Sized Yarn Abrasion Resistance, Hairiness Gain & Add-On Adequacy

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 8 inputs are read from the form on every keystroke: Unsized Yarn, Sized Yarn, Size Add-On on the Tested Yarn, Abrasion the Loom Demands, Hairiness Before Sizing, Hairiness After Sizing, Warp Sized and Size Solids Cost.
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 Add-On Above What the Loom Needs together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Add-On That Just Meets Demand, Weavability Index, Abrasion Improvement, Cycles Gained per Point of Add-On, Hairiness Reduction, Size Solids Saved, Size Solids Saved and Value of the Surplus — 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

Do not act on this in one step. The honest use is to run the size box down in half-point stages toward 9%, testing abrasion and watching the warp stop rate at each stage, and to stop at the first sign of movement in either. The calculation says the headroom exists; only the loom says how much of it is real, because the demand figure came from one fabric on one machine and the slope came from one pair of specimens.

How to use it

1. Work through the input groups in order — Abrasion Test Pair and Hairiness & Economics. 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 Add-On Above What the Loom Needs in the dark results panel — that is the headline figure, expressed in %.
4. Check the supporting rows underneath (Add-On That Just Meets Demand, Weavability Index, Abrasion Improvement, Cycles Gained per Point of Add-On, Hairiness Reduction, Size Solids Saved, Size Solids Saved and Value of the Surplus) 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 Add-On Above What the Loom Needs 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 — Add-On Above What the Loom Needs 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 Unsized Yarn) shows how much of the gap in Add-On Above What the Loom Needs 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 slope is a chord between two measured points and is only reliable near the tested add-on; abrasion resistance against add-on saturates, so extrapolating far below the tested point understates the true resistance and far above it overstates it. Abrasion cycle counts are highly variable specimen to specimen - coefficients of variation of 20 to 30% are normal - so both figures should be means of at least twenty breaks, and a difference smaller than the scatter is not a difference. The demand figure is specific to a machine group and a construction and must be re-established when either changes. Hairiness reduction is reported from the values entered and is not used in the add-on arithmetic; it is the second reason sizing exists and it saturates at a different add-on than abrasion does. Nothing here accounts for size recipe: a change of polymer at constant add-on can move the abrasion figure more than a two-point change of quantity.
• Every input is bounded to the range normal practice occupies (Unsized Yarn 1 to 2000 cycles, Sized Yarn 1 to 5000 cycles and Size Add-On on the Tested Yarn 0.5 to 25 %, 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

• ASTM D629 - quantitative analysis of textiles, the reference route to size add-on by desizing.
• ASTM D5647 - measuring hairiness of yarns by the photo-electric apparatus.
• ISO 16549 - textiles, unevenness of textile strands, capacitance method.
• ASTM D2256 - tensile properties of yarns by the single-strand method, for the strength side of the sizing balance.

Questions people ask