Coated is a state

The finishing field on this site ends with a collecting essay. It found that every quantity computed here divides cleanly into those that are properties of a fabric and those that are properties of a fabric in a stated condition — and that the second kind had been quoted throughout without the condition. A cloth’s dimensions mean nothing until somebody says whether it is off the loom, dry-relaxed, wet-relaxed or fully relaxed.

This essay is the same move on a different axis, and the axis is coarser. Coated is a condition too, and it is one no number on this site has ever said it was or was not in.

What makes it worth an essay rather than a footnote is that the change is not uniform. A coating does not scale the site’s results by a factor or add a term to them. It reverses two of them, halves one, adds to one, changes three in kind, and leaves exactly one pointing the same way.

What a coating actually does #

One sentence covers all of it: a film bonds the crossings.

Every mechanical result on this site rests on the crossings being free. The trellis has inextensible threads that can rotate where they cross, and that freedom is the whole reason a cloth on the bias stretches by a third while nothing in it stretches at all. A tear runs because threads slide together and share a load. A cloth does not mind a hole because the cut threads hand their load to their neighbours through friction rather than through a continuum. A cloth wicks because there are channels between and inside the threads.

Bond the crossings and none of those mechanisms exists. The trellis becomes a sheet with a shear stiffness; the threads cannot gather; the load path becomes continuous; and the coarse channel system is closed.

That is not a modification of the model. It is a different model with the same picture.

The two that reverse #

Most of the table changes a result in kind, which is unsurprising once the mechanism is stated. Two of them change its sign, and both are worth stating because both are results this site argued at length.

A cloth does not mind a hole — until it is coated. A film with a hole in it loses two thirds of its strength whatever the hole’s size, because a continuum concentrates stress at an edge. A woven cloth loses only the threads that were cut, because each thread carries its own load and hands it back to its neighbours a short distance away. That is one of the clearest results in the applied field, and it is a statement about a fabric whose crossings are free. Coat the cloth and the load path is continuous again, and the concentration comes back.

Air permeability goes to nought. An uncoated cloth’s permeability follows its open area, which is one minus the cover, and this site has the arithmetic. A coated cloth’s is zero, exactly, and the whole open-area calculation stops being about anything. That is not a large change in a number; it is a quantity ceasing to be a function of the thing it was a function of.

The one that keeps its sign, and why it is the interesting one #

Exactly one row of the table points the same way in both states, and it is the one the previous rung is about.

A closer sett means more threads and more load in an uncoated cloth. A closer sett means a smaller span for the film and a higher burst pressure in a coated one. Two entirely different mechanisms, and both say the same thing: closer is stronger.

That is worth noticing because it is the only place where an intuition carried across the boundary happens to survive. Everywhere else in the table, reasoning about a coated fabric with an uncoated fabric’s model gives an answer that is wrong in kind and sometimes wrong in sign, and the fact that one row comes out right is a coincidence of two mechanisms rather than a sign that the model transfers.

The one that is halved #

Wicking is the row that is neither reversed nor removed, and it is the most informative.

A cloth has two capillary systems and they are one to two orders of magnitude apart: the coarse holes between the threads, and the fine channels between the fibres inside a yarn. This site has essays on both, and on the fact that the two are treated as independent when they are not.

A coating closes the coarse system and leaves the fine one alone. So a coated fabric still wicks — along its yarns, inside them, at the rate the fibre packing decides — and does not wick through its holes at all. Half the mechanism survives, and it is the half nobody draws, because every diagram of a cloth wicking shows the hole between four threads.

That has a practical consequence which is well known and not usually explained this way: a coated fabric can be perfectly waterproof through its face and still carry water along a cut edge or a stitch line, because the yarn’s interior is a continuous wick that the coating never touched.

What was counted, and how #

Only one row of this table is a computation and it is the previous rung’s: the bound on what a film holds over one hole, the ratio result that follows from it, and the crossing between the film’s bound and the cloth’s own strength. Everything drawn in this essay’s curves comes from there.

The table itself is a collection, and it is labelled as one. Each row names a quantity this site computes elsewhere, says what the uncoated model gives, says what the coated case gives, and classifies the change: reversed, changed in kind, halved, added to, or unchanged in sign. The classification is the content and it is asserted rather than left to a reader — the machinery requires that at least two rows reverse and that exactly one keeps its sign, because a table in which everything changed the same way would be a table with no structure in it.

That is the same discipline the finishing field’s collecting essay used. A collection of results is only worth making if the collection has a shape, and the shape has to be checkable.

The row that is added to rather than changed #

One row of the table behaves differently from the other six and it is worth a paragraph, because it is the row a buyer meets first.

Areal weight is a sum. This site computes a fabric’s grams per square metre as four products in the yarn — two setts and two counts, with a crimp correction — and no term in it appears alone. A coating adds a term, and the term is often the largest one: a hundred and twenty micrometres of PVC at the density of a plasticised polymer is well over a hundred grams per square metre, which is more than many of the cloths it is spread on.

So a coated fabric’s weight is not a fabric weight with a correction. It is two numbers of comparable size added together, and every quantity this site derives from a fabric’s weight — its cover, its yarn count at a stated sett, its comparison with another construction — is a statement about the substrate rather than about the product.

That is a mundane observation and it is in the table for the same reason the others are: the uncoated number is quoted everywhere, it is correct, and nothing anywhere says which of the two states it belongs to. A specification listing a base fabric at 220 g/m² and a coating at 180 is being perfectly honest and is describing an object whose measured weight is 400, of which the part this site can compute is a bit over half.

The seven rows do not switch at the same coating weight #

Treating coated as a single state is what makes the table legible, and the seven rows almost certainly cross the boundary at different places. Saying which would need the film’s mechanics, which this site does not have; saying that they differ needs only the mechanisms already stated.

Permeability fails all at once. Air goes through a fabric if there is any continuous path through it, so the permeability does not fall gradually as a coating thickens — it survives, largely undiminished, until the last hole closes, and then it is nothing. A coating that covers ninety-nine per cent of the face is not a fabric with one per cent of its permeability; it is a fabric with rather more than one per cent of it, because the remaining holes are the largest ones and flow through a hole grows much faster than its area.

The trellis fails gradually. Shear is a network property: a crossing that is bonded cannot rotate and a crossing that is free can, and a sheet with a scatter of bonded crossings still shears, less freely, because the free ones take up more rotation each. There is presumably a fraction at which the bonded crossings form a spanning rigid cluster and the mechanism stops, and that is a percolation question this site cannot answer — but it is plainly not the same fraction as the one that closes the last hole.

So the two are duals of one another and are not the same threshold. Permeability dies when the holes stop percolating; the trellis dies when the bonds start percolating; and a lattice generally admits both at once over a range of coverages. A lightly coated fabric that is already airtight and still drapes is therefore not a contradiction, and neither is one that has gone stiff while still leaking. Both are ordinary, and the table has no column for either.

This state, unlike the other, is one-way #

The analogy to relaxation state is exact in the shape of the argument and breaks in one respect, and the break has a methodological consequence worth stating.

A relaxation state is somewhere a fabric can be moved to and back from. Wet a dry-relaxed cloth and it goes to the wet-relaxed state; dry it and it comes back. That is why the finishing field’s finding could be checked at all: one specimen can be measured in several states, so the differences between states are differences within a fabric rather than between fabrics.

Coated is somewhere a fabric can only be moved to. Nothing takes the film off, so a coated fabric’s uncoated properties can never be measured on the same specimen. Every row of this table is therefore a comparison between two objects — a piece that was coated and a piece from the same roll that was not — and it inherits whatever those two pieces differ by. On a fabric that is being coated in a continuous process, the piece measured uncoated has also not been through the heat, the tension and the passage over the rollers that the coated piece has, and every one of those changes a fabric’s relaxation state.

So the two axes interact in a way the table cannot show: the uncoated column is a fabric in one relaxation state and the coated column is a fabric in another, and no experiment separates the coating from the process that applied it. That is the honest reason the table is labelled a collection rather than a measurement.

Where the model stops #

“Coated” is treated as one state and it is at least three. A surface coating that sits on the face, a coating that penetrates between the yarns, and a laminate bonded to a separate membrane behave very differently, and only the first is what the crossings-bonded picture describes. A lightly coated fabric may retain much of its trellis behaviour.

Nothing here computes the film’s own mechanics beyond the burst bound. How stiff a coated fabric is in shear, how it bends, how it recovers — all of that needs the film’s modulus and its bond to the yarn, and this site has neither.

The table’s rows are not equally certain. The permeability row is exact and trivial. The hole row is a statement about which of two models applies, and where the changeover happens for a partially penetrating coating is not computed. The wicking row assumes the coating closes the coarse system completely, which a thin or porous coating does not.

And a coating adds mass. The areal-weight row is in the table because a coating is often the larger term — a 120 micrometre PVC film is well over a hundred grams per square metre, which is more than many of the fabrics it is spread on — and every weight this site computes from four products in the yarn is a weight of the uncoated cloth.

The generalisation #

The move worth carrying is the one the finishing field made first: when a body of results turns out to share an unstated condition, the useful thing is not to add the condition to each result but to collect the results and classify how each responds to it.

Adding the condition to each essay would be a footnote fifteen times over. Collecting them shows something none of them contains: that the responses are of five different kinds, that two of them reverse, and that exactly one survives — which is a statement about the model rather than about any of its outputs.

The diagnostic that produces it is worth stating plainly. Find the assumption every result shares — here, that the crossings are free — and ask what changes if it fails. Results that depend on it strongly will reverse; results that depend on it weakly will change in kind; results that do not depend on it at all will survive, and those are the ones that were about something else all along.

Who found it, and when #

Coated fabrics have been made since the early nineteenth century and everything in the table is known in practice. Nobody tests a coated fabric for air permeability. Nobody cuts a coated fabric on the bias expecting it to drape. Tear tests for coated fabrics are a different standard from tear tests for cloth, precisely because the mechanism is different. And the fact that a waterproof fabric wicks along a cut edge is why seam sealing exists as an industry.

What is not usually done is putting them in one table and noticing that they are the same fact seen seven times. The reason is that the seven belong to seven different test standards and seven different specialists, and nothing in the specification of a coated fabric says “here is the list of things that stopped being true”.

This site is in an unusual position to make the list, because it has computed all seven for the uncoated case from one model. That is what makes the collection possible and it is also the honest limit of it: the coated column is what the mechanism says, not what a test would report.

Where the ladder goes next #

The coating ladder has two rungs and stops where the film’s own mechanics begins. What it would need next is a modulus — the film’s stiffness and its bond to the yarn — and with that the shear behaviour of a coated fabric becomes computable, which would replace the “changed in kind” entries in the table with numbers.

Sideways, the state axis this essay is a second copy of is a dimension without a state; the mechanism a coating removes is the bias and the tear; the result it reverses is a cloth does not mind a hole; and the half of the wicking that survives is the fine pore system inside the yarn. The rung below is what a coating adds, which is the only number in the whole ladder.