Textile Structure
how cloth is put together
Knits and other structures

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.
16 min read 7 figures A mechanism, not a materialStructure before fibreMeasured, not claimed

Worth reading first: The loop · A figure shows by its shine, not its step · Why stockinette curls.

Turn a piece of plain jersey over. The two sides do not look alike, and the fabric is one colour, one yarn and one stitch throughout. The usual account is that one side shows the "V"s and the other shows the “purl” ridges, which is a description of the picture rather than an explanation of why one is smooth and bright and the other is dull and grainy.

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.
Fig. 1 One loop and its neighbours, drawn as the paths the yarn takes. The two legs run along the wale and are the straightest parts of that path; the head and the two feet are arcs, turned through the thickness of the fabric. Which of those a reader is looking at depends entirely on which side of the cloth they are on, and that is the whole of what follows.

The claim

The two faces of a plain knit carry their crowns at right angles, and one of them carries lines while the other carries points.

Three consequences, and the third is a connection to a fabric that could hardly be less like a jersey.

The face has crown line. A leg is the straightest part of the loop and it runs down the wale, so it presents a ridge exactly as a float does — and the fabric’s face reflects into a fan across the wales.

The back has crown points. A head is an arc turning over the wale, so its highest place is a summit rather than a ridge, and it reflects into no preferred direction at all.

And that is a damask, made a different way. A damask’s figure and ground have crowns at right angles and trade places when the cloth is turned. A jersey has the same two orientations, on its two faces, and it needs neither two weaves nor a jacquard to do it.

The argument

A knitted loop is one continuous path and it does not distribute itself evenly between the two sides.

Follow it. The yarn comes up from below through the head of the loop underneath, runs up the wale as a leg, turns over at the top through the head, comes back down as the second leg, and turns under at the bottom through the feet. The legs are on the face; the head and feet are on the back.

The legs are nearly straight and the heads are not. A leg spans one course — a few hundred micrometres — and its curvature over that span is gentle, because the loop’s sharp turns are at its top and bottom. A head is a turn of about half a wale spacing in radius, which is the tightest bend in the whole path.

So the face presents nearly straight lengths of yarn running along the wale and the back presents arcs running across it, and everything that follows is the same argument as for a float: a nearly straight length has crown line, a tight arc has a summit, and a summit is a point.

single jersey as an array. One cell per needle per course, over 2 repeats each way. K knits a new loop and casts the old one off, T tucks the yarn into the loop below without casting off, M misses the needle and floats past it. The margins carry the two conditions: a wale with no K in it never casts off, and a course with no K in it is never caught by anything. Both hold here.
Fig. 2 The knit as an array, which is how this collection usually treats it — knit, tuck and miss, three symbols where a weave has two. That representation says which loops exist and nothing about where the yarn is; the surface question needs the path rather than the array, and the path is where the two faces come from.

What was counted, and how, and how crudely

Much more crudely than anything else in this ladder, and the reason is that this collection has no solved loop geometry.

The knit’s dimensions come from Munden’s constants, which are measurements: courses and wales per unit length are each a constant divided by the loop length, and the constants are empirical. They say how many loops there are and nothing whatever about the yarn’s path between them.

So the model here is stated and is the crudest defensible one: a leg is taken as straight over a stated fraction of one course spacing, and a head as a semicircular arc of half a wale spacing. At a loop length of 3.5 millimetres in the dry-relaxed state the fabric has 14.3 courses and 11.4 wales to the centimetre, giving a wale spacing of 875 micrometres and a course spacing of 700 — and, with legs taken as half straight, about 1.14 millimetres of face crown line per square millimetre against 4.9 crown points per square millimetre on the back.

Only two things are claimed and neither depends on the guess. The two faces carry their crowns in perpendicular directions, and the face carries line where the back carries points. Both follow from which part of the loop is on which face, which is a topological fact about knitting, and both are asserted across the whole range of the free fraction and across three loop lengths.

Why the face is the smooth side

The trade calls the leg side the “technical face” and the head side the “technical back”, and prefers the face for anything where appearance matters. The surface says why in three ways at once.

It has line rather than point crowns, so its bearing curve opens as a square root rather than linearly — the face touches on more of itself at any given depth, exactly as a floated weave does against a plain one.

It has an orientation, so it returns a directional highlight and the back does not. A jersey’s face has a subtle sheen running across the wales and its back is matt.

And its crowns are more evenly spaced. The legs are two per loop and parallel; the heads are one per loop and are the tightest bend in the yarn, standing proud of everything around them. A back is a field of isolated bumps, which is what “grainy” means.

The bearing curves of 2 weaves in one cloth. How much of the plan is within a given depth of the highest point, for plain, 2/2 twill — all in sheeting, all at the same sett, the same counts and the same thickness. They differ only in their drafts. At a hundredth of the cloth's thickness the last of them is touching 3 times the area of the first, and the gap widens as the depth shrinks, because the curves do not merely differ by a factor — they have different exponents. A crown that is a line opens as the square root of the depth and a crown that is a point opens in proportion to it.
Fig. 3 The comparison the knit sits between: a surface of points against a surface of lines, in woven cloth. A jersey’s back behaves like the first and its face like the second, on the same piece of fabric — which is a difference no woven fabric has between its own two sides unless it is a figured cloth.

What the numbers do as the fabric is knitted tighter

The loop length is the one variable a knitter really controls, and both faces answer to it in the same direction and by different amounts.

At a loop length of 2.5 millimetres the fabric has a wale spacing of 625 micrometres and a course spacing of 500, giving about 1.60 millimetres of face crown line per square millimetre and 9.6 crown points per square millimetre on the back. At 3.5 millimetres those become 1.14 and 4.9; at 5 millimetres, 0.80 and 2.4.

Both fall as the loop lengthens, and the back falls twice as fast. The face’s crown line goes as the reciprocal of the wale spacing — one power of the loop length — while the back’s crown density goes as the reciprocal of the cell area, which is two powers.

So a tightly knitted fabric is much more strongly two-faced than a loose one, and a very loose knit approaches a surface in which both sides are sparse and neither dominates. That matches what an eye reports: a fine-gauge jersey has an obviously bright face and a dull back, and an open hand-knit has two sides that look much more alike.

It also says which fabrics show a colour difference between their faces, which is a nuisance in garment making. The effect is largest in fine gauges, which is exactly where a garment is most likely to be cut with a panel reversed and where the reversal will be most visible.

What a miss stitch does

The one construction that puts a genuine float into a weft knit is the miss, where a needle takes no yarn and the yarn passes across the back of one or more wales.

Knit, tuck and miss established what those three do to the fabric’s dimensions and its extension. The surface adds one more: a miss is a float, and a float is a plateau, and a plateau is crown line on the back.

So a fabric with misses has crown line on both faces — legs along the wales on one side, misses across the wales on the other. That is a construction with two perpendicular sets of ridges on two sides of one fabric, which is exactly the damask situation again, and it is why single-jersey fabrics with float patterns show their pattern so strongly on the reverse.

And it is why a miss can be seen from the face. A missed wale has no loop drawn in it at that course, so the legs there are longer and lie differently, and the disturbance is visible as a change in the direction of the crown line rather than as a change in anything’s height.

half-cardigan, 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.
Fig. 4 The three stitches drawn as paths rather than as symbols. A knit puts two legs on the face and a head on the back; a tuck puts an extra length of yarn on the back without drawing a new loop; and a miss lays a straight float across the back, which is the only genuine plateau a weft knit has.

What the two faces do to a measurement

Three instruments give different answers depending on which way up a jersey is presented, and none of the standards for knitted fabric says which side to use.

A thickness gauge rests on the heads if the back is up and on the legs if the face is. The heads are the tightest bend in the yarn and stand proud of everything; the legs are a field of parallel ridges. So the two sides do not measure the same thickness, and the difference is a property of the loop rather than of the fabric.

A gloss reading is directional on the face and nearly isotropic on the back, and the face’s reading depends on which way the wales run relative to the plane of incidence — the same azimuth dependence a woven cloth has, with the wale playing the warp’s part.

And a friction measurement returns two numbers for one fabric. Sliding something across the face runs it along the ridges or across them; sliding it across the back runs it over a field of bumps. That is a large part of why knitted fabrics’ friction data scatter so badly between laboratories.

The practical form: a knitted fabric has two surfaces and a specification that does not say which one has been measured has left the answer open, by an amount that is not small.

Where the two faces cross over

A surface of lines and a surface of points do not merely differ; they differ by an amount that depends on how hard the fabric is being pressed, and the two orders cross. That crossing can be located, and locating it says which of the two faces is the one an instrument will find.

A cylinder of radius R indented by δ contacts over a width of 2√(2Rδ), so a face carrying L millimetres of crown line per square millimetre contacts over 2L√(2Rδ) — a square root in the depth. A summit indented by the same δ contacts over a circle of area 2πRδ, so a back carrying N points per square millimetre contacts over 2πNRδ — linear in the depth.

Set them equal. The radius cancels once and the crossing depth is L² ÷ (2RN²π²), which with the dry-relaxed figures — 1.14 millimetres of line, 4.9 points, a yarn radius of 84 micrometres — comes to

33 micrometres.

Below that the face is in contact with more of itself than the back is; above it the back overtakes, because circles growing linearly eventually beat lines growing as a root.

Thirty-three micrometres is a fifth of a yarn diameter, which puts it firmly in the light-touch regime. So a hand, a fingertip, a light rub and a gloss reading all meet a face that touches more; a thickness gauge pressing at its standard load does not. The two faces swap which of them is the more contacting somewhere between a caress and a measurement, which is an uncomfortable place for a crossover to sit and is a plausible part of why knitted friction and handle data disagree so much between laboratories.

The number is an estimate on an estimate and should be read as an order rather than a value — the crown line rests on a guessed leg fraction and the crossing goes as its square. What is not an estimate is the form: a root against a linear, so a crossing exists, exactly one, and the face is on the light side of it. No refinement of the loop path can move which side is which.

One miss outdoes the whole face

The other quantity worth putting a number on is the miss, because the essay’s claim that a float-patterned jersey shows its pattern more strongly on the reverse turns out to be an understatement.

float 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.
Fig. 5 One miss in a jersey, as yarn. The float lies on the face over two wales and nothing else on that face is more than a leg long — so a single miss puts more unbroken yarn on the surface than the whole of the knitted face does, which is the sense in which it outdoes it.

A miss over one wale carries the yarn from a loop to the loop two wales away, a span of about two wale spacings — 1.75 millimetres — and it does so over the two loop cells it crosses, which at 875 by 700 micrometres apiece is 1.23 square millimetres. That is 1.43 millimetres of crown line per square millimetre of back.

The face carries 1.14.

So a single miss per repeat puts more crown line on the back of a jersey than the entire face carries, and it does it in a direction at right angles to the face’s. A float-patterned single jersey is therefore not a fabric with a pattern on its back; it is a fabric whose back has become the more strongly lined of its two surfaces, which is why such fabrics are so often used reversed and why the patterning reads as a deliberate surface rather than as the underside of something else.

It also sharpens the damask comparison the essay makes. A damask’s two regions have comparable crown line in perpendicular directions, which is what makes its contrast about two to one and reversible. A plain jersey’s two faces are perpendicular but very unequal in kind — line against points — so the comparison is an analogy. Add misses and it stops being an analogy: two faces, comparable crown line, perpendicular directions, one fabric, one yarn. The nearest thing in this collection to a damask made without a jacquard is a float-patterned jersey seen from both sides.

Where the model stops

There is no loop path. That is the whole limitation and it is a large one: everything numerical above rests on a leg taken as straight over a guessed fraction of a spacing. A proper knitted-loop geometry — of the sort Peirce’s is for weaving — would let the crown line be computed rather than estimated, and this collection does not have one.

The loop is taken as lying in a plane. It does not: a knitted loop is three-dimensional, its legs are displaced out of the fabric’s plane, and the two faces are not mirror images. That is precisely what makes a jersey curl, and it is a real asymmetry that the flat model cannot represent.

Nothing here has yarn twist in it. A knitted fabric’s face shows the twist of its yarn strongly — it is why a jersey leans — and a twisted yarn’s surface has its own helical ridges running at the twist angle, which are a second set of crowns at a scale below this one.

And no pressure. Everything about a knit’s response to being pressed is a bending problem rather than a compression one, as the compression essay records: the bearing curve is still the right description of what is in contact and the law relating depth to load is not the woven one.

Why the curl and the two faces are the same fact

Stockinette curls, and it curls in a direction that depends on which edge it is: the top and bottom roll towards the face, the sides towards the back.

half-cardigan as an array. One cell per needle per course, over 2 repeats each way. K knits a new loop and casts the old one off, T tucks the yarn into the loop below without casting off, M misses the needle and floats past it. The margins carry the two conditions: a wale with no K in it never casts off, and a course with no K in it is never caught by anything. Both hold here.
Fig. 6 A structure that puts yarn on both faces deliberately. Why the curl and the two faces are the same fact is that both follow from where the yarn sits relative to the fabric’s mid-surface — and a fabric that balances the one balances the other.

That asymmetry and this essay’s asymmetry are the same asymmetry. The loop puts different parts of the yarn on the two sides, so the two sides have different amounts of yarn in them and different bending stiffnesses along the two axes — and a sheet with different properties on its two faces bends until it has relieved the difference.

So a jersey’s curl is visible evidence for the surface claim. A fabric whose two faces were made of the same thing would have nothing to curl about, and the fabrics that do not curl — rib, interlock, garter — are exactly the ones knitted so that each face gets legs.

That is a satisfying arrangement. The surface argument and the curling argument are independent readings of one structural fact, they were made in two different phases of this collection about two different properties, and each is a check on the other.

The generalisation

A fabric made of one continuous path has two faces made of different parts of that path, and the parts differ in curvature.

cross tuck as an array. One cell per needle per course, over 2 repeats each way. K knits a new loop and casts the old one off, T tucks the yarn into the loop below without casting off, M misses the needle and floats past it. The margins carry the two conditions: a wale with no K in it never casts off, and a course with no K in it is never caught by anything. Both hold here.
Fig. 7 A structure that alternates which face it favours. The generalisation is that a fabric made of one repeated part has as many surfaces as the part has faces, and a knitted loop has two — so any structure built from it can put either on the outside, course by course.

That is the transferable statement, and it separates knitting from weaving in a way this collection has not previously had a word for. A woven cloth’s two faces are made of the same parts of two different thread systems — a crossing seen from above and from below — so its two sides differ in which system is on top. A knitted fabric’s two faces are made of different parts of one thread, so they differ in what shape the yarn is making.

The consequence is that a woven fabric’s two faces can be made identical by balancing the weave, and a knitted fabric’s cannot be made identical at all. A plain knit has no balanced version, because there is no arrangement in which the legs and the heads are on the same side.

That is also why the fabrics that do have matching faces — rib, interlock, purl — are made by knitting on two beds, so that each face gets legs from its own set of needles. Rib and interlock is that argument told through the dimensions; this is the same construction seen from the surface.

One caution goes with that. The curl direction is decided by a bending asymmetry and the surface claim is about crown orientation, and the two are consequences of the loop rather than of each other — so agreement between them is corroboration and not proof. A construction could in principle have one without the other. None of the ordinary ones does.

Who found it, and when

The distinction between the technical face and the technical back is as old as machine knitting and is in every text. The reason usually given is that the face shows the legs and the back the heads, which is a description.

What the surface adds is why that matters: a leg is a ridge and a head is a summit, so the two faces are two different kinds of surface rather than two views of one. And it identifies the situation with a damask’s, which is a connection between a jacquard-woven linen and a knitted vest that nothing else in this collection would have produced.

Where the ladder goes next

To the two finishes that replace a surface rather than reading it: a coating fills the crowns before it bridges the holes, which is the volume above the bearing curve, and friction is two surfaces rather than one, which is what happens when a fabric meets another fabric instead of a plate.

Where this goes next

The knitted loop. One thread, bent into a course of loops, each of them drawn through the loop below. Nothing here is straight, which is why a knit extends in every direction while a woven cloth extends only on the bias. The loop A knit is one thread bent into loops, each drawn through the loop below. Nothing in it is straight, which is why it stretches in every direction while a woven cloth stretches only at an angle. A damask's figure and ground trade places when the cloth is turned. A satin 8 figure on a sateen 8 ground in sheeting — one cloth, one set of threads, one sett, and the ground is the figure's own complement. Their total specular areas are within a few per cent of one another, so neither is intrinsically the brighter. What differs is the direction: the figure's crowns run with the warp and the ground's with the weft. So the contrast between them is 2.0-to-one with the light coming from 8° and 0.47-to-one from 90° — it reverses, exactly, a quarter turn apart. That is what makes a damask visible in one colour, and it is not the step in its surface: the step is fifty micrometres and returns no light at all under a diffuse illumination, while this contrast is a factor of 2.0 and is present whenever there is a direction in the light. A figure shows by its shine, not its step A damask is one cloth in one colour and its pattern is plainly visible. This collection attributed that to the step in its surface — fifty micrometres of relief, computed from the interlacing rates. The step is real and returns almost no light. What makes the figure visible is that its crowns run at right angles to the ground's, so the two trade places when the cloth is turned. 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.

Reads more easily once this is understood

Essays that name this one as worth reading first.

Shares its objects with

Essays naming at least two of the same things, that neither author linked.

Named objects

A flat tag is an object no other essay names yet.

CourseCrown lineKnit geometryLoopMunden constantsSpecular areaSurface heightWale