Wicking borrows drying area from the cloth that is not touching

A sweating cloth wicks as high as the room can dry it fed a strip of cloth at its foot with a rate of sweat, and found that the cloth rises to the supply over twice the evaporation, whatever it is made of, until its fine pores’ capacity — past which the holes between its yarns fill. It ended by admitting that a shirt is not fed at the foot of a strip. It is fed across the whole of the skin it touches, and the cloth over that skin is losing water from one face, not two.

That changes which part of the cloth is the bottleneck, and the answer turns wicking from a property of a fabric into a way of borrowing area.

Through its thickness the cloth is never the limit #

Sweat reaching the inside face of a pressed cloth has to cross the cloth to the outside face, where the room can take it. The path is the thickness — 0.38 millimetres for the sheeting used throughout — and the fine pores between the fibres drive water along it with their whole capillary suction, 62 kilopascals.

By Darcy’s law that path could carry about 187 million grams of water per square metre per hour. A body at rest sweats 15; hard work, twelve hundred. The cloth’s capacity to pass sweat through itself is five orders of magnitude above anything a body asks of it.

So the question that mattered for the strip — how much can the fine system carry? — does not arise for a pressed patch. The patch’s fine pores are full almost at once and stay full, and the only rate that can limit it is the one on the other side of its outer face: how fast the room takes water away. The strip essay’s capacity was a capacity for carrying water along the cloth, over tens of centimetres, where the path is a thousand times longer than the thickness and the flow a thousand times harder.

A patch pressed flat floods at the room’s own rate #

A patch of cloth pressed to skin loses water from its outer face at the room’s evaporation rate $E$, and from its inner face at nothing, because the inner face is against skin. If the sweat rate $S$ is below $E$, the patch keeps up: the face dries as fast as the skin feeds it, and the cloth stays at a steady damp with its holes open.

If $S$ is above $E$ and the patch has nowhere else to send the surplus, the water accumulates. A cloth pressed flat everywhere floods as soon as the sweat outruns the room’s evaporation, and in an ordinary room at 100 grams per square metre per hour that is less than light work. In still air at 20 it is barely above rest.

The flood is not instant. The surplus first fills the fine pores the patch has not yet saturated — 111 grams per square metre for this sheeting — and only then the holes between the yarns.

At light work in an ordinary room that takes 2.2 hours; at a run, 17 minutes; at hard work, six. These are the times a close-fitting garment has before the wet patch spreads, and they are set by the room and the sweat, with the cloth entering only through its fine-pore water.

Free cloth above the patch is borrowed area #

Most garments do not touch everywhere. Above the patch of contact there is cloth hanging free, losing water from both faces, and the patch’s surplus can be wicked up into it. That is exactly the strip of the earlier essay, fed at its foot with $(S - E)s$ per metre of width, where $s$ is the patch’s height.

The free cloth wets to the height where its two faces evaporate the surplus:

$$h = \frac{(S - E)\,s}{2E},$$

and the whole wetted area, patch plus free cloth, is

$$\frac{s + h}{s} = 1 + \frac{S - E}{2E}$$

times the patch’s own. The contact’s size has cancelled. The drying area a sweat rate needs is set by the sweat and the room alone: at a run in an ordinary room, three times the area of skin in contact, whether the contact is a hand’s breadth or a whole back. Wicking is how the garment gets that area — it borrows it from the cloth that is not touching.

The contact decides whether the cloth can reach it #

What the contact’s size does decide is whether the free cloth can supply the area. The free strip can carry water up only to its drying ceiling, half a metre in an ordinary room, and at the capacity the earlier essay found. A tall contact needs a tall wetted strip above it, and if that exceeds what the strip can carry, the surplus stays in the patch and floods it.

The two halves of the argument meet on one chart. The area a sweat needs rises with the sweat and is the same for every contact; the area free cloth can lend a contact is a level line, lower for a taller contact because the same strip has to serve more skin.

So the flood threshold for a contact with free cloth above it is

$$S_{\text{flood}} = E + \frac{0.989\cdot 2E\,h^*}{s},$$

the room’s own rate plus the strip’s capacity shared over the contact. A run floods any contact taller than 247 millimetres in an ordinary room; hard work, any taller than 90; light work, none shorter than two metres. The share 0.989 is the flood point the earlier essay found — the holes fill in the last one per cent of the strip’s capacity — and it enters here unchanged.

Why a tight top soaks through and a loose one does not #

That is the everyday observation the arithmetic accounts for, and it accounts for it without a word about fibres. A close-fitting top touches the back over forty centimetres; a loose shirt touches it at the shoulder blades and not between. At a run in an ordinary room the tight top needs three times its contact area to dry and cannot reach it — the free cloth above a forty-centimetre contact would have to wet to eighty centimetres and can manage fifty — so it floods. The loose shirt’s contacts are a few centimetres tall and each has a whole panel of free cloth to borrow from.

The same cloth, cut two ways, is dry in one and soaked in the other. A garment’s fit is a wicking specification, and a much more powerful one than its fibre: halving the contact height doubles the sweat rate it can carry above the room’s own, while the choice between fine and coarse fibres moved the strip’s capacity by a factor of two over a sevenfold change in diameter.

A flooded patch clings, and clinging makes the contact taller #

The flood has a consequence the steady arithmetic does not follow and cannot ignore. A cloth whose holes are full of water is a cloth held to the skin by the water’s own surface tension: a wet shirt clings. And clinging is contact. The patch that floods grows, the free cloth above it shrinks, and the threshold, which falls as one over the contact’s height, falls with it.

So a flood is not a state a garment reaches and stays at; it is the start of a spread. A tight top at a run floods over its forty centimetres of contact, clings further, and the contact that has to be served grows while the cloth that could serve it becomes contact too. The same run in a loose shirt, whose contacts are short enough never to flood, never starts the spread. On this account the difference between a shirt that stays dry and one that soaks through is a threshold with feedback on one side of it, which is why the change from one to the other is sudden rather than gradual.

What flooding costs the wearer is the holes. Half the air goes through a tenth of the holes, and a hole full of water passes none, so the flooded patch stops breathing where it most needs to. A cloth stops having holes before it stops passing air found how much of a cloth’s air goes through its biggest openings; those are the openings the surplus fills last, because a big hole’s own suction is the weakest. And the water swells the yarns it soaks, as what water does to a thread found, closing the holes that are left.

The room sets both thresholds #

Every threshold here has the room’s evaporation in it twice: once as the pressed patch’s own limit, and once inside the free strip’s capacity, which grows as roughly the root of the evaporation.

In still air at 20 grams per square metre per hour, a pressed patch floods at barely more than rest, and at a run any contact taller than about nine centimetres floods. In a wind at 1,500, a pressed patch holds out through hard work, and the free cloth adds more. So a garment that stays dry on a cycle ride soaks through on a treadmill at the same effort, and the difference is the air moving past it, not the effort or the cloth. The time a wick takes runs the same way: a wind shortens the drying time and the approach to the ceiling together.

Fit is the specification, and the air decides which fit #

The thresholds turn into a rule a designer can use. For a given activity and a given air, there is a tallest contact the garment may make with the body, and everything about the cut follows from keeping below it.

On a run in an ordinary room, contacts must stay under a quarter of a metre, which a close-fitting top cannot do across a back. Under hard work they must stay under nine centimetres, which only a loose shirt manages. On a bicycle the answer reverses. The rider’s own speed puts the air at something like the wind in this account’s table, 1,500 grams per square metre per hour, and a cloth pressed flat against the skin then floods only above that — above hard work. So a cycling jersey can be skin-tight and stay out of flood at efforts that would soak a running shirt of the same cloth cut the same way, and the difference is not the cloth or the effort but the air the wearer makes by moving.

That is a reading of a familiar split — tight jerseys on bicycles, loose shirts on runners — and it comes straight out of the one quantity every threshold here contains. The same garment worn on a turbo trainer indoors, with the rider not moving through the air, is on a pressed patch in an ordinary room and floods at light work.

What the fibre is left with #

After the contact, the room and the sweat have taken their shares, the cloth’s own properties are left with two jobs. The first is the fine-pore water a pressed patch must fill before it floods, which a cotton’s own water found is set by the construction far more than the fibre. The second is the free strip’s capacity, which the fibre and packing move as the drying balance found — permeability against suction.

Neither of those is the property a wicking test measures, which is a height in a dish. The pore that wicks is the pore that leaks, and the finest pores set that height; on a body, the finest pores’ only job is to be present — any cloth whose fine pores are a few micrometres across has five orders of magnitude of through-thickness capacity to spare.

The model named #

The pressed patch is a height $s$ of cloth held against skin, fed across its face at the sweat rate $S$, evaporating from its outer face at $E$ and not at all from its inner face. The through-thickness flow is Darcy’s across the cloth’s 0.38 millimetres under the fine pores’ full suction, with the fine system’s permeability as the earlier essays computed it. The free cloth above is the drying strip of those essays, fed at its foot with the patch’s surplus $(S - E)s$ per metre of width, wetting to $(S - E)s/2E$ below its capacity and flooding at 98.9 per cent of it. A patch with no free cloth fills its fine pores with the surplus and then its holes. The rooms and sweat rates are the brackets the earlier essays used: 20, 100, 400 and 1,500 grams per square metre per hour from each face, and 15, 150, 500 and 1,200 for rest, light work, a run and hard work.

What was counted #

The tallest safe contact at 61 sweat rates in each of four rooms; three contacts drawn to scale at a run; the time to fill a pressed patch’s fine pores at 50 sweat rates in three rooms; and the through-thickness capacity once, for the model sheeting. The flood share and the strip’s capacity are the earlier essay’s, recomputed here, not re-derived.

What the picture cannot show #

The inner face does not evaporate at nothing everywhere. Where a garment touches, the skin’s side is closed; where it lifts away, the inner face loses water to the air gap, which is warm and humid and far slower than the room. The free cloth here loses at the full room rate from both faces, which is the most it could. A real loose shirt borrows less area than this and floods somewhat sooner.

The contact is a height and not a shape. Real contacts are patches of every outline, fed through the whole of their area and bordered by free cloth on all sides rather than above. A patch with free cloth on four sides has four times the edge to hand its surplus across, which raises every flood threshold here; the one-sided strip is the least generous case.

The cloth is dry to start and the skin is the only source. Rain, a spill or a previous hour’s sweat change the starting fine-pore water, and a garment already partly wet has less of the 111 grams to fill before it floods. And the whole calculation is steady: a run that stops after twenty minutes never reaches the steady state at all, which is what the drying time decides.

Who found it, and when #

Garment designers and sports physiologists have long known that fit, air movement and evaporation dominate how wet a shirt gets, and that a fabric’s laboratory wicking figure predicts little of it. Darcy’s law is from 1856 and the drying strip is the earlier essays’.

What is done here is to put the pieces together and find that the contact’s size cancels from the area a sweat needs, so that the whole role of wicking on a body is to borrow drying area, and that a contact floods at a height set by the strip’s capacity over the surplus.

Still open: what the air gap takes #

Everything above treats a loose garment’s inner face as open to the room. It is not: between a shirt and a back is a layer of air a few millimetres to a few centimetres thick, warmed by the skin and humidified by it, and the inner face evaporates into that layer at a rate that depends on how fast the layer is ventilated.

That rate is the missing number in every loose garment’s balance. If it is near the room’s, a loose shirt borrows nearly twice the area this account gave its free cloth; if it is near nothing, the free cloth dries from one face and borrows half. The calculation is a ventilated channel with a wet wall on one side and a warm wet wall on the other, and it would say whether a garment’s cut should aim to keep the gap still, for warmth, or moving, for drying.