Why satin shines

A satin lining and a cotton sheet can be made of the same fibre, at the same count, on the same loom. One of them shines and the other does not, and nothing about the fibre explains the difference.

The explanation that is usually offered — that silk is lustrous and cotton is not — survives because satin is very often silk and sheeting very often is not. It is the wrong variable. A mercerised cotton satin shines; a spun silk plain weave is nearly matt. What changed was the length of thread that lies on the face without interruption, and that is a number the draft decides.

What a cylinder does with light #

The whole argument rests on one fact about cylinders, and it is worth being exact about it because the everyday intuition — that a shiny thing has a bright spot on it — is about spheres.

A sphere illuminated by a distant source has one specular point: exactly one place on it where the surface normal bisects the angle between the light and the eye. Move the eye and the point moves, but there is only ever one.

A cylinder is different. Its normals do not vary along its axis at all, so if the specular condition is satisfied at one point on the surface it is satisfied at every point on the same line parallel to the axis. A cylinder does not return a bright spot. It returns a bright line, running the whole length of the cylinder.

That is why a bundle of parallel filaments looks the way it does, why a coil of wire has a stripe down it rather than a dot, and why the highlight on a satin runs along the warp.

So the highlight is as long as the float #

A thread in a woven cloth is not one long cylinder. It is a cylinder for as long as it stays on the face, and then it dives under a pick and is hidden. The next time it appears it is a new cylinder, displaced downward by a thread diameter’s worth of geometry and, in every weave but a satin, at a different phase from its neighbours.

So the length of the highlight is the length of the float. Not approximately: exactly, up to the small foreshortening at each end where the thread begins to turn down.

That is the whole mechanism, and it converts a visual property into an integer that the matrix already knows. An eight-end satin has warp floats of seven, so its highlights are seven picks long. A plain weave has floats of one, so its highlights are one pick long.

The number that matters is in inches, not in picks #

A float of seven picks is not the quantity a person sees. What is seen is a length on the cloth, and converting picks to inches needs the sett — how many picks are in an inch — which the weave also decides.

That conversion cuts the other way, and it is the first thing in this argument that is not obvious. A satin can be set far more densely than a plain weave in the same yarn, because a thread that rarely changes face rarely needs room to bend. So the same float of seven picks spans fewer inches in a satin than seven picks would span in an openly set cloth.

The figures compute the conversion at each weave’s own densest setting in a yarn a fortieth of an inch across, because comparing two weaves at a sett one of them cannot be woven at is not a comparison at all.

The plain weave jams at twenty picks to the inch, so its floats of one are a twentieth of an inch. The eight-end satin jams at thirty-two, so its floats of seven are 0.219 inches — four and a third times as long, not seven times. The denser setting repays about two-fifths of the advantage, and the rest survives.

What was counted, and how #

Nothing above was measured on a photograph. Each figure walks the matrix that produced its own drawing.

For each end in the repeat, the runs of consecutive picks over which that end stays on the face are collected. Every run is a float and every float is one band. The bands are then checked against the matrix in a way that would catch a drawing error: their total area must equal the number of warp-up cells the balance calculation reports, and a band longer than the longest float the matrix contains is refused outright.

Two further quantities fall out of the same walk. The count of highlights per square inch is the number of float-starts per unit area, which is the product of the two setts divided by the float length. And the length of a highlight in inches is the float divided by the picks per inch.

They move in opposite directions, and that is the point. Total reflecting area is fixed by the warp cover and by nothing else, so a long float does not put more thread on the surface. It puts the same thread on the surface in fewer, longer pieces.

What is conserved, and it is not the area #

The two quantities are said above to move in opposite directions, and their product is worth writing down because it is exactly constant and the constant is a number a specification already carries.

Highlights per unit area is the ends per inch times the float-starts per inch along each end, which is the picks per inch divided by the float. Each highlight is the float divided by the picks per inch long. Multiply:

total highlight length per square inch = (warp sett) × (picks ÷ float) × (float ÷ picks) = the warp sett.

The float cancels, the pick density cancels, and what is left is the number of ends per inch and nothing else.

Check it against the two cloths above. The plain weave has four hundred highlights per square inch, each a twentieth of an inch long: twenty inches of bright line per square inch, and its warp sett is twenty. The twelve-end satin has a hundred and seven highlights of 0.321 inches: thirty-four inches of line, and its warp sett is thirty-two. The small residual is the foreshortening at each end of a float, which the exact statement ignores and the drawing does not.

That is a sharper conservation than the one stated above, and it says what a weave can and cannot do.

A weave cannot change how much bright line a cloth returns. That is fixed by the warp sett — which is to say by how many cylinders there are per inch across the cloth, since each contributes one continuous line of specular condition regardless of how often it dives under. Choosing a satin over a plain weave does not add a millimetre of highlight.

What a weave chooses is the number of pieces it is cut into. One quantity, divided n ways or m ways, and lustre is the word for a small n.

And the only way to raise the total is to set the warp closer, which raises it in exact proportion. So the two levers are genuinely different: the sett buys more line and the weave buys longer pieces of it, and a cloth that is both closely set and long-floated is bright for two reasons that multiply rather than overlapping.

That also explains why the partial repayment in the section above came out as it did. A satin sets denser, so it has more total line as well as fewer pieces — and the length of each piece is the total divided by the count, so the denser setting shortens each highlight while lengthening the sum. The four and a third rather than seven is those two movements against each other, and now both of them have a name.

The perceptual step, stated as an assumption #

Here is where the geometry stops and something else begins, and the honest thing is to mark the boundary rather than to walk over it.

Everything to this point is a statement about where light goes. It is exact and it is checkable. The step from fewer, longer highlights to this cloth looks lustrous is a statement about a visual system, and this site has no model of one.

What can be said without over-claiming is that the two surfaces differ in a way that has nothing to do with how much light they return. Four hundred specks per square inch and a hundred and seven bands per square inch, in the same fibre at the same cover, return the same total. The difference is entirely in the spatial distribution, and the human word for that distribution is lustre.

There is a further consequence which is geometric and therefore safe to assert: a long highlight survives being viewed obliquely and a short one does not. Tilt the cloth and every highlight foreshortens by the same factor, but a speck that was a twentieth of an inch across becomes invisible long before a band of a fifth of an inch does. That is why a satin’s shine tracks across the cloth as it moves, and why a plain weave has no such behaviour to lose.

Why scattering is what makes it a satin and not a twill #

A 7/1 twill has warp floats of seven, exactly as an eight-end satin does. By the argument so far the two should be equally lustrous, and they are not: the twill reads as a directional, striped cloth.

The reason is that the twill’s interlacings line up and a satin’s are placed so that no line forms. In a twill, the ends of the highlights are arranged along a diagonal — every band starts one pick above its neighbour — so the eye is given a strong second pattern, made not of thread but of interruptions, and it finds it immediately.

A satin’s move is chosen so that the interruptions scatter. What is being scattered, in the language of this essay, is the ends of the highlights — and a field of long bands with randomly placed breaks reads as an unbroken field, while the same bands with their breaks in a line read as stripes.

What the same argument says about the back #

A satin is warp-faced: almost all the warp is on the face and almost all the weft is behind it. So the back of an eight-end satin is a weft-faced satin with weft floats of seven, and by every argument in this essay it should shine too.

It does. A satin lining is lustrous on both sides, and the two lustres differ only in direction: the face’s highlights run warpwise and the back’s run weftwise. Where the warp and the weft are different yarns — which is the usual case in a lining, the warp being the finer and more continuous — the two faces differ in how bright the shine is and not in whether there is one.

This is a small prediction and it is worth making because it is falsifiable by picking up any satin-lined jacket. A theory of lustre resting on fibre would have to say that both faces are silk and leave it there.

The price, which is the same number #

Everything a satin gains here is bought with the same quantity, and the bill comes in the essay next along this ladder. A float of seven picks is seven picks of thread with nothing holding it down, and the same length that makes the highlight long makes the snag long.

The two figures are the same calculation with opposite signs on it, which is the strongest form the argument takes: lustre and fragility are not correlated properties of satin, they are one property counted twice. A cloth cannot be given one without the other by any choice of fibre, finish or setting, because the quantity behind both is an integer in the draft.

The confound worth separating out #

There is a second mechanism that also produces lustre, it is genuinely about the fibre, and confusing the two is the reason the fibre explanation is so durable.

A raw cotton fibre is a collapsed, twisted ribbon. Its surface is convoluted along its length, so the specular condition is satisfied at scattered points rather than along a line, and the linear-highlight argument does not apply to it at all. Mercerisation — caustic soda under tension, patented by John Mercer in 1850 and made lustrous by Horace Lowe’s addition of tension in 1889 — swells the fibre into a round cross-section and takes the convolutions out. What was a twisted ribbon becomes a cylinder, and cylinders behave as this essay describes.

So mercerised cotton shines more than raw cotton in the same weave, and that is a fibre effect. A satin shines more than a plain weave in the same fibre, and that is a weave effect. They multiply rather than compete, which is why a mercerised cotton satin is the most lustrous cotton cloth available and why the two explanations have never been forced to separate in ordinary experience.

The separation is easy to state as a test. Hold the weave constant and vary the fibre: the change is in whether the individual filaments are cylinders. Hold the fibre constant and vary the weave: the change is in how long each cylinder runs before it is interrupted. Both are real; only the second is computable from a draft, and only the second is what this site claims to know anything about.

Silk gets the credit for the same reason mercerised cotton does. A silk filament is a smooth, near-triangular rod hundreds of metres long, which is about as close to an ideal cylinder as a natural fibre gets — and silk is also, historically, the fibre strong and fine enough to be woven into long floats without the float breaking. The fibre and the weave arrived together, and the credit went to the one with a name.

Who worked it out #

The optical half of this is older than the textile half and comes from a different subject entirely. That a cylinder produces a linear highlight rather than a point one is elementary specular geometry, known long before anybody applied it to yarn, and it is the same fact that makes a scratched metal surface produce a streak — the basis of what computer graphics later called anisotropic reflection and modelled explicitly, in James Kajiya’s 1985 treatment of anisotropic surfaces and in the work on hair and fibre rendering that followed.

The textile half was arrived at empirically and much earlier. Weaving manuals of the nineteenth century state plainly that lustre increases with float length and give tables of satins by order, in the tone of a craft fact. What they do not do is give the reason, and the absence is conspicuous: manuals of that period are usually happy to explain a mechanism when they have one.

The two halves were not put together until fabric appearance became a subject with instruments attached — gloss meters and goniophotometers, from the 1950s onward — and the measurement that settled it is straightforward once it can be made. Lustre measured as the ratio of specular to diffuse reflection tracks float length across weaves within one fibre, and tracks it far more strongly than it tracks fibre across weaves.

The order in which the two halves arrived is the usual one for this subject: the practice was right for centuries and the explanation arrived from outside.

Where the ladder goes next #

The next rung is the cost of the same float, in abrasion, where the length that makes a highlight long makes a broken end long as well. After that comes tear, where the trade’s explanation and the geometry part company, and then the limit a designer works to, which is the constraint all of this eventually runs into.

The neighbouring argument is which satin to weave, since the order fixes the float and the move fixes the scatter, and this essay has shown that both are doing work.

What the pictures here cannot show. Every figure on this page is a plan of where the highlights are, drawn in flat colour. None of them is a rendering: no figure here computes a reflectance, and the bright line down each band is a marker for a location rather than a simulation of one. The claim being made is about the geometry of the surface, and a picture that looked convincingly shiny would be evidence about the renderer rather than about the cloth.