of magnitude; it fails because it is too short. A knit reaches its working extension at a couple of newtons per metre, so one stitch of an ordinary seam carries a few millinewtons against a thread that breaks at several newtons. What runs out is length: a sewing thread's reserve is the pitch plus twice the fabric's thickness, so the extension a seam can give is twice the thickness times the stitches per unit length, and nothing about the thread's strength enters.
What settles it: 2.01 mN carried against a 3.74 N breaking load — a margin of 1863 — while 7.5 stitches per centimetre are needed to reach 50 per cent extension on a 0.33 mm fabric. Argued in A seam must give what the knit gives.
A knit is the soft fabric.
True in extension and false in bending, and the two are usually conflated. Computed the same way as this site's woven cloths — the yarn's own rigidity times the length of yarn per unit area times the fourth power of the cosine of the angle each element makes with the bending direction — a plain jersey lands inside the woven band rather than below it. Where it is genuinely soft is extension, by three decades, because looping converts a tensile problem into a bending one.
What settles it: 1.57 and 3.40 µN·m per unit width against 1.35 to 4.50 for the woven cloths — while its extensional stiffness is 3.53 N/m against 1.14e+5 for the same yarn laid straight. Argued in A knit bends more easily along its courses.
What this index is not
two things it is often taken for
It is not a list of things weavers get wrong. Every claim here is one a competent person says, and most of them are shorthand for something true — the trouble is that the shorthand travels and the domain does not. A rule of thumb with its conditions stripped off is indistinguishable, in a sentence, from a measurement.
Nor is it a claim that the computations here are the last word. Each rests on a model, and the model is named on the page where the argument is made: a weave matrix knows nothing about yarn, a trellis knows nothing about stiffness, and a geometric jamming model is not a mechanical one. Where a number depends on which model produced it — the jammed sett and the cloth thickness are the clearest case — both are given rather than blended.