Textile Structure
how cloth is put together
Concept

Knit geometry — where it appears

A knitted fabric's dimensions as a function of its loop length, through constants that belong to one structure and one state. The constants have no yarn property in them at all, which is the empirical content of the result and rules out several mechanisms at once.

Named by 7 essays across 2 fields — each of them below, with the objects they name alongside it.

A knit's dimensions come from its loop length. Courses and wales per centimetre against loop length, for a plain weft-knitted fabric in one relaxation state. Neither axis carries a yarn count, a fibre or a machine gauge, and that is the finding: every plain knit measured sits on these two curves whatever it is made of.

A knit's dimensions come from its loop

A relaxed plain knit's courses, wales and stitch density depend on the loop length and on nothing else — not the yarn count, not the fibre, not the machine gauge. The constants are measured rather than derived, and the interesting thing about the published set is that it does not quite satisfy its own arithmetic.

finishing · Knit geometry The loop that costs nothing to extend. A plain knitted loop at rest and extended by 35 per cent, with the arcs marked. The arcs' radius is the diameter of the yarn the loop wraps, 0.167 mm, and it is set by contact rather than by the fabric's dimensions — so extending the fabric lengthens the legs and bends nothing further. The bending energy is 0.0176 N·mm at both, and the model therefore asks no force at all for an extension a woven cloth would refuse. What the drawing cannot show is what a real knit's first few per cent do cost, which is friction and yarn flattening and is not a bending property.

A knit is soft because it bends

Ask the same energy question of a woven cloth and a knitted one and the answers are not different by a factor — they are different in kind. A woven cloth's bending energy changes the moment it is extended. A knitted loop's does not change at all, exactly, over the whole of its extension, because its arcs are held to a radius by contact rather than by the fabric's dimensions.

knits · Knit A loop's cell, dry and wetted. One stitch of a 20 tex cotton jersey at a 3.50 mm loop, drawn inside the rectangle of one wale by one course that its own dimensions give. The thread is drawn at its own width, and it already fills 1.129 of the cell dry — more than the whole of it, which is what an opaque jersey looks like from above. Wetting takes it to 1.355. So the reason a knit does not build a swelling pressure is not that it has room; it is that its dimensions are a loop length times a constant with no yarn diameter in them, so there is no closure condition to fail. What the drawing cannot show is the third dimension: the legs lie over one another rather than overlapping in the plane, which is exactly why an occupancy above one is possible.

A loop has no closure condition

A woven cloth can run out of room: its two systems must supply its whole thickness between them, and past a certain swelling they cannot. A knit has no such equation, so no critical swelling and no pressure. The obvious explanation — that a knit is open and has somewhere to put the swelling — is false, and the arithmetic refuses it.

knits · Knit Munden's states against the fibre swelling. What a plain knit does between its relaxation states, beside the swelling of the fibre it is made of. Going from dry-relaxed to wet-relaxed a jersey loses 5.66% along its courses and 2.44% across its wales, and going on to fully relaxed it loses 9.1% and 7.0%. The fibre swells 20%. Two things rule the swelling out as the cause: it is several times the whole change, and the change is markedly anisotropic while a swelling enters both of a loop's dimensions through the same loop length. What the bars cannot show is what does cause it, which is friction — water lets the loops move to where the yarn's own bending had been trying to put them.

A knit's change of state is not its swelling

A jersey is smaller wet-relaxed than dry-relaxed, by 5.7 per cent along its courses and 2.4 across its wales. Water is obviously involved, so the swelling is the obvious cause. Two things rule it out, and both are properties of the constants rather than measurements of a fabric.

knits · Knit single jersey, as loops. Three courses of the same structure drawn as yarn. A knitted needle takes a new loop through the one below; a tuck takes the yarn into the loop below and leaves it on the needle, so that loop is held for another course; a miss floats straight past. Six needles is as many as a loop diagram can carry, which is why the array beside it exists.

A jersey has two surfaces

The face of a plain knit shows the legs of its loops, which run along the wale; the back shows the heads and feet, which run across it. So the two faces carry their crowns at right angles — the same situation as a damask's figure and its ground, in a fabric with no warp, no weft and no float.

knits · Knit Whether a cloth's hairs can reach one another. n_A λ² for each construction in this site's table — the hairs per square millimetre times the square of their own length, which is the pure number that asks whether a hair can touch its neighbour. It is a count times an area, so it has to be a pure number. Every one of them is under one, which means no ordinary woven cotton cloth has a hair layer at all: it has isolated whiskers on a bare surface. The dashed line is the threshold. The spread across the whole table is only 1.9-fold, because the density goes as the sett times the root of the count and those move in opposite directions as a cloth is made finer — so construction is almost powerless here, and everything that crosses this threshold does so by finishing rather than by weaving.

A knit gives up its fibres more easily

Knitwear pills and shirting does not, and the fibres are often the same fibres. The difference is a count of yarn per unit area and a pressure between threads, and both of them push a knit over a threshold that a woven cloth of the same yarn cannot reach.

knits · Knit What the third dimension changes, and by how much. Every number the planar loop model produced, beside the same number with the climb in it, for a 20 tex cotton jersey at a 3.5 mm loop. Four of the five fall and none moves by as much as four per cent, which is the useful part of the answer: the planar model was not wrong about a jersey, it was a projection of the right curve. What it could not have at all is the quantity that is not on this list — the force through the fabric's thickness, 7.81 mN a stitch, which a model with no thickness has nowhere to put.

The constants say nothing about thickness

Munden's two constants give a knitted fabric's wale and course spacings from its loop length alone, and the tightness factor collapses every fabric's shape onto one curve. Neither reaches the third dimension: two knits that are one knit in plan are two different thicknesses.

finishing · Knit geometry

Named alongside it

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

Loop lengthCourseStitch densityTightness factorWaleFrictionJammingLoopMoistureMunden constantsRelaxationSwelling

All concepts