Textile Structure
how cloth is put together
Concept

Wool — where it appears

A scaled protein fibre whose surface friction is directional, which is why it felts and no other common fibre does. Water widens the gap between its two coefficients rather than lubricating them, so felting is a wet process for a reason the ratchet can state.

Named by 5 essays across 2 fields — each of them below, with the objects they name alongside it.

The ratchet a wool fibre is. A fibre with its scales, and the two strokes of one cycle of agitation. The push is the same in both directions; the distance is not, because the scales resist tip-first motion more than root-first. Every cycle therefore nets a displacement in one direction, and no amount of further agitation undoes it.

The ratchet that makes wool felt

A wool fibre is covered in scales pointing one way, so it slides more easily root-first than tip-first. Agitate it and the motion is symmetric while the result is not — every cycle nets a displacement in one direction, and no amount of further agitation undoes it.

finishing · Felting What a shrink-resist treatment has to do. Net displacement per cycle of agitation as a treatment closes the gap between the two friction coefficients. The chemistry is sold as gluing the scales down; what it has to achieve is arithmetic — make the fibre slide equally well both ways and the ratchet has nothing to rectify.

Shrink-resist is one number

Machine-washable wool is sold as a coating that glues the scales down. What the treatment has to achieve is narrower and more exact — make the fibre slide equally well in both directions, and the ratchet has nothing left to rectify, whatever the friction happens to be.

finishing · Felting The ratchet a wool fibre is. A fibre with its scales, and the two strokes of one cycle of agitation. The push is the same in both directions; the distance is not, because the scales resist tip-first motion more than root-first. Every cycle therefore nets a displacement in one direction, and no amount of further agitation undoes it.

Why felting needs water

Wool felts in a wash and not in a drawer, and the usual explanation is that water lubricates the scales. It does the opposite of that. Water lowers one of wool's two friction coefficients and raises the other, so it widens the gap the ratchet rectifies — and what follows is a saturating function of the ratio, not of either coefficient.

finishing · Felting Thirty micrometres is a buckling load. The wool fibre diameter at which a protruding end reaches the measured threshold for prickle, against how far it protrudes. A fibre end pressed against skin is a column held at the cloth and free to slide at its tip, so it buckles at 20.19EI/ℓ² and carries no more load than that; below the threshold it bends away and is felt as touch, above it the load stands and is felt as pain. At a two-millimetre protrusion — which the hair model behind these figures puts in the top fifth of a wool's population — the threshold diameter is 32 µm, bracketed at 29–34 by the range of the measured force. Neither the thirty micrometres nor the two millimetres was put in. The band is the force bracket, and the fourth power in I = πd⁴/64 is what makes the boundary sharp: at a mean of 21 µm and a spread of 24%, 3.2% of the fibres are over it, and it is that few per cent that decides whether a garment can be worn.

Prickle is a buckling load

The wool trade specifies comfort against skin by the percentage of fibres coarser than thirty micrometres, and the thirty is a measured boundary with no derivation attached. It is a column formula: solve for the diameter at which a protruding fibre end stops bending away and starts standing its ground, and thirty micrometres falls out.

applied · Prickle A fibre end prickles only inside a window. The lengths at which a wool fibre end can press on skin with the measured threshold force, against its diameter. Above the rising curve the end is too long a column and lies over before it reaches the force. Below the falling curve it is too short to sink far enough into a skin of 30 kPa to reach it. The two meet at 23.2 µm and 1.08 mm, and no fibre finer than that prickles at any length. A 30 µm fibre prickles between 0.83 and 1.79 mm.

A fibre end prickles only inside a window

A fibre end pressed against skin has two ways to fail to hurt. Too long, and the column lies over before it reaches the force a nerve answers to. Too short, and the tip cannot sink far enough into something as soft as skin to push that hard. The two limits run opposite ways with diameter and they cross, so a fibre below one diameter cannot prickle at any length at all — and that diameter has no protruding length in it. It also settles a sum left unweighed: a crop at 1.1 mm makes a wool cloth two and a half times worse, and one at 0.6 mm removes the prickle.

applied · Prickle

Named alongside it

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

FeltingFrictionBuckling loadFibre diameterFibre migrationHair layerIrreversibilityPopulationPrickleProtrusion lengthShrink-resistAgitation

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