Textile Structure
how cloth is put together
Series

Bias — the series

4 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. A trellis sheared 30°. The net at an angle, with every thread segment exactly the length it started at. The extension along the diagonal is the bias stretch, and it is a change of shape rather than a change of length.

    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.

    part 1 · mechanics
  2. How far the bias goes, and where it stops. Extension along the bias against shear angle, with the angle at which the threads jam marked for three settings. The curve is geometry and so is the wall — a more closely set cloth reaches it sooner.

    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.

    part 2 · mechanics
  3. A cloth laid over a sphere. Every thread segment is exactly one pitch and none has stretched. What has changed is the angle at each crossing, and the amount is decided by the surface — a developable one costs nothing and a curved one costs more the further the cloth goes.

    Shear locking in a composite preform

    Laying a woven reinforcement over a mould is the bias mechanism doing useful work, and it stops dead at the angle where the threads jam. Where the cloth wrinkles is a geometric prediction with a radius attached.

    part 3 · mechanics
  4. The angle a pressurised hose wants. A fixed length of yarn wound on a cylinder at a stated angle, with the radius and length the geometry gives, beside the volume it encloses as the angle varies. The maximum is at arctan √2 — 54.74° — with no material constant anywhere in it, and the same angle comes out of balancing the hoop and axial stresses, which is a different calculation with the same answer.

    The angle a hose wants

    A braided hose has one angle at which pressure neither lengthens it nor shortens it, and the angle is arctan √2 — 54.74° — with no friction coefficient, no modulus and no fitted constant in it. Two arguments that share no algebra arrive at the same number, and which side of it a hose was braided on decides which way it moves.

    part 4 · applied

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