Textile Structure
how cloth is put together
Concept

Air permeability — where it appears

How much air a fabric passes at a stated pressure drop, quoted as a face velocity in millimetres per second at a hundred pascals. It is two paths in parallel — the channels between the threads, which the construction controls, and the pores inside the threads, which it does not — so it has a floor set by the yarn rather than by the loom.

Named by 8 essays across 5 fields — each of them below, with the objects they name alongside it.

When a knit has a hole between its loops, and when it has none. A loop's occupancy is its length times its diameter over the cell it sits in, and Munden's constants make that cell ℓ²/(k_c·k_w). The loop length cancels once and what is left is d·k_s/ℓ, where k_s is Munden's own stitch-density constant — so whether a knit has a hole between its loops depends on d/ℓ and on nothing else: no gauge, no count, no fabric dimension. The three curves are the three relaxed states of 20 tex cotton. Each crosses one at a loop length of 3.34, 3.63, 3.95 mm respectively, and a jersey is knitted at 2.63 to 3.44 mm — the shaded band. Every commercial jersey is therefore on the wrong side of the threshold in at least two of its three states: it closes its own holes as it relaxes, and its air goes through its threads rather than between them.

A knit has no hole to lose

Every argument in this ladder is planar: threads at a spacing, a rectangle between four of them, a channel down it. Applied to a jersey it returns nothing at all, and the nothing is the finding. A loop's occupancy is its diameter times Munden's own stitch-density constant over its loop length, with no gauge and no fabric dimension in it — and the whole commercial range of tightness is on the wrong side of the threshold.

knits · Knit geometry What a muslin passes, against how closely it is set. A muslin's air permeability at 100 Pa as the sett is closed from 6.9 to 34.2 threads per centimetre, with the two paths separated. The channels between the threads carry 8285 mm/s at the open end and 1330 at the close one, and they go to zero when the cloth jams. The threads themselves carry 1.7 to 6.4 mm/s and never go to zero at all, because a thread is sixty per cent fibre whatever the sett is. Extended to a cloth with no channel left, that path is 8.1 mm/s — a floor set by the yarn rather than by the construction, and a specification asking for less has asked for a fabric that cannot be woven from this yarn at any sett.

A cloth stops having holes before it stops passing air

Close a woven cloth up and the channels between its threads shut. What passes through it does not go to zero, because a thread is sixty per cent fibre and forty per cent air and stays that way whatever is done to the construction. So a fabric's permeability has a floor, the floor belongs to the yarn rather than to the weaver, and no sett on any loom reaches it.

applied · Permeability Four ways of closing a muslin, and the floor under all of them. The same muslin at four states: as woven, calendered to 3:1, wetted so its fibres swell by 20 per cent, and with the channel between its threads gone altogether. Air permeability at 100 Pa falls from 3505 mm/s to 8.1 — a factor of 434 — and stops there. The last figure is not a cloth with no holes in it: it is a cloth whose only remaining path is through the threads, which are sixty per cent fibre whatever is done to the construction. That number is the floor, it is a property of the yarn, and no sett reaches it. Note that the two middle routes are not in a fixed order: a 3:1 calender closes more than this swelling and a 2:1 calender closes less, so which is the stronger depends on how far each is taken.

A windproof cloth is at its yarn's limit

Windproof is a threshold on air permeability, and it is the only fabric specification on this site that the construction cannot settle. No weavable sett of an ordinary shirting yarn gets within two hundred times of it, layering the cloth barely helps because the resistance is inertial rather than viscous, and the floor set by the yarn's own porosity lands on the same order as the threshold with a fivefold bracket around it.

applied · Permeability Where Poiseuille's rule starts being true of a cloth. Every account of a fabric's air permeability quotes the fourth power: flow down a channel goes as the fourth power of its width, so a small change of sett is a large change of flow. That is Poiseuille's result and it is about the viscous drop. A channel through a cloth is about as long as it is wide and the air in it is moving fast, so most of the pressure goes on giving that air its kinetic energy instead — and the inertial term does not depend on the hole's size at all. Plotted against cover, the viscous share of the drop runs from 1.0 per cent in an open muslin to 61.6 in a close one, passing half at a cover of 0.571. Quoting the fourth power alone below that is wrong by a factor rather than by a correction: at the open end it overstates the flow 98-fold.

The fourth power is a close cloth's rule

Every account of a fabric's air permeability quotes the same thing: flow down a channel goes as the fourth power of its width, so a small change of sett is a large change of flow. That is Poiseuille's result, it is about the viscous drop, and in an open cloth the viscous drop is two per cent of the pressure. The rule becomes true as the cloth closes, and where it starts being true is a number.

setting · Permeability A yarn's diameter is a contour, not a length. The fraction of the space beside a 20 tex cotton yarn that is occupied by hair, against height, grossed up from the modelled population by the measured split between the long and short populations. At the yarn's own surface it is 8.9% — the layer is almost entirely gap — and it falls away exponentially from there. Every instrument that reports a yarn diameter is picking a contour of this curve, and the contours are far apart: a threshold that needs half the space filled is never met at all, one that needs a twentieth is met at 355 µm, and a hair counter triggers out at 2353 µm. The earlier model gave the layer a single thickness of 25 µm, which is a fair description of where most of the material is and wrong about its extent by more than a decade. What the curve cannot say is which contour any particular instrument uses, which is a fact about the instrument.

A cloth is more opaque than it is closed

Opacity is not cover — this collection established that already and left the discrepancy attributed to the thickness of the threads. Part of it is not in the threads at all. A hair standing in a hole blocks light exactly as well as a thread does and costs nothing in air.

pattern · Opacity A slot and a square of the same area do not pass the same air. A hole of 62500 square micrometres, drawn out from a square to a slot twenty times longer than it is wide, at constant area throughout. The open area is unchanged by construction and the flow is not: it falls to 39 per cent of the square's. Two things move the same way and neither is a correction to the other — the hydraulic diameter falls as the rectangle is drawn out, and the shape factor rises from 14.23 for a square towards 24 for an infinitely thin slit, which is Shah and London's result quoted rather than derived. This is why a weave's float matters to what it passes even where its cover does not: a float lays parallel threads side by side and the hole beside it is a slot.

A satin's hole is a slot

Two cloths at the same cover have the same open area, exactly, and do not pass the same air. A float lays parallel threads side by side and the hole beside them is long rather than square, and drawing a hole out at constant area cuts what it passes to two fifths — because the hydraulic diameter falls and the shape factor climbs, and both of them move the same way.

weaves · Float Where a muslin's warmth actually is. A muslin's own thermal resistance is 0.0108 m²K/W, and the still-air layer clinging to its outside is 0.12 — so 92 per cent of what a person is wearing is air that is not in the cloth. Wind takes it: the boundary layer thins as the square root of the speed, and above a few metres per second the air is also being driven straight through the fabric, which shorts out whatever resistance the fabric had. The pair leaves 22 per cent of the still-air value at 16 m/s. Both mechanisms take away air rather than cloth, which is why a windproof layer works and a thicker weave does not, and why the fibre — which the conductivity bracket could not separate anyway — never enters this figure.

The wind takes the air and not the cloth

A shirting's own thermal resistance is eight per cent of what a person wearing it has; the other ninety-two is a still-air layer half a millimetre thick clinging to its outside. Wind destroys both, and it destroys the larger one first and by a mechanism that has nothing to do with the fabric — so a windproof layer works by keeping air still rather than by resisting heat.

applied · Insulation Where a muslin's air goes, as the cloth is set closer. A permeability computed from the average hole says nothing about which holes the air uses, and once the holes have a spread the answer is: not many of them. Two curves, both over the same population of holes — the share of the flow carried by the widest tenth, and how few of the holes carry half of it. At 16 ends per centimetre the cloth is nearly democratic: the widest tenth takes 12% and half the air needs 45% of the holes. At 44 the widest tenth takes 53% and half the air goes through 8.8%. Both inputs move together as the cloth closes — the spread in the holes rises because the spacing is fixed and the diameter is not, and the exponent rises because the pressure drop stops being inertial — so the concentration rises faster than either.

Half the air goes through a tenth of the holes

A permeability computed from the average hole says nothing about which holes the air uses. Once the threads have a spread, the answer is: not many of them — and in a close cloth, half the flow leaves through less than a tenth of the openings.

setting · Permeability

Named alongside it

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

Clear openingCover factorOpen areaInertial lossPoiseuille flowFibre volume fractionHydraulic radiusKozeny carmanPacking factorBoundary layerCanopy criterionCoating

All concepts