Textile Structure
how cloth is put together
Series

Pressure — the series

4 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. What a knitted band presses a limb with. Pressure against extension for a 20 tex cotton band at a 3.5 mm loop, wrapped round a 30 mm radius — a wrist. The pressure is the fabric's own tension per unit width divided by that radius, and the tension is the loop's bending with the relaxed shape as the yarn's natural one, so nothing here is fitted. Over the range a cuff is actually used across it runs from a twentieth of a millimetre of mercury to 0.85. The shaded bands are what a compression garment is specified at, and the curve does not reach the lowest of them until 277 per cent — which is not a cuff, it is a fabric stretched almost to the point where its yarn runs straight.

    What a cuff presses with

    A rib cuff holds a sleeve on a wrist, so it must be pressing. Divide its own recovery force by the radius it is wrapped round and the pressure comes out at eight tenths of a millimetre of mercury — a fiftieth of the lightest medical compression, and two orders below what the same fabric resists being squashed with.

    part 1 · applied
  2. A tube of an elastic band knitted 157 mm round, up one leg. A tube knitted 157 mm round from an elastic band, pulled up an illustrative leg and read at four stations. At each the tube is stretched by the leg's circumference over its own, pulls back with the band's tension at that stretch, and presses with that tension over the leg's radius: ankle 22 cm, stretched 40%, 20.0 mmHg; lower calf 29 cm, stretched 85%, 32.1 mmHg; calf 36 cm, stretched 129%, 39.4 mmHg; below the knee 34 cm, stretched 116%, 37.6 mmHg. The calf is pressed 1.97 times as hard as the ankle. What the bars cannot show is the leg's own give, which a firm tube flattens and which changes the radius the law divides by.

    A tube of one size presses the calf harder than the ankle

    A band presses a limb with its tension over the limb's radius, so it is easy to conclude that a band grips hardest where the limb is thinnest. That is true of a band held at one tension, and no knitted tube is. A tube knitted to one size is stretched further wherever the leg is thicker, and its tension rises faster than the radius does: an elastic tube pressing an ankle at twenty millimetres of mercury presses the calf at thirty-nine, and a cotton jersey tube presses its calf three and a half times as hard as its ankle. A stocking graduated the other way has to pull hardest where it presses less.

    part 2 · applied
  3. The pressure a band puts on a calf with a ridge down its front, point by point. The section of a calf with a ridge down its front modelled as the convex hull of 2 circles, 360 mm round, with a band on it tensioned so that a round limb of the same girth would be pressed at 20.0 mmHg. The band rides the hull: on each arc it presses with its tension over that circle's radius, and on the straight stretches between arcs it presses nothing. shin ridge 214 mmHg over 2.4% of the girth, calf muscle 21 mmHg over 68.9% of the girth; 29% of the girth carries no pressure at all. The spikes are drawn outward from the band with length proportional to the pressure.

    A band presses where the limb turns

    Every compression pressure is quoted as a band's tension over the limb's radius, and a limb has no radius. It has a curvature that changes all the way round, and a band presses each point with its tension times the curvature there. The round-limb number survives exactly — as an average over the band's length — and is the pressure almost nowhere. On a calf with a ridge down its front the ridge takes ten times it and the flat face beside it takes none; on an ankle, two bones and a tendon carry nearly three quarters of the force on under a fifth of the girth.

    part 3 · applied
  4. A graduated stocking knitted in 8 equal steps. The pressure a stocking knitted as 8 steps of fixed girth puts on the illustrative leg from ankle to knee, against the smooth graduation from 20 mmHg at the ankle to 12 below the knee that it approximates. The steps are equal in height. The rings, the pressure change along each step, run 4.79, 3.96, 3.32, 2.82, 2.43, 2.12, 0.87, 0.92 mmHg from the ankle up; the largest is 4.79 mmHg.

    A stepped stocking should step most at the ankle

    A graduated stocking asks for a girth that rises smoothly up the leg, and a knitting machine gives it one girth, then the next. Over each step the tube is one size on a stretch of leg that is not, so it presses harder at the top of the step than at the bottom, and the pressure up the leg is a saw-tooth. Each tooth is the leg's change of girth across the step divided by the girth squared — so it is largest just above the ankle, where the leg is thinnest and widening fastest. Eight equal steps leave a ring of 4.8 mmHg there; eight steps spaced by the leg's own shape leave 2.7 everywhere.

    part 4 · applied

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