Let-Off Torque, Warp Tension Swing & Take-Up Load

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 7 inputs are read from the form on every keystroke: Ends in the Warp, Tension per End, Warp Yarn Count, Yarn Tenacity, Full Beam Diameter, Empty Beam Barrel Diameter and Fabric Width in Reed.
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 Total Warp Sheet Tension together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Tension Swing, Full to Empty, Beam Torque at Full Diameter, Beam Torque at Empty Barrel, Torque Ratio, Tension per End at Empty Beam, Specific Tension, Fraction of Breaking Load Used, Torque Change per cm of Diameter and Take-Up Load Across the Cloth — 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

The 10% of breaking load is the check that matters: it sits in the accepted 8 to 15% band, so the setting is sound at the mean radius. But 97.36 cN at the empty beam is 23% of breaking load, and that is why warp breaks cluster in the last few metres of a beam on machines with mechanical let-off. The defect is real, it has a shape, and it is entirely predicted by the radius ratio.

How to use it

1. Work through the input groups in order — Warp Sheet and Beam & Cloth. 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 Total Warp Sheet Tension in the dark results panel — that is the headline figure, expressed in N.
4. Check the supporting rows underneath (Tension Swing, Full to Empty, Beam Torque at Full Diameter, Beam Torque at Empty Barrel, Torque Ratio, Tension per End at Empty Beam, Specific Tension, Fraction of Breaking Load Used, Torque Change per cm of Diameter and Take-Up Load Across the Cloth) 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 Total Warp Sheet Tension 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 — Total Warp Sheet 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 Ends in the Warp) shows how much of the gap in Total Warp Sheet Tension 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

• The tension swing assumes an uncompensated constant-torque let-off with the brake set at the mean radius, which is the worst case; compensated weight-lever mechanisms reduce it and electronic let-off with back-rest feedback removes it, so treat this figure as an upper bound unless the compensation is known to be correctly set. Tension per end is taken as uniform across the sheet, which it never is: ends at the selvedge and ends crossing a badly wound beam patch can carry substantially more, and the peak end tension rather than the mean is what breaks. Dynamic tension during beat-up peaks well above the static value calculated here - typically 20 to 40% higher at the moment of beat-up - so the fraction of breaking load quoted is a static figure and the instantaneous loading is worse. Yarn tenacity should be the sized single-end value at the actual test conditions, not the unsized figure from the spinning report.
• Every input is bounded to the range normal practice occupies (Ends in the Warp 100 to 30000, Tension per End 1 to 500 cN and Warp Yarn Count 2 to 400 tex, 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 2062 - determination of single-end breaking force and elongation of yarns.
• ASTM D2256 - tensile properties of yarns by the single-strand method.
• ISO 1144 - textiles, universal system for designating linear density, the tex system.
• ISO 3572 - textiles, weaving, definitions of general terms and basic weave structures.

Questions people ask