Leno Weave Crossing End Tension Calculator

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 6 inputs are read from the form on every keystroke: Crossing Amplitude, Pick Spacing, Let-off Compensation, Standard Warp Tension, Yarn Stiffness and Yarn Breaking Load.
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 Crossing End Tension together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Extra Path Length, Extra Let-off Required, Strain from Shortfall, Added Tension and Share of Breaking Load — 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 Crossing End Tension 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 — Leno Geometry and Yarn. 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 Crossing End Tension in the dark results panel — that is the headline figure, expressed in cN.
4. Check the supporting rows underneath (Extra Path Length, Extra Let-off Required, Strain from Shortfall, Added Tension and Share of Breaking Load) 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 Crossing End Tension before a trial is booked, so machine time and material in Narrow Fabrics, Tapes & 3D Weaving are committed against a calculated figure rather than an estimate.
• Costing and quotation — Crossing End Tension 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 Crossing Amplitude) shows how much of the gap in Crossing End Tension each variable explains.
• Teaching and study — the accepted ranges bracket normal Narrow Fabrics, Tapes & 3D Weaving practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.

Assumptions and limits

• Keep the share of breaking load well under the level where fatigue sets in: the crossing end sees this peak on every pick, not once. Treat a rising figure as a let-off problem before touching yarn quality.
• Every input is bounded to the range normal practice occupies (Crossing Amplitude 0.1 to 30 mm, Pick Spacing 0.1 to 50 mm and Let-off Compensation 0 to 100 %, 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