Textile Structure
how cloth is put together
Concept

Rib — where it appears

A two-bed knit whose wales alternate between the two faces, so the fabric folds on itself and recovers strongly across its width. Its extension is a geometric consequence of the fold rather than anything about the yarn.

Named by 14 essays across 4 fields — each of them below, with the objects they name alongside it.

Why one curls and the other does not. A knitted loop is not symmetric front to back. Worked every course the same way, the asymmetries add along the edges and the fabric rolls; worked alternately, consecutive courses point opposite ways and cancel.

Why stockinette curls

A knitted loop is not symmetric front to back. Work every course the same way and the asymmetries add up along the edges; alternate them and they cancel. That is the whole difference between a fabric that rolls and one that lies flat.

knits · Knit 1×1 rib — alternate wales to the back. A knitted fabric seen in section across the wales. Alternate wales pulled to the back fold the fabric like a concertina, so its relaxed width is a projection; pulling it wide unfolds the section and no yarn changes length while it happens.

Rib and interlock

A rib fabric is a plain knit folded like a concertina, and its enormous widthwise stretch is the fold opening out. Nothing in it is elastic, and the extension available is a cosine.

knits · Knit A beat at 19.1 mm from grids at 0.5 mm. Two grids at 0.5 and 0.5 mm pitch, the second turned by 1.5°, over a 30 mm window. The dashed rules are one predicted beat period apart. The pattern between them is 38 times the pitch of either grid and neither grid has anything at that scale.

Watered silk is a beat

Fold a ribbed cloth on itself and press it, and a figure appears at a scale neither ply has — fifty times the rib pitch, wandering across the piece. It is the difference of two wavevectors, it is enormous because the angle is tiny, and no two pieces match because no two are folded at the same angle.

pattern · Moire rib-float in section. A two-bed structure seen in section across the wales, over 3 repeats of course 1. The front bed's loops sit on the upper line and the back bed's on the lower one, offset by 0.5 of a needle pitch because the gating is rib. Of the 2 floats in the repeat, 2 lie in the gap between the beds and 0 on a surface. The upper panel is the fabric at the machine and the lower one is the same course with the beds closed up, which is what happens when the fabric is cast off — and neither panel is a relaxed fabric, because the loops are drawn as arches of one size and a real one settles wherever the yarn's bending leaves it.

A second bed changes what a float is

Every float so far has been on a surface, because every knit so far has had one needle bed. Put a bed behind it and the yarn runs in the gap between them — and over the whole enumeration of two-bed structures, 1,248 floats of 1,272 lie inside the cloth, on no surface at all.

knits · Two-bed Why a cuff is ribbed. The force a knit pulls back with, over the range a cuff is used across. It rises the whole way — 0.79 N per metre at 23% to 3.38 at 104% — and it is small throughout, which is the combination a cuff needs and almost nothing else supplies. A rib gets its extension by geometry, folding alternate wales to opposite faces so that its relaxed width is about half its opened one, and it gets its recovery from the loop reconfiguring. Neither is the yarn stretching, which is why a cuff made of a fibre with no elastic recovery at all still works.

A rib pulls back on a force the loop supplies

A cuff has to give a great deal at almost no load and come back reliably, and no ordinary material does both. A rib gets its extension from folding, which is geometry, and its return from the loop reconfiguring, which is now a computable force — under four newtons a metre over the whole range a cuff works across.

knits · Two-bed A rib crosses a gap where a jersey crosses a diameter. A one-by-one rib in section across 5 wales, drawn at a bed gap of 3 yarn diameters — 0.501 mm — because the relaxed gap of a rib is a measurement this collection does not hold and every figure of one says what it was drawn at. Alternate wales sit on opposite beds, so every sinker loop between them travels the whole gap. In a jersey the same yarn climbs one diameter, 0.167 mm. That single difference takes the contact force from 38.30 mN at 11.7° out of the fabric to 72.51 mN at 16.2°, and the through-thickness part from 7.81 mN to 20.17 mN.

A rib climbs a gap

A jersey's yarn crosses one diameter between interlacings because that is what a crossing of two threads is. A rib's crosses the whole distance between the two beds. Nothing else in the model changes, and that one length is the whole mechanical difference between the fabrics.

knits · Two-bed How much of a fabric's yarn crosses between the beds. The share of half periods that cross from one bed to the other, read off each structure's own traverse rather than quoted. It is the mechanical difference between these fabrics in this account: a half period that crosses climbs the whole bed gap and one that does not climbs a yarn diameter. Single jersey and a tubular fabric come out at zero — the tubular one because its two faces are made on separate courses and never meet — and a one-by-one rib comes out at one, with every sinker loop crossing. A two-by-two rib is at a half, which is the number a reader would guess and is here counted.

Where a two-bed fabric's yarn is

Thirteen named structures, and for each of them the share of its yarn that crosses between the beds — read off its own traverse rather than quoted. It separates the fabrics into three groups, and one of the groups turns out not to be a fabric at all.

knits · Two-bed A rib is quietest at a gap of two diameters. The through-thickness force of a one-by-one rib against the bed gap it is knitted at, in units of the yarn's own diameter. It does not rise from the bottom, and the dip is geometry rather than noise: a crossing is shared between the two half periods either side of its sinker loop, and each of those also carries the interlacing's own diameter — one climbing with it and one against. At a gap of two diameters the second half period climbs nothing at all, and the fabric is at its quietest through its own thickness. Above that both halves climb the same way and everything rises together, which is the regime a real rib is knitted in: 14.8 mN at 5 diameters against 7.0 mN at two.

A rib is quietest at two diameters

Open the beds of a rib and everything about it should get stronger. It does not. The through-thickness force falls to a minimum at a bed gap of exactly two yarn diameters and rises on both sides of it, because a crossing's climb and an interlacing's own climb cancel there.

knits · Two-bed Which knitted fabrics lie flat, counted from the structure matrix. The curl balance of every named two-bed structure this site holds, with a tuck counted in full on the bed that took its yarn: the yarn a repeat puts on the front bed minus the yarn it puts on the back, over the total. A fabric lies flat exactly when it is zero, and the criterion has to put single jersey at one end and a one-by-one rib at the other or it is worth nothing — which it does, at 1.00 and 0.00. What it is for is the rest: a tubular fabric balances because it is two jerseys facing opposite ways, both cardigans balance because a tuck holds yarn on the bed that took it, and half-milano and a three-by-one rib come out front-heavy — which is what they are and what they do. 6 of the 13 structures curl.

Which knitted fabrics lie flat

Curl was explained here by counting face changes between courses, which works for stockinette and garter and reaches nothing else. The same question turns out to be a signed sum over a structure's own grid — and it answers for every fabric a two-bed machine can make, including the ones nobody has a rule for.

knits · Two-bed How much of a fabric's yarn crosses between the beds. The share of half periods that cross from one bed to the other, read off each structure's own traverse rather than quoted. It is the mechanical difference between these fabrics in this account: a half period that crosses climbs the whole bed gap and one that does not climbs a yarn diameter. Single jersey and a tubular fabric come out at zero — the tubular one because its two faces are made on separate courses and never meet — and a one-by-one rib comes out at one, with every sinker loop crossing. A two-by-two rib is at a half, which is the number a reader would guess and is here counted.

A tube and an interlock balance for different reasons

Two structures come out identically flat on a signed count and are as unalike as two knitted fabrics get. One is two jerseys that curl in opposite directions and are joined at the edges; the other is a fabric whose every course crosses. Telling them apart needs a different question asked of the same grid.

knits · Two-bed What leaving the plane costs, which is less than nothing. Bending energy a stitch against how far the yarn climbs between one interlacing and the next, for a 20 tex cotton jersey at a 3.5 mm loop. The curve falls. A climb is not an extra bend added to a curve that was otherwise unchanged; it is part of the straight line the thread has to span, so a longer climb leaves less slack to be spent on curvature. At a jersey's own climb of one diameter the energy is 24395 nJ against 25060 for the planar model — 2.7% lower, where an earlier estimate on this site put the ride at three per cent of the loop's bending and had the sign the other way round. At a rib's climb of three or four diameters the fall is 33%.

A rib's relaxation is not its bending either

A jersey does not settle where its bending energy is least, and this collection has said so for several rungs. A rib does not either, and the model now says how far from least it would have to go: sixteen yarn diameters of bed gap before the yarn runs out, against the two or three a machine is set to.

finishing · Shrinkage A knit's warmth is its thickness, and a rib's thickness is a machine setting. Thermal resistance in tog for a 20 tex cotton at a 3.5 mm loop, for a plain jersey and for a one-by-one rib at four bed gaps. The bar is the lower bound and the mark beyond it is the upper — Wiener's two bounds on a mixture of fibre and air at the fabric's own fibre fraction, which is 26.6% for the jersey and falls to 8.9% for the widest rib. The jersey holds 0.088 tog and the rib at five diameters 0.334 — a factor of 3.8, bought entirely by opening the beds. Every one of these is a small fraction of the still-air layer that clings to a garment's outside, which is worth about 1.2 tog on its own.

A knit is warm because of where its yarn is not

Warmth is a thickness of still air, and until a knitted fabric had a thickness there was nothing to compute. It has one now, and the answer is that a rib's warmth is a machine setting: opening the beds from two diameters to five nearly trebles the fabric's resistance without changing a gram of yarn.

applied · Insulation What a knitted band presses a limb with. Pressure against extension for a 20 tex cotton band at a 3.5 mm loop, wrapped round a 30 mm radius — a wrist. The pressure is the fabric's own tension per unit width divided by that radius, and the tension is the loop's bending with the relaxed shape as the yarn's natural one, so nothing here is fitted. Over the range a cuff is actually used across it runs from a twentieth of a millimetre of mercury to 0.85. The shaded bands are what a compression garment is specified at, and the curve does not reach the lowest of them until 277 per cent — which is not a cuff, it is a fabric stretched almost to the point where its yarn runs straight.

What a cuff presses with

A rib cuff holds a sleeve on a wrist, so it must be pressing. Divide its own recovery force by the radius it is wrapped round and the pressure comes out at eight tenths of a millimetre of mercury — a fiftieth of the lightest medical compression, and two orders below what the same fabric resists being squashed with.

applied · Pressure A rib crosses a gap where a jersey crosses a diameter. A one-by-one rib in section across 5 wales, drawn at a bed gap of 3 yarn diameters — 0.501 mm — because the relaxed gap of a rib is a measurement this collection does not hold and every figure of one says what it was drawn at. Alternate wales sit on opposite beds, so every sinker loop between them travels the whole gap. In a jersey the same yarn climbs one diameter, 0.167 mm. That single difference takes the contact force from 38.30 mN at 11.7° out of the fabric to 72.51 mN at 16.2°, and the through-thickness part from 7.81 mN to 20.17 mN.

A run cannot cross a bed

A dropped stitch unroves because its neighbour above can pull it out along a path that costs almost nothing. In a rib the neighbour above is on the other bed, and the path goes through the gap — so a run in a two-bed fabric has to pay for a climb before it can take a single loop.

applied · Damage

Named alongside it

The objects these essays reach for when they reach for this one.

Two-bedNeedle bedInterlockCurlLoopCloth thicknessConnectivityContact forceCourseElasticaLoop lengthMiss

All concepts