Textile Structure
how cloth is put together
Series

Crimp — the series

6 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. Pull it lengthways and it narrows. The same cloth before and after a small extension along the warp. No thread has stretched: the extension came out of the warp crimp, that crimp went into the weft, and the fabric is narrower for it.

    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.

    part 1 · setting
  2. Pull it lengthways and it narrows. The same cloth before and after a small extension along the warp. No thread has stretched: the extension came out of the warp crimp, that crimp went into the weft, and the fabric is narrower for it.

    What crimp interchange actually conserves

    Pull a cloth lengthways and it narrows, because the crimp moves from one system to the other. Inextensibility says that much and no more — it is one equation short of an answer, and the second equation everybody uses is an assumption with a name.

    part 2 · setting
  3. 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.

    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.

    part 3 · applied
  4. The energy well, and where the cloth sits in it. The bending energy of a sheeting at every state on its own constant-thread-length locus, plotted against how the crimp divides between the two systems. The minimum is at 1.22 and the value every Peirce solution here is drawn at is 1.00, marked. The well's depth decides how firmly the ratio is settled, which is why an open scrim's measured crimp scatters and a close sheeting's does not. What the plot cannot show is the friction that stops a cloth reaching the bottom, which turns the minimum into a band.

    The crimp ratio is not a measurement

    Peirce's geometry is two thread systems, four unknowns and three equations. It cannot say how the crimp divides between warp and weft, so every cloth solved so far has been drawn at a ratio somebody chose. Give the threads a stiffness and the missing equation arrives — and for six of the eight cloths in the table it arrives with no material constant in it at all.

    part 4 · setting
  5. The crimp ratios a dense shirting can have. Poplins in 15 tex warp and 20 tex weft at 22 picks, from 32 ends per centimetre to 52. Each bar is the interval of warp-to-weft crimp ratios the construction admits at all: the warp must supply at least the thickness the weft cannot reach, and at most what it can reach itself. The rule at one is this site's standing default. It sits inside the interval up to 44.18 ends per centimetre and outside it beyond — so for a dense shirting an equal division of the crimp is not merely the wrong assumption but a geometric impossibility. The 44-end poplin this site's own cloth table called impossible for a long time sits a fifth of an end below that limit, which is why the solver failed on it: its feasible interval was real and narrow, and a bisection on the whole range walked away from it.

    The cloth that was called impossible

    This site's own table of fabrics carries a note saying a real 44-end poplin has no solution in its geometry at all, and that the poplin row was therefore set at 32 ends. The cloth solves. What had no solution was the search — a bisection that treated a state it could not reach as evidence of having gone too far, and walked away from the answer every time.

    part 5 · setting
  6. Shrinkage from wetting, cloth by cloth. The change in each cloth's relaxed construction when its threads swell by 20% across and 1.2% along. Both states are least-energy states of their own constant-thread-length locus, which is the only comparison the locus admits: its minimum is a state at its own sett, so it may be compared with another minimum and not with a quoted construction. Positive is smaller. Every cloth that has a wet state closes up except the cheesecloth, which opens by half a per cent because the fibre's extra hundredth of length outruns the extra crimp a thicker partner costs. What the bars cannot show is the three cloths that are missing, which have no wet state at all.

    Wetting moves a cloth to another locus

    A cloth's constant-thread-length locus is built at a fixed thickness. Swelling changes the thickness, so a wetted cloth is not somewhere else on its own locus — it is on a different one, and the distance between the two least-energy states is the shrinkage. Five of the eight cloths here have a wet state, and one of them gets bigger.

    part 6 · setting

All series