Woven Construction Feasibility Checker

The formula

This is the expression the tool evaluates. Every term is named underneath, with the unit it must be supplied in.

How the result is derived

Step by step, from the values you type to the figure on screen.

1. Ends per inch are converted to ends per centimetre and divided by the ends-per-dent draft, giving the reed density the construction actually requires.
2. Warp and weft cover are each computed as thread density over the square root of count — the square root because a yarn diameter scales that way, not linearly with count.
3. The two are combined by Peirce's relation, which subtracts the overlap where warp crosses weft so the area is not counted twice.
4. Each of the three demands is divided into its corresponding machine limit to give a margin, and the three margins are directly comparable because each is a pure ratio.
5. The smallest margin is reported as the answer, because the binding constraint is what stops a fabric, and the other two ceilings are irrelevant until it is relieved.

What each input means

Where to read each value on the floor, the unit it must be in, and the range the tool accepts.

What the tool returns

The headline figure and every supporting value it is built from.

Worked example

Substituting

A routine 120x60 poplin, feasible with 27% in hand — and the interesting part is how close the reed and cover margins are. Two independent ceilings arriving within 0.001 of each other is not coincidence: at 2 ends per dent a plain weave runs out of reed and runs out of room at roughly the same construction. Raise the draft to 3 ends per dent and the reed margin jumps to 1.9x while cover stays at 1.27x, so cover becomes the binding limit and the reed stops being the thing to argue about.

How to use it

1. Work through the input groups in order — Target Construction and Machine Limits. The defaults are a realistic case, so you can change one value at a time and watch what moves.
2. There is no calculate button. Every figure recalculates as you type or drag, which is what makes this usable for a what-if sweep rather than a single answer.
3. Read Feasibility Margin in the dark results panel — that is the headline figure, expressed in ×.
4. Check the supporting rows underneath (Reed Density Required, Cover Factor, Total Ends, Reed Margin, Cover Factor Margin and Loom Speed Margin) before acting on the headline — they are where an implausible input usually shows itself first.
5. Reset to defaults returns every field to the reference case, which is the quickest way to check whether a surprising result came from the tool or from an input you had changed earlier.

Where this is used

• Costing a buyer's specification before quoting — establishing that the construction can be woven at all, on the looms the order would actually run on.
• Reed selection and drawing-in planning, where the ends-per-dent draft is the cheapest variable to change and often the one that rescues a construction.
• Loom allocation — a construction with a loom-speed margin near 1 belongs on the fast machines, and one with headroom can go anywhere.
• Arguing a specification back to a customer with a number rather than an opinion, by naming which of the three ceilings the fabric breaks and by how much.

Reading the result

Typical bands and what each one is telling you.

Assumptions and limits

• A uniform draft — every dent carries the same number of ends. Fancy, mixed-dent and cramming drafts have to be checked dent by dent, and this tool will read them as easier than they are.
• The Peirce cover factor with a constant of 28, which is the cotton convention. The constant is exposed as an input because it is a convention rather than a physical constant.
• Cover factor is weave-blind. A plain weave at K 24 is far harder to produce than a 3/1 twill at the same figure, so the maximum cover factor belongs to the weave, not to the mill.
• The count is nominal. Real yarn runs coarser than its label often enough that a margin under 1.05 should be treated as no margin.
• Geometry only. Yarn quality, sizing, shed geometry and warp tension decide whether a feasible construction actually runs, and none of them appear here.

Standards and further reading

• ASTM D3775 — warp end and filling pick count of woven fabrics, the measurement this tool takes as its input.
• ISO 7211-2 — determination of the number of threads per unit length in woven fabrics.
• F. T. Peirce, "The Geometry of Cloth Structure", Journal of the Textile Institute, 1937 — the origin of the cover factor relation used here.

Questions people ask