The float decides

Ask what makes satin shiny and the usual answer is silk. It is not: satin in cotton is shiny, and silk in plain weave is not particularly. What makes satin shiny is that a length of thread lies uninterrupted on the surface, long enough for light to reflect off it as if off a rod rather than scattering from a rough field of crossings.

That length is the float, and this essay is the case that it is the single most consequential number in woven structure.

What it is, precisely #

A float is a run of consecutive intersections at which the same thread is on the face. A warp float runs down a column of the draft; a weft float runs along a row.

Plain weave has floats of one everywhere: nothing is ever on the face twice in a row. A 2/2 twill has floats of two. A 3/1 twill has warp floats of three and weft floats of one. An eight-end satin has warp floats of seven.

Two details in the definition earn their place.

It is measured round the repeat. A draft tiles, so a run that reaches the edge of the repeat continues into the next copy. Counting only inside the drawn block gets the answer wrong at every repeat boundary, which is to say everywhere in the actual cloth.

Warp and weft floats are different numbers. A warp-faced weave has long warp floats and short weft ones, and quoting a single “float length” for such a cloth loses the asymmetry that defines it.

Where the number comes from #

Every float length quoted on this site is counted rather than measured off a picture, and the procedure is short enough to describe.

Take the draft as a matrix. For a warp float, walk down a column; for a weft float, walk along a row. Because the repeat tiles, the walk is cyclic — rotate the sequence until it does not begin in the middle of a run, then measure each run. The longest run of the relevant value is that thread’s longest float, and the cloth’s float length is the largest over all threads.

Two failure modes are ruled out by doing it this way. A float that straddles the repeat boundary is counted correctly rather than split in two. And a figure cannot quietly acquire a caption from a different weave, because the caption is generated from the matrix that produced the drawing.

That is a small thing on a page about one weave and a large thing across a site with a hundred and fifty figures, where the alternative is a hundred and fifty opportunities to transpose two numbers.

Lustre #

Light reflecting from a rough surface scatters in every direction and the surface reads as matt. Light reflecting from a smooth one reflects specularly and the surface reads as shiny.

A woven cloth’s surface roughness is set by how often the threads cross. Plain weave presents a field of crossings at the finest possible pitch, so it scatters. A satin presents lengths of thread lying parallel and uninterrupted, so it reflects, and the reflection has a direction — which is why satin changes appearance as it is turned, and why a satin garment cut with panels running different ways looks like two different fabrics.

None of that is a fibre property. Silk is lustrous in its own right because the filament is smooth and untwisted, and that adds to the effect, but the structural contribution is available in any fibre. Cotton sateen is the demonstration.

Snagging, which is the same fact #

The property that sells a satin and the property that ruins it are the same property.

A float is a length of thread lying on the surface with nothing holding it down. That is what makes it reflect, and it is also what lets a fingernail, a splinter or a cat get under it and pull. Once pulled, the thread has nowhere to go: it is gripped at both ends of the float and the slack has to come from somewhere, so the cloth puckers.

Plain weave essentially cannot snag, because there is no length to get under. That is not a virtue somebody engineered in; it is the same fact as its lack of lustre, seen from the other side.

Abrasion #

Rubbing wears the parts that stand proudest, and in a woven cloth that is the crowns of the floats.

In plain weave the crowns are numerous, small and evenly distributed, so wear is spread over a great many short lengths and the cloth thins gradually. In a satin the crowns are few and long, so the same rubbing concentrates on a small fraction of the surface. A satin wears through in patches, and when it does the weft shows through the face because the warp floats have gone.

This is the property behind a rule that sounds like snobbery and is engineering: hard-wearing cloth is plain or twill, and satin is for things that are looked at more than they are rubbed.

Tear strength, which runs the other way #

Here the ordering reverses, and the mechanism is worth having because it is genuinely counterintuitive.

A tear propagates by breaking threads one at a time at the tip. Whether that is easy depends on how many threads share the load at the tip — and that depends on whether the threads can move.

In plain weave every thread is gripped at every intersection and cannot slide. A thread at the tear tip takes the whole load alone and breaks; the next takes it alone and breaks; and the tear runs.

In a satin the threads are gripped rarely and can slide. At a tear tip they bunch together, several sharing the load, and the tear stalls. The cloth deforms rather than parting.

So the loosely interlaced structure — weaker in every intuitive sense, softer, more easily snagged — is harder to tear. The same reasoning explains why ripstop fabrics work by inserting stronger threads at intervals rather than everywhere, and why a very tightly set plain weave can tear more easily than a looser one of the same yarn.

Drape #

Bending a cloth means bending the threads in it. A thread that interlaces at every intersection is already bent at every intersection and has little compliance left; a thread that runs straight for seven intersections has a long unbent length that can bend freely.

So a long-float cloth drapes and a short-float cloth stands. That is why satin falls in soft folds, why taffeta — plain weave in a crisp filament yarn — holds a shape, and why the same fibre can produce a fabric for a ballgown or for a lampshade depending on nothing but the weave.

Setting #

The last consequence is the least obvious and the most useful.

A thread that changes face has to bend, and a bend takes room — the crossing thread has to pass through, and the bending thread has to go round it. So the number of interlacings in a repeat controls how tightly the cloth can be packed before the threads jam against each other.

Fewer interlacings mean fewer bends mean a denser possible setting. A satin in a given yarn can be set half as much again as a plain weave in the same yarn, which is why satins are heavy for their fineness and why comparing two fabrics by thread count without knowing their weaves is comparing nothing at all.

The same idea outside weaving #

Float length is a woven-cloth notion, and the underlying quantity is not.

In a knitted fabric the corresponding number is the length of yarn in a loop, and it does the same work: a long loop gives a soft, open, extensible, snag-prone fabric and a short one gives a firm, dense, stable fabric. Knitters call it stitch length or loop length, it is the single most controlled variable in knitting, and the reason is exactly the reason float length matters here.

In a braid it is the length between crossings, which sets how far the structure can change diameter. In a nonwoven there is no equivalent at all, because there are no regular crossings to run between — which is one of the reasons nonwovens behave so unlike either woven or knitted cloth.

The general statement is that any structure made by interlacing has a characteristic free length between constraints, and that length controls compliance. It is a structural principle rather than a textile one, and it turns up in chainmail, in netting and in fibre-reinforced composites for the same reason.

Two floats, two directions #

A point that gets lost when a cloth is described by a single number.

A 3/1 twill has warp floats of three and weft floats of one. Its two faces therefore behave differently: the warp face is lustrous, snag-prone and wear-prone; the weft face is matt and firm. Denim is exactly this, and everything people know about how jeans wear — the indigo face going white along the creases while the pale back stays put — is the warp floats abrading away.

A satin is the extreme version. Warp floats of seven and weft floats of one, so the two faces are nearly different fabrics, and a satin used with the wrong face out is simply the wrong cloth.

The designer’s constraint #

Read forwards, everything above is a menu. Read backwards, it is a constraint, and that is how it is actually used.

A designer does not usually choose a float length. They choose a use, and the use fixes a maximum. Upholstery has to survive rubbing, so the floats have to be short; a curtain has to fall, so they have to be long; a shirt has to do a bit of both, so it lands on plain weave or a fine twill. The weave is then whatever satisfies the constraint and looks right.

The constraint is sharpest in figured weaving. A jacquard design is drawn as a picture and then realised as a weave, and the picture will happily specify a warp float thirty ends long if nobody stops it. Such a float is not cloth: it is a thread lying loose across a third of an inch, waiting to be pulled. So figured designs are worked over with a maximum float rule, breaking long runs by inserting a tie-down point — and the art is putting the tie-downs where they do not disturb the picture.

That is also where the integrity check earns most of its keep, because a designed weave is exactly the case where nothing guarantees the result is one cloth. A rule-generated satin is safe by construction. A hand-worked figure is not.

How fast each of the seven moves #

A table of directions is a weaker statement than a table of rates, and two of the seven have rates that can be written down. Having them changes what the table is for: the directions say which way to go and the rates say when to stop.

Crimp falls as one over the repeat. A warp float of f means the end changes face once every f + 1 picks, so the number of bends per unit length is the pick density divided by f + 1, and the crimp is very nearly proportional to it. Against a plain weave, where the end bends every other pick, that is a crimp ratio of 2 ÷ (f + 1): two thirds for a 2/2 twill, a half for a 3/1, two fifths for a five-end satin, a quarter for an eight-end. A satin carries less than half a plain weave’s crimp in the same yarn at the same sett, which is why a satin’s length is so much more nearly its thread’s length and why it takes so much less warp to weave.

Sett rises as the 0.39 power of it. The trade’s own rule for the densest setting a weave allows — Brierley’s, fitted on cotton and in use for a century — makes the maximum sett proportional to the ends per repeat divided by the intersections per repeat, raised to that power. For a satin the intersections are two whatever the repeat, so the index is (n ÷ 2)^0.39.

The five-end satin’s 1.43 is the essay’s own claim that a satin can be set half as much again as a plain weave, arrived at from the trade’s exponent rather than from the assertion — so the two agree, which is the check worth having.

Why nobody weaves a twenty-end satin #

The two rates together answer a question the table of directions cannot, and the answer is the reason the trade’s weaves cluster where they do.

Setting rises as the 0.39 power of the float and snagging rises as the first power, because a snag needs a length to get under and the length available is the float itself. So doubling the float buys thirty-one per cent more sett and doubles the reach of a fingernail.

That ratio is bad at every float and it gets worse with every doubling, because a fixed proportional gain is being bought with an ever larger absolute cost. Going from a plain weave to a five-end satin buys 43 per cent and exposes four intersections. Going on to a twelve-end satin buys another 41 per cent and exposes eleven.

So the density argument for a long float runs out early and the lustre argument does not. Lustre keeps improving with float, because a longer uninterrupted length is a better mirror, and it is not competing against the same cost curve. Which is exactly the pattern in what gets woven: the weaves chosen for density stop at five or eight ends, and the ones that go beyond — the long satins, the twelve- and sixteen-end constructions — are chosen for surface and are made in fibres and finishes where snagging is accepted.

The same arithmetic explains the figured-weaving rule quoted above from the other end. A maximum float rule in a jacquard design is not a compromise between two goods; it is a limit on a cost that grows linearly against a benefit that has already flattened out. Past about eight there is nothing left to buy, and every further intersection is exposure with no return.

What float length does not decide #

Three limits, because the claim in this essay is strong and should not be overstated.

It does not decide what a cloth is made of, and structure never settles everything. Absorbency, warmth, wet strength and chemistry are fibre properties. A satin in polyester and a satin in silk have the same structure and are not the same fabric to wear.

It does not survive finishing unchanged. A raised or brushed cloth has had its surface deliberately disrupted, so the float lengths in the draft no longer describe what a hand touches. Flannel is plain or twill woven and then raised, and its surface has almost nothing to do with its floats. The same caution applies to any number quoted from a geometric model.

It does not decide integrity. Long floats correlate with the structures that fall apart — the four-by-four census finds no separable draft with floats under three — but the correlation is not a rule, and a long-float weave can be perfectly sound while a short-float one is not.

The number in one place #

It is worth collecting the whole argument, because a claim this broad should be checkable at a glance.

Seven properties, one variable, and the direction of every one of them is fixed by it. Two of them — tear strength and setting — run opposite to the naive expectation, which is a reasonable test that the account is doing work rather than restating an intuition.

No other structural quantity in this subject reaches that far. Interlacing count reaches equally far, and it is the same quantity read the other way, which is the point rather than a coincidence.

Where the float is lengthened without anybody asking #

One place a float grows is worth flagging, because it happens as a side effect of a construction chosen for a quite different reason.

Reversing a twill — the ordinary way of turning a rule into a figure — makes the floats on either side of the seam meet, and if they are in phase they join. A two-two twill has a longest float of two. Reversed about the turn it becomes three; reversed on a point it becomes four, twice the parent twill’s.

A float of four in a cloth designed around a float of two is a place that snags and wears differently, and it lies in a line down the seam where it is most conspicuous. Nothing about the drawing announces it, and the reversal was chosen for the pattern rather than for the float. Broken and herringbone twills enumerates the reversals and finds the rule that holds at every width.

Where the ladder goes next #

The same quantity from the other side is interlacings and firmness, where the trade is derived rather than described.

The geometric consequence is how close threads can be set, which turns the interlacing count into a number of threads per inch.

And the constraint on how a satin’s few interlacings may be arranged is the satin theorem, which rules out an order that every weaver has been told to avoid and few have been told why.

What the pictures here cannot show. A float mark is a computation drawn on a draft, not a feature of a cloth. Lustre, snagging and abrasion are all consequences of that structure in a real yarn with a real finish, and no figure here draws a thread’s surface, its hairiness or its twist — all of which contribute to every property in this essay.