Weave Repeat, Shafts & Ashenhurst Maximum Sett

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. The 5 inputs are read from the form on every keystroke: Warp Up, Warp Down, Twill Step, Yarn Count and Actual Ends per Inch.
2. Each value is checked against the accepted range in the input table below. A value outside its range stops the calculation rather than producing a misleading figure — the results blank out and a message appears.
3. The validated values are substituted into the expression above, which resolves Maximum Sett together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Repeat, Ends, Repeat, Picks, Shafts for a Straight Draft, Warp Float Length, Weft Float Length, Intersections per Repeat, Float as Share of Repeat, Yarn Diameters per Inch, Yarn Diameter and Sett as Share of Maximum — come from the same pass, so they always describe the same case as the headline figure.
5. Results are rounded for display only. The full-precision value is used throughout the chain, so reading a rounded intermediate figure back into the tool by hand can shift the last digit.

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

The tool loads with this case already solved — the Maximum Sett shown above is its answer. Change one value and the difference from this baseline is the sensitivity of the result to that variable.

How to use it

1. Work through the input groups in order — Weave and Yarn & Sett. 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 Maximum Sett in the dark results panel — that is the headline figure, expressed in epi.
4. Check the supporting rows underneath (Repeat, Ends, Repeat, Picks, Shafts for a Straight Draft, Warp Float Length, Weft Float Length, Intersections per Repeat, Float as Share of Repeat, Yarn Diameters per Inch, Yarn Diameter and Sett as Share of Maximum) 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

• Process planning — establishing Maximum Sett before a trial is booked, so machine time and material in Weaving & Fabric Construction are committed against a calculated figure rather than an estimate.
• Costing and quotation — Maximum Sett is an input to the cost sheet, and quoting from a worked number rather than a remembered one is what keeps a margin intact.
• Troubleshooting — when the floor result drifts from plan, entering the measured values (starting with Warp Up) shows how much of the gap in Maximum Sett each variable explains.
• Teaching and study — the accepted ranges bracket normal Weaving & Fabric Construction practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.

Assumptions and limits

• Ashenhurst is a nineteenth-century rule of thumb that has survived because it is close enough and nothing simpler replaced it. Its yarn diameter comes from a constant of 28 over the square root of the English count, which assumes a round, uniformly packed cotton yarn at ordinary twist - so it is optimistic for a soft, low-twist or open-end yarn, which is flatter and packs differently, and it does not describe a filament yarn at all. Read the maximum sett as an upper bound for a comparable cotton cloth and not as a physical constant. The intersection count is fixed at two per repeat, which is right for a simple twill or a regular satin where each end rises once and falls once, and wrong for a weave with more than one float per repeat in the same direction, such as a rib, a hopsack or a broken twill; those need their intersections counted from the actual point paper. Shafts are given for a straight draft, which is the maximum a weave ever needs and often more than the minimum - a pointed, skip or grouped draft can weave the same structure on fewer, and any repeat sharing a factor with the twill step reduces further, which is why the count divides by the greatest common divisor here. A sett utilisation above about ninety-five percent is weavable but unforgiving: shed clarity falls, warp abrasion rises and the loom will find every weak end in the beam.
• Every input is bounded to the range normal practice occupies (Warp Up 1 to 12 ends, Warp Down 1 to 12 ends and Twill Step 1 to 6 ends, and so on for the rest). Those bounds are guard rails against typing errors, not a claim that the formula fails one unit outside them.
• The calculation is deterministic: the same inputs always give the same result. It carries no allowance for machine condition, operator skill, ambient conditions or lot-to-lot material variation unless an input above explicitly represents one.
• Nothing is sent anywhere. The maths runs in your browser, so the numbers you type never leave the page.

Questions people ask