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The thread: A mechanism, not a material

Cloth on the bias stretches half as long again while no thread in it stretches at all. The deformation is kinematic — a trellis closing — and almost every explanation given for it is wrong.
shear 30°bias +22.5%across -29.3%area 87%locks at 60°every segment checked against its own lengthno thread stretches Mechanics and drape

The bias is a mechanism

Cloth cut at forty-five degrees stretches by a third and springs back, while the threads in it stretch by nothing at all. Almost every explanation given for this is wrong, and the right one is not about elasticity.

a course runs acrossa wale runs down5 wales × 4 coursesevery loop passes through the one below itweft knit Knits and other structures

The loop

A knit is one thread bent into loops, each drawn through the loop below. Nothing in it is straight, which is why it stretches in every direction while a woven cloth stretches only at an angle.

as wovenwarp crimp 8.0% · weft 4.0%pulled 3% along the warpwarp crimp 4.9% · weft 7.1%warp thread 108.0 and weft 104.0 — unchanged in bothboth thread lengths checked, not assumed3% pull Setting and geometry

Crimp, and why cloth narrows when it is pulled

A thread in cloth is longer than the cloth it crosses. Pull the fabric one way and that extra length is taken out of one direction and put into the other, so the cloth gets narrower without a single fibre stretching.

the dots mark which way each course facesstockinette — every course the same0 face changes · curlsgarter — alternate courses reversed5 face changes · lies flatface changes counted, not the curl itself Knits and other structures

Why stockinette curls

A knitted loop is not symmetric front to back. Work every course the same way and the asymmetries add up along the edges; alternate them and they cancel. That is the whole difference between a fabric that rolls and one that lies flat.

0%10%20%30%40%15°30°45°60°cover 40%locks at 66°, +38%cover 60%locks at 53°, +34%cover 80%locks at 37°, +26%extension along the biasshear anglethe yarns never stretch; the net changes shape Mechanics and drape

The locking angle

The bias runs out at an angle that yarn diameter and thread spacing decide between them. It is the number behind whether a cloth will go round a curve, and it has nothing to do with how strong the fabric is.

a sphereworst shear 22.2°cells closelocks at 57°nothing jamsthe fishnet construction, every segment checkeddoubly curved Mechanics and drape

Why clothes need darts

A flat cloth goes round a cylinder for nothing and cannot go round a sphere at all without shearing. The amount of shear is decided by the curvature, and when it exceeds what the threads allow, something has to be cut out.

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