Textile Structure
how cloth is put together
Concept

Bending length — where it appears

How far a strip of cloth reaches over an edge before its own weight bends it to a stated angle: a stiffness with the fabric's weight divided out. It is the quantity every buckling and drape argument on this site runs on, and it is measured with a ruler and an angle rather than with a load cell.

Named by 5 essays across 2 fields — each of them below, with the objects they name alongside it.

The cantilever test. A strip of cloth pushed out over an edge until its tip has drooped to the stated angle. The overhang at that moment gives the bending length, and cubing it with the mass per unit area gives the flexural rigidity.

Bending stiffness and the drape coefficient

Two standard measurements try to say how a fabric hangs. One measures a length and cubes it; the other measures an area and, on the geometry, turns out to be answering a different question from the one it is asked.

mechanics · Drape Wrinkles 127 mm apart. A 300 mm width of a 120 g/m² cloth whose bending length is 20 mm, held under 5 newtons per metre across it and compressed. It cannot carry the compression in the plane, so it leaves the plane, at a wavelength the bending rigidity and the tension settle between them: 127 mm, which is 2.4 wrinkles across the width. The amplitude is drawn and is not computed — this arithmetic sets the spacing and says nothing about the depth.

A cloth cannot carry a push

The net model that runs this site's mechanics has no bending stiffness at all, so it buckles under any compression whatever, into wrinkles of any wavelength whatever. What picks the wavelength is the competition the net leaves out — and the answer is a quarter power, which is why a wrinkle is so hard to change.

mechanics · Buckling The number the drape test does not record. A 150 mm specimen over a 90 mm pedestal, for fabrics from limp to stiff. The curve is the fold count the buckling argument predicts — three quarters of a power of the specimen's radius over its own bending length — and it runs from 2 folds to 11. The number beside each mark is the drape coefficient the same specimen would report, which moves by a few points across the whole range.

The nodes a drape test throws away

A drape test lays a circular specimen over a pedestal, photographs the shadow and reports one number. The specimen also falls into a definite number of folds, which is a buckling mode set by the fabric's own bending length — and the standard method observes it, does not record it, and reports the number it is least sensitive to.

mechanics · Buckling The two calculations a yarn's stiffness admits. A bundle of 9 fibres bent with the fibres free to slide and with them locked together. Free, the rigidity is the sum of the fibres': 0.00141 N·mm² for a 30 tex cotton yarn. Locked, it is the fourth power of the yarn's own diameter: 0.689. The ratio is the fibre count over the square of the packing factor, 490, and nine fibres are drawn where the yarn has 176. What the drawing cannot show is where a real yarn sits between them, which is a question about friction rather than about fibre.

A yarn's stiffness is a bracket, not a number

Two calculations are available for how stiff a thread is in bending, and both are exact. One treats the fibres as free to slide and gives the sum of their stiffnesses; the other treats them as locked and gives a solid rod. They differ by the fibre count, which for an ordinary cotton yarn is a factor of five hundred — and no measurement of the fibre narrows it by anything at all.

mechanics · Yarn stiffness What the count moves at 150 grams. Plain cotton cloths that all weigh 150 g/m², from 20 tex to 200 tex, with sett and crimp solved together. Thickness, which is two yarn diameters, rises 3.16 times across the line; the cover factor of each thread system falls 2.75 times; their product with one plus the crimp is the same number at every count, because the weight has fixed the volume of fibre and the count only decides whether it is laid out flat or stacked up.

A weight fixes the fibre and not the drape

Every plain cotton cloth of 150 grams a square metre contains the same fibre, and the count decides only how it is arranged. Across the counts that can make that weight, thickness rises threefold and cover falls in step, so their product holds still. The bending length does something stranger: at the bound a woven yarn actually sits near, it depends on neither the count nor the weight, only on the fibre.

setting · Weight

Named alongside it

The objects these essays reach for when they reach for this one.

CantileverDrapeFlexural rigidityAreal densityBending rigidityBucklingDrape coefficientSpecificationWrinkleCloth thicknessCover factorCrimp

All concepts