The diameter that does need a state

One of this collection’s firmest rules is that a fabric dimension quoted without its relaxation state is not a measurement. It was arrived at the hard way — two shape constants taken from different rows of one table put every occupancy on a ladder five per cent out — and it has been applied twice.

First to a knitted fabric’s two plan dimensions, which move by ten per cent between the states.

Then to its thickness, which turned out not to need a state at all, because it is two yarn diameters and the interlacing that sets it does not relax.

That second rung ended with an item recorded as unfinished, and this is it.

What was left open #

The thickness rung’s conclusion was three categories where the collection previously had one rule.

A dimension that friction leaves needs a state. The wale spacing, the course spacing, and everything computed from them.

A dimension that contact fixes does not. The thickness, and only the thickness.

And a dimension of the yarn rather than of the fabric needs a state of its own. The yarn’s diameter changes when it is wet, which is a fibre property rather than a structural one.

The third was stated and not developed, and it was recorded as belonging with the swelling ladder rather than with the state one. It belongs to both, and the joining is this rung.

Why it is a state and not a variable #

The obvious objection is that a yarn’s diameter changing with moisture is not a relaxation state, and it is worth answering because the answer sharpens the rule.

The three relaxation states — dry-relaxed, wet-relaxed, fully relaxed — are defined by a procedure: what the fabric has been through. Two of them involve water and one does not.

A yarn’s diameter depends on its current moisture content rather than on its history, so the two are not the same kind of variable. A fabric that has been wet-relaxed and then dried has its wet-relaxed spacings and its dry diameter.

So the rule needs a second half rather than an extension: a fabric has a relaxation state and a moisture state, and a dimension needs whichever it depends on.

Spacings need the first. Diameters need the second. And the thickness, which is two diameters, needs the second and not the first — which is a correction to the previous rung’s conclusion that it needs neither.

The correction #

That is worth stating flatly, because it changes a result this collection published.

The thickness rung concluded that a knitted fabric’s structural thickness is the same in all three relaxation states, exactly, because the thickness is two yarn diameters and neither the diameter nor the interlacing appears in the relaxation constants.

That is right about relaxation and it is incomplete. Two of the three states are defined by procedures involving water, and a fabric while it is wet has a thickness a tenth larger, because its yarn does.

So the honest statement is: the structural thickness is the same in all three relaxation states when measured dry, and is a tenth larger when measured wet.

The original claim was made for a dry measurement without saying so, which is exactly the error the rule exists to prevent, made by the rung that was applying the rule.

What else moves with it #

Every quantity in this collection that contains a yarn diameter is a quantity that needs a moisture state, and the list is longer than it looks.

The thickness, as above, by a tenth.

The cover factor, which is a sett times a diameter, by a tenth — so a wet cloth is more covered than a dry one at the same sett, before any shrinkage.

The tightness factor of a knit, by a tenth, which moves every dimensionless result computed from it.

The fibre volume fraction, by the square, since it is an area ratio.

And the flattening a fabric demands, which falls because the clearance is fixed and the yarn is bigger.

Five quantities, all of them routinely quoted, none of them usually carrying a moisture state.

Why the omission survived #

The reason is worth understanding, because it is the same reason most omissions in this collection survive.

Almost every measurement anybody makes on a fabric is made conditioned: at a standard temperature and humidity, on a specimen that has been allowed to equilibrate. That is what a testing standard specifies and it is what every laboratory does.

So in practice every diameter, every thickness and every cover factor in the literature is a conditioned one, and they are all comparable with one another. The moisture state is held constant by convention, so it never has to be stated.

The convention breaks in exactly two places. A wet process, where the fabric is being handled at a moisture content nothing like the standard one. And a comparison between fibres, since a cotton at standard conditions holds eight and a half per cent of its weight in water and a polyester holds under a half.

That second is the more insidious. Two conditioned yarns of different fibres are not at the same moisture content at all, so a comparison between them at “standard conditions” is a comparison at two different states.

The fibre comparison problem #

Following that through gives a real difficulty with this collection’s own tables.

A yarn’s diameter is computed from its count, its fibre’s density and a packing factor. The density used is the dry fibre’s.

At standard conditions a cotton holds 8.5 per cent regain, a viscose 13, a wool 15, and a polyester 0.4. So a conditioned cotton yarn is carrying water that a conditioned polyester yarn is not, and its diameter is correspondingly larger than the dry arithmetic gives.

That is a systematic error in every cross-fibre comparison this collection makes, and its size is a few per cent — smaller than the diameter’s own uncertainty from the packing factor, and not nothing.

The fix is not to abandon the tables; it is to state that they are dry-basis, and to note that a conditioned comparison across fibres carries a bias of a few per cent in the direction of the more absorbent fibre.

What a specification should say #

Putting the rule in usable form, since the point of a rule is that somebody can follow it.

A fabric’s plan dimensions need a relaxation state: dry-relaxed, wet-relaxed or fully relaxed.

A fabric’s thickness needs a load and a moisture state, and does not need a relaxation state.

A yarn’s diameter needs a moisture state and does not need a relaxation state.

And a fibre’s density needs a moisture state too, which is where the whole thing starts, and is the one that is universally quoted dry without comment.

Four dimensions, three different requirements, and the current convention names one of them.

That is not a large change to make. A number quoted as “conditioned” carries the moisture state implicitly and correctly; the difficulty is only that different fibres condition to different moisture contents, so “conditioned” is a different state for each of them.

What was counted, and how #

The swelling figures are the collection’s own wet-ladder table: a fibre’s diameter swelling from saturation, and a yarn’s wet-to-dry diameter ratio of about 1.10 for a cotton, arrived at by finding that a yarn’s own voids cannot absorb its fibres’ swelling.

The five affected quantities are the collection’s own, and the movement in each follows from the diameter by the power it enters at: first for the thickness, the cover and the tightness factor; second for the volume fraction; and inversely for the flattening.

The regains are standard values and are quoted.

Nothing here is a new solve. The rung is a rule extended and a published result corrected.

What a wet measurement would actually read #

The rung says a wet fabric’s structural thickness is a tenth larger, and it is worth saying what a gauge would report, because the two are not the same.

A measured thickness is the structural thickness plus a hair layer, and a wet fabric’s hair layer is not a wet dry one. Water lays hairs down against the surface — the same effect that makes a wet head of hair look flat — so a wet fabric’s hair layer is thinner than a dry one’s.

So the two move in opposite directions. The structural thickness rises by a tenth; the hair layer falls; and what a gauge reads is their sum.

Which wins depends on the fabric. A fine, smooth, filament fabric has almost no hair layer and its gauge reading should rise by nearly the full tenth. A hairy woollen has a hair layer that is a substantial fraction of its measured thickness, and its reading could easily fall.

That is a distinctive and testable prediction: a wet fabric’s measured thickness should rise for a smooth one and fall for a hairy one, at the same structural change. And it is the same shape of argument the thickness rung made about relaxation, where the structural thickness did not move and the measured one did.

Where the model stops #

The wet-to-dry ratio has a range of its own, from 1.05 to 1.20, so every “tenth” above is between a twentieth and a fifth.

Intermediate moisture contents are not computed. A fabric at fifty per cent relative humidity is between the two and nothing here says where.

And the swelling is treated as instantaneous. A yarn takes time to absorb and to dry, and a fabric being measured while it is drying is at neither state.

Nor is the anisotropy fully carried. A fibre swells across and barely along, so a yarn’s diameter rises and its length does not — which is what makes the whole argument work — and a yarn’s length does rise by about one per cent, which is a correction nothing here makes.

The two states, drawn as a pair #

It helps to hold the two kinds of state apart with a picture of what each does.

A relaxation state moves the fabric’s spacings and leaves its yarn alone. A fully relaxed jersey has its courses ten per cent closer than a dry-relaxed one and exactly the same yarn in them.

A moisture state moves the yarn and leaves the spacings alone — on the timescale of a wetting, before the fabric has had a chance to relax.

So the two are orthogonal, and a fabric can be at any combination of them: dry-relaxed and wet, fully relaxed and dry, and so on. Four combinations from two states, and this collection has been computing one of them.

That orthogonality is what makes the correction clean. Nothing has to be recomputed, because every number was computed at one point of a two-dimensional state space and the point was simply not named.

Why the wet-relaxed state is the confusing one #

One state does mix the two and it is the one whose name causes the trouble.

Wet-relaxed is a relaxation state defined by a procedure that involves water: the fabric is wetted, allowed to relax, and dried without restraint. So a “wet-relaxed” fabric is one that has been wet and is now dry.

That is a name that invites exactly the wrong reading. A wet-relaxed measurement is a dry measurement of a fabric with a history, not a measurement of a wet fabric.

The trade’s own terminology is at fault here rather than anybody’s reasoning, and the defence is the same as everywhere else in this collection: write the procedure rather than the name. “Wetted, relaxed, dried, measured dry” cannot be misread; “wet-relaxed” can and is.

The generalisation #

The rung is an instance of a failure mode that is specific to a collection with rules in it.

A rule that is applied by a person can be applied incompletely, and the incompleteness is invisible because the rule was followed.

The thickness rung applied the state rule carefully, considered three dimensions, categorised them, and produced a conclusion. It did not notice that one of its own categories was a dimension of a different object with a different kind of state, because the rule as written did not distinguish.

That is not carelessness. It is what happens when a rule’s scope is narrower than its wording, and the defence is to write the scope down: this rule is about relaxation states of a fabric, and a yarn has a moisture state that is a different thing.

This collection has other rules with the same exposure. The rule that every count must be enumerated rather than quoted is about counts of arrangements and says nothing about counts of measurements. The rule that every figure names the model that produced its numbers is about figures and not about tables.

Neither is wrong. Both would benefit from a sentence saying what they are not about.

Which of the collection’s results the correction touches #

An accounting, because a published result has been corrected and a reader is owed a list.

The thickness prediction stands for a dry fabric, which is what every thickness measurement in the trade is made on. Its claim of state-independence stands for relaxation.

Its claim of state-independence in general does not. A wet fabric is thicker, by whatever its yarn swells.

Every dimensionless knitted result stands, because the tightness factor and the diameter move together and the results are functions of their ratio.

Every absolute result computed at a diameter needs a moisture state attached, and none of them carries one. That is a labelling fix rather than a recomputation: the numbers were computed at the dry-basis diameter and are correct for it.

And the cross-fibre comparisons carry a small bias, because conditioned fibres hold different amounts of water and the diameters are dry-basis.

Four categories, one correction, one bias, and no number in the collection changes. That is the best kind of correction to have to make, and it is the kind a collection gets to make when its results are computed from stated inputs rather than fitted.

Who found it, and when #

That fibres swell with moisture and that the swelling is anisotropic is old and universal.

That a yarn’s diameter therefore depends on its moisture content is equally old, and is why every diameter measurement specifies a conditioning.

What is this collection’s own is the correction to its own published result: a knitted fabric’s structural thickness is state-independent for relaxation and state-dependent for moisture, and the rung that established the first did not say the second.

The finding was recorded as an open item at the time — that the yarn’s own diameter needs a state of its own, and that it belonged with the swelling work — so it is a shortfall closed rather than a defect found, which is the difference a written queue makes.

What it would take to carry moisture properly #

If the collection wanted to carry a moisture state rather than assume one, the change is small and worth specifying.

Every diameter here comes from one function: a count, a fibre density and a packing factor. Adding a regain argument to it, defaulting to the dry basis, would let every downstream quantity be computed at any moisture content.

The fibre density would need a regain-dependent form, which is elementary — a fibre holding water is a mixture of fibre and water at known densities — and the swelling anisotropy is already in the collection’s tables.

What would then be possible is the thing this rung has had to assert rather than compute: a fabric’s dimensions and clearances at any moisture content, including the standard conditioned one, so that a cross-fibre comparison could be made at genuinely matched states.

That is perhaps half a day and it would close a bias that runs through every table on the site. It is recorded here rather than done, which is what a shortfall queue is for.

Where the ladder goes next #

The wet group closes here and this work turns to the contact ladder’s consequences for woven cloth, where the flattening a knitted fabric demands turns out not to apply and a different question does.

A sett is a statement about how much room threads take, and a thread’s room depends on its section. What a sett is when the yarn is not round puts a section into a condition that has always assumed one.