Textile Structure
how cloth is put together
Generator

The stitch density that makes the strongest seam

The stitch density that makes the strongest seam
The stitch density that makes the strongest seam. Seam strength against stitch density, as the two limits that decide it: the sewing thread crossing the seam, which rises with the stitches, and the fabric the needle perforates, which falls. The seam is the lower of the two, so the optimum is where they cross — and whether the fabric line falls at all is decided by the clear gap between threads against the width of the needle.

Seam strength against stitch density, as the two limits that decide it: the sewing thread crossing the seam, which rises with the stitches, and the fabric the needle perforates, which falls. The seam is the lower of the two, so the optimum is where they cross — and whether the fabric line falls at all is decided by the clear gap between threads against the width of the needle.

7 essays call tradeoff. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the weave its essay argues about.

Where it is called

Changing this generator changes every one of these figures.

A fabric to fill and a fabric to load. Fill time against the sett of a woven reinforcement, with the two limits a part imposes. Stiffness wants fibre, which wants a close sett; the resin has to arrive before it gels, and the channels between the tows — which is what carries the flow — close as the sett rises. The interval between the two is where a fabric can exist, and it narrows with the size of the part. Cloth doing a job

A fabric to fill and a fabric to load

A reinforcement has to hold as much fibre as possible and still let a resin through it, and the two demands are the same decision pulling opposite ways. Both bounds are computable, the interval between them narrows as the square of the part, and past a certain size it is empty — which is the most useful thing the arithmetic says.

 A filter cloth has two jobs. Opening size against sett for a woven filter cloth, with the two limits that specify one: the soil is retained below the retention line, and the water passes above the open-area floor. They pull opposite ways, so the answer is an interval in the sett — and for a fine enough soil there is no interval at all. Cloth doing a job

A filter cloth has two jobs

Hold the soil back and pass the water. The first wants a close sett and the second wants an open one, so a filter cloth is not a fabric but an interval — one that is sometimes a single sett wide, and for a fine enough soil is empty. The empty case is the useful one, because it says the answer is not a woven cloth at all.

 A membrane is cut smaller than it is. Warp and fill compensation against how far the crossings flatten under prestress. With the thread lengths and the cloth's thickness both fixed there is no strain available at all — the closure condition determines the state — so the whole of the compensation is the crossings squeezing and the crimp coming out. The direction that arrives with less crimp gives back less, which is why a warp compensates less than a fill. Cloth doing a job

A membrane is cut smaller than it is

A tensioned fabric roof is cut to a pattern smaller than the shape it will take, because stressing it makes it grow. At a fixed cloth thickness a prestress can only interchange crimp — one direction grows and the other shrinks — so everything that makes both directions grow is the crossings flattening, which is the one quantity here this site cannot compute.

 How much of the curvature a cloth can take without being cut. The dart angle a spherical cap still demands after the fabric's own shear has absorbed what it can, against how closely the cloth is set. The total the cap demands is fixed by Gauss–Bonnet and is the same for all of them; what changes is how much of it the trellis can supply before its threads jam. An open cloth drapes a hemisphere with no dart at all; a closely set one has to be cut from the start. Cloth doing a job

A hemisphere costs one full turn

The total angle a pattern must remove to cover a hemisphere is exactly 360 degrees, and it is the same for a hat and for a stadium dome. What changes with the fabric is how much of that the cloth can supply by shearing instead of by being cut — and that is a property of the sett, computed from the angle at which its threads jam.

 The stitch density that makes the strongest seam. Seam strength against stitch density, as the two limits that decide it: the sewing thread crossing the seam, which rises with the stitches, and the fabric the needle perforates, which falls. The seam is the lower of the two, so the optimum is where they cross — and whether the fabric line falls at all is decided by the clear gap between threads against the width of the needle. Cloth doing a job

The stitch that weakens the seam

More stitches per centimetre put more sewing thread across a seam and more holes through the cloth beside it, so seam strength rises, crosses and falls. Whether the fabric line falls at all is decided by the clear gap between two threads against the width of the needle — the same arithmetic a filter cloth is specified by, doing a different job.

 A cloth does not mind a hole. Strength left after a hole, against the width of the hole, for a woven cloth and for a film of the same width. The cloth's threads carry their own load, so it loses exactly the threads the hole removes and the loss is linear. The film is a continuum, so a hole of any size at all costs it the stress concentration factor — quoted from Kirsch's elasticity solution, not derived here — and the size of the hole does not enter. Cloth doing a job

A cloth does not mind a hole

A hole in a film costs it two thirds of its strength whatever the hole's size, because a continuum concentrates stress at an edge. A cloth's threads carry their own load and hand almost nothing to their neighbours, so a hole costs exactly the threads it removes — a loss that is linear in the hole, independent of the sett, and zero for a slit along the load.

 A tear breaks threads or pulls them out. The grip a cloth has on a thread at the tip of a tear, against the sett, with the thread's own strength drawn across. Below the line the thread slides and the yarns group, which is the trade's explanation of why a loose weave tears well; above it the thread breaks where it is and grouping never happens. The essay that asked it could not compute this: it needed a friction, and the fancy weaves supplied one. Cloth doing a job

A tear stops where the grip is

This collection asked whether a loose weave tears better and had to answer that the geometry could not say — it supplies a grip count and a slack, and neither is a force. The fancy weaves brought a friction. With it the question has an answer — a cloth's threads slide up to a computable sett and break above it — and a ripstop grid has a bound with no free parameter in it.

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