Textile Structure
how cloth is put together
Series

Cover — the series

6 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. The same thread count, twice. Two cloths with identical thread counts and different yarn. The count is the same number in both; the fraction of the surface the threads actually occupy is not, and that fraction is what thread count is usually taken to mean.

    Thread count is not quality

    It counts threads. It says nothing about how much of the cloth they cover, it can be inflated by counting plies, and it ranks fabrics in nearly the wrong order. The quantity it is mistaken for is cover factor, and that one is computable.

    part 1 · setting
  2. Balanced, and not. Three weaves in section along one warp end, with the share of the face each thread system takes. The share is the mean of the matrix; what follows from it — which system wears, which carries the colour — does not follow from the matrix at all.

    Balance, and what an unbalanced cloth does

    How much of the surface each thread system takes is the mean of the weave matrix, and it is one of the very few quantities in this subject that can be read straight off. Almost nothing that follows from it can.

    part 2 · setting
  3. Where the twenty-eight comes from. The setting a cotton cover factor of 28 prescribes, and the setting at which the threads would cover the surface geometrically, against yarn count. They are one curve: the trade's scale is Peirce's diameter with the units taken out. Below them is the sett at which each weave actually jams, which is a fixed fraction of it.

    Where the cover factor comes from

    A cotton cover factor is threads per inch over the root of the count, and the scale says twenty-eight means a covered surface. The twenty-eight is not a convention: it is the reciprocal of Peirce's yarn diameter, and the trade's practical ceilings of fourteen and twenty-two fall straight out of it.

    part 3 · setting
  4. The hole between four threads. Three millimetres of a woven filter cloth in plan, with one clear opening dimensioned and a grain of the soil it must retain drawn at the same scale. Every hole in the repeat is this size — a woven cloth's pore distribution is a single value, which is why it is specified by an opening size while a nonwoven needs a curve.

    The hole between four threads

    A woven cloth's holes are all the same size. That is not an approximation — it is what a repeat means — and it is the whole reason a woven filter is specified by one number while a nonwoven needs a curve. The number is the spacing less the diameter, which this site has been computing since its first questions about setting.

    part 4 · applied
  5. How open a muslin is, against where the light is. One minus the cover is a cloth's openness to a light directly behind it, and for this muslin it is 37.9 per cent. Move off the normal and a line of sight has to clear the hole at the top of the cloth and the same hole one thickness below, so what it can use falls as t·tan α is taken off each side — reaching nothing at 36.1° across the ends. Averaged over the whole sky with Lambert's cosine weighting, the cloth is 5.36 per cent open — 7.1 times less than the covering rule says, and the whole of the difference is the thickness. One minus the cover is the openness of a cloth with no thickness, and no cloth has none.

    One minus the cover is a cloth with no thickness

    The covering rule says a cloth's openness is one minus its cover factor, and this collection derived it and has used it ever since. It is the answer for a light directly behind the cloth. Move the light and a line of sight has to clear the hole at the top of the fabric and the same hole one thickness below, so the openness falls, and it reaches nothing at thirty-six degrees. Averaged over the whole sky a muslin is a seventh as open as the rule says.

    part 5 · setting
  6. The section the fabric asks for, beside the one the model drew. A 20 tex cotton yarn in cross-section, at 900 times life size. The circle is what every solve in this collection has assumed: a diameter of 0.167 mm from the count and the packing factor. The ellipse has the same area and a minor axis of 78% of it, which is the closest the fabric's own adjacent courses come to one another — 0.130 mm. Nothing about that number was fitted to a fabric. It falls out of a solve that knew nothing about flattening, and it lands inside the range the trade reports for yarn in cloth, which this collection has carried as a free parameter ever since it first put a number on a sett.

    What a flattened yarn does to its cover

    A cover factor is a sett times a diameter, and it decides how much of a cloth is thread and how much is hole. A flattened yarn is a third wider than a round one of the same area, so a cloth of flattened yarn covers more at the same sett — and every opacity, permeability and shade computed from a round diameter is wrong in one direction.

    part 6 · setting

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