Textile Structure
how cloth is put together
Generator

The angle a pressurised hose wants

The angle a pressurised hose wants
The angle a pressurised hose wantsA 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.45.0° to the axis, 4 turns of one length of yarnbelow the neutral angle — inflating shortens and fattens itradius 0.0281 · length 0.707 · 4 turns of one length of yarnlengthdiameter00.50011.50220406080winding angle to the axis, degreesvolume enclosed, arbitraryarctan √2 = 54.74°radius and length from the yarn length; the maximum found by searchneutral 54.74°

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.

4 essays call helix. 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

Every figure listed here is drawn from this one rule.

What a balanced cloth wastes under pressure. The fraction of a balanced fabric's fibre that is along for the ride, in a stress field of each ratio. A closed cylinder is exactly two to one — the ratio of the two areas the pressure acts on — so a balanced cloth reaches its limit around the circumference with the axial system at half its capacity, and a quarter of the fibre is doing nothing. Cloth doing a job

An inflated cylinder wants an unbalanced cloth

Balance is a virtue in almost every other cloth. Under pressure it is a defect with a size — a closed cylinder carries exactly twice the stress around its circumference as along its axis, so a balanced fabric reaches its limit in one direction with a quarter of its fibre doing nothing at all.

 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. Cloth doing a job

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.

 An inflated tube in section at 0.5, 1, 1.6 times its wrinkling moment. The cross-section of an inflated tube of 100 mm radius at 50 kPa, bent by 0.5 times, 1 times, 1.6 times its wrinkling moment of 78.5 N·m, with the outside of the bend at the top. Each stroke is the wall's axial tension at that point: the pressure's even 2.5 kN/m with the bending's cosine added. At half the wrinkling moment the inside is still in tension; at the wrinkling moment it falls to nothing; past it the inside has gone slack over a dashed arc and the rest carries both the pressure's end force and the moment. What the drawing cannot show is the wrinkles themselves, whose wavelength a cloth's bending stiffness decides and this section leaves out. Cloth doing a job

An inflated beam wrinkles at a moment with no cloth in it

An air-filled tube can be used as a beam because the pressure pulls its cloth taut along its length, and a cloth that cannot carry a push can carry a bending moment for exactly as long as that pull outweighs it. The inside of the bend goes slack at πpr³/2 and the tube folds at πpr³ — seventy-nine and a hundred and fifty-seven newton metres for a tube a fifth of a metre across at half a bar — and there is no property of the cloth in either. The cloth decides how far the beam bends on the way, and how much pressure it can be pumped to.

 Where an air arch first wrinkles under snow over the whole span. A semicircular air arch 4 m across, pinned at both feet, of a tube 200 mm across at 50 kPa, under snow over the whole span; beside it, unrolled from the left foot to the right, the share of the tube's wrinkling budget πpr³/2 spent at each section when the first wrinkle forms, with the thrust's part, N·r/2, shaded darker. The first wrinkle forms 25° above the right foot, at 167 N per metre of span, where the moment of 60.2 N·m compresses the inside of the curve and the thrust is 336 N; there the thrust has taken 21 per cent of the budget. Judged by its moment alone the arch would carry 218. Cloth doing a job

An air arch pays for its thrust out of its pressure

An inflated tube bent into an arch was expected to start with its inside wall pulled differently from its outside, and to wrinkle where that difference and the load's moment combined worst. It does not: a curved tube is pulled along its length at exactly the straight tube's pr/2, all the way round. What the arch spends its pressure on instead is the thing every arch exists to make — its own thrust — which takes a fifth of the wrinkling budget at the haunch of a shelter arch under snow and more than half on a tight one.

The whole library · All essays