Textile Structure
how cloth is put together
Concept

Needle bed — where it appears

One row of needles on a knitting machine, which decides one plane of loops; a second bed facing it is what makes a rib or a tube possible. Its needles are the fabric's wales, so a structure's width in wales is a machine setting rather than a property of the yarn.

Named by 12 essays across 4 fields — each of them below, with the objects they name alongside it.

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 tubular, as a graph of its wales. Every wale of tubular as a node — 2 on the front bed and 2 on the back — with one chain per course joining everything that course takes yarn on, because a course is one traverse of one yarn. The nodes are filled by which component they fall into. This structure comes out as 2 fabrics: F0+F1 and B0+B1. The same answer is obtained a second way, by walking every partition of the wales and asking whether any course straddles it, and the two are required to agree.

Does a double jersey hang together

Two beds knitting with nothing passing between them are two fabrics that happen to have been made at once. Of 6,561 two-bed arrays, 1,135 are fabrics and 50 of those are two fabrics — and 28 of the 50 split across the beds rather than along them, so neither half is a layer.

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 The force at an interlacing, which no longer lies in the fabric. A crossing of a relaxed jersey in section on the left, with the thickness expanded 3×, and on the right the contact force drawn at the angle the solve gives it — which is a true angle, unlike anything in the section beside it. The head of one course and the feet of the next lie one yarn diameter apart through the fabric, 0.167 mm, so the interlacing is not a point in a plane and the force at it is not in one either. It comes out at 38.30 mN a stitch, turned 11.75° out of the fabric: 37.50 mN along the wales, which is what friction has to hold, and 7.81 mN through the thickness, which is what holds the two faces apart. Divided by the area a stitch occupies the second is 15.1 kPa, or 113 mmHg — a pressure, and the quantity a compression measurement reports.

How thick a knit is

Two centre lines pass at a diameter and each has a radius on either side, so a plain jersey is two yarn diameters thick with nothing fitted. It does not depend on the gauge, it lands inside the band of this collection's woven cloths, and it is lower than any gauge will read.

knits · Knit 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.

How dense a knitted fabric is

A fabric's areal weight is what the trade specifies and it says nothing about bulk. Divide it by a thickness and the answer is a density — 0.40 grams a cubic centimetre for a jersey, a quarter of the fibre it is made of — and that quarter, the share of the volume that is not air, is the number every other property follows.

setting · Weight 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 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-bedRibInterlockCloth thicknessLoopConnectivityContact forceCourseLoop lengthMissTightness factorWale

All concepts