Textile Structure
how cloth is put together
Concept

Prickle — where it appears

The sting a cloth gives when stiff fibre ends press into the skin hard enough to fire its pain nerves. It is mechanical rather than allergic: an end fires a nerve only if it can carry the threshold force without buckling, and the fourth power of its diameter decides that.

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

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.

Buckling loadFibre diameterHair layerPopulationProtrusion lengthWoolCoefficient of variationFibre finenessOrder statisticRaisingSingeing

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