Generator

The sett moves the flux and not the height

A 20 tex cotton yarn woven at every sett from 8 to 34 threads per centimetre. Above: the hole between the threads lifts from 27 to 234 mm as the cloth closes, while the space between the fibres lifts 6.37 m at every one of them — so the cloth's maximum is the flat line, and the sett does not touch it. Below: the permeability of those holes falls by a factor of 292 over the same range. Both curves are monotone, so there is no optimum — only an interval, ending at the jam at 34.6 threads per centimetre.

3 essays call wick-curve. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the weave its essay argues about.

Where it is called

Changing this generator changes every one of these figures.

Setting and geometry

The sett decides how much, not how high

Every rung of this ladder so far has found the sett deciding something. This one finds it deciding nothing at all: a cloth's maximum rise is 6.37 m at eight threads per centimetre and 6.37 m at thirty-four, because the sett cannot reach inside a yarn.

Two pore systems in one cloth — 24 threads per centimetre. A plain weave of 20 tex cotton in section, at 24 threads per centimetre, so the yarn is 167 µm across and the clear hole between two picks is 250 µm. That hole's hydraulic radius is 124.8 µm. Inside the yarn, fibres 14 µm across packed at 0.6 leave spaces of hydraulic radius 2.33 µm — 53 times finer, and by Jurin's law 53 times higher: 6.37 m against 119 mm. The yarn's interior is magnified 6 times and the two discs at the foot are the only part drawn at one scale.

Cloth doing a job

How high a cloth wicks

A woven cloth has two capillary systems and they are a factor of twenty to a hundred apart. The one every diagram draws — the hole between four threads — lifts 119 mm. The one nobody draws, inside the yarn, lifts 6.37 m.

The coarsest pore and the finest, in one muslin. A muslin's two pore systems asked the same question. Water at a contact angle of 120° is held back by a pore of radius r at a head of 2γ|cos θ|/ρgr, so the hole between four threads — hydraulic radius 134 µm — holds 56 mm of water, and the space between the fibres inside a thread — 2.50 µm — holds 2975 mm. Water takes the cheapest path, so the cloth leaks at the first of them and the second is never asked. Turn the contact angle round to a wetting one and the same two radii give a rise instead, and now it is the finest that decides, because that is the one that lifts highest: 5950 mm. One expression, two ends of a distribution, and the fabric's two properties read opposite ends of it.

After the loom

The pore that wicks is the pore that leaks

A cloth's water resistance and a cloth's wicking are one expression, read at the two ends of a contact angle. The geometry cannot be chosen to give both, because it is the same geometry; the only thing that decides which a fabric does is a finish. And the two questions do not even read the same pore — a rise is set by the finest and a leak by the coarsest, so the same cloth lifts water three metres and holds it back at fifty-six millimetres.

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