Shed Geometry, Warp Strain & Abrasion Exposure

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 9 inputs are read from the form on every keystroke: Top Shed Line Deflection, Bottom Shed Line Deflection, Cloth Fell to Heald, Heald to Back Rest, Yarn Breaking Extension, Pick Density, Loom Speed, Warp Density and Reed Dents.
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 Mean Warp Strain at Full Shed together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Top Minus Bottom Strain, Top Shed Line Strain, Bottom Shed Line Strain, Strain as Share of Breaking Extension, Abrasion Exposure Index, Shed Cycles per Metre of Cloth, Shed Cycles per Hour, Top Shed Angle at the Heald, Total Heald Traverse and Ends per Dent — 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

Substituting

Move the fell-to-heald distance from 300 mm to 250 mm and the top strain rises to 0.4064% - a 31% increase from a 50 mm setting change nobody would record as significant. That sensitivity is why front shed distance is the first thing to check when warp breaks rise after a style change, and why it is worth calculating rather than eyeballing.

How to use it

1. Work through the input groups in order — Shed Geometry and Yarn & Construction. 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 Mean Warp Strain at Full Shed in the dark results panel — that is the headline figure, expressed in %.
4. Check the supporting rows underneath (Top Minus Bottom Strain, Top Shed Line Strain, Bottom Shed Line Strain, Strain as Share of Breaking Extension, Abrasion Exposure Index, Shed Cycles per Metre of Cloth, Shed Cycles per Hour, Top Shed Angle at the Heald, Total Heald Traverse and Ends per Dent) 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 Mean Warp Strain at Full Shed before a trial is booked, so machine time and material in Warping, Sizing, Weaving & Fabric Formation Control are committed against a calculated figure rather than an estimate.
• Costing and quotation — Mean Warp Strain at Full Shed 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 Top Shed Line Deflection) shows how much of the gap in Mean Warp Strain at Full Shed each variable explains.
• Teaching and study — the accepted ranges bracket normal Warping, Sizing, Weaving & Fabric Formation Control practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.

Reading the result

Typical bands and what each one is telling you.

Assumptions and limits

• This is the static geometric strain at full shed and it understates the true loading in two ways. The shed opens and closes once per pick, so the strain is dynamic and the yarn sees a strain rate rather than a held extension; at 550 rpm the full cycle occupies about 0.1 s. And beat-up superimposes a further tension peak, typically 20 to 40% above the static value, at the moment the reed drives the pick home. The calculation treats one heald frame with one pair of distances; on a loom with graduated shed the frames differ and each should be computed separately. Back rest height and its vertical offset from the warp line change the top-bottom split substantially and are not modelled here - only the deflections at the heald are taken as given. The abrasion index is a relative ranking quantity for comparing constructions on one machine, not an absolute break rate.
• Every input is bounded to the range normal practice occupies (Top Shed Line Deflection 1 to 120 mm, Bottom Shed Line Deflection 1 to 120 mm and Cloth Fell to Heald 50 to 900 mm, 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.

Standards and further reading

• ISO 3572 - textiles, weaving, definitions of general terms and basic weave structures.
• ISO 2062 - determination of single-end breaking force and elongation of yarns.
• ISO 7211-2 - woven fabrics, construction, determination of number of threads per unit length.
• ASTM D2256 - tensile properties of yarns by the single-strand method, for breaking extension.

Questions people ask