Dye Strength Assay, Dosing Correction & Stock Yield

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: Dye in Stock, Nominal Strength, Assayed Strength, Dye Cost, Recipe Dose and Batch Weight.
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 Corrected Dose together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Strength Ratio, Dose Increase, Depth Shortfall if Uncorrected, Dye per Batch, Corrected, Extra Dye per Batch, Batches this Stock Makes, Batches if it were Full Strength, Batches Lost to the Deficit, Stock at Nominal Strength and Value of the Strength Deficit — 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 Corrected Dose 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 — Lot and Recipe. 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 Corrected Dose in the dark results panel — that is the headline figure, expressed in % owf.
4. Check the supporting rows underneath (Strength Ratio, Dose Increase, Depth Shortfall if Uncorrected, Dye per Batch, Corrected, Extra Dye per Batch, Batches this Stock Makes, Batches if it were Full Strength, Batches Lost to the Deficit, Stock at Nominal Strength and Value of the Strength Deficit) 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 Corrected Dose before a trial is booked, so machine time and material in Dyeing, Printing, Color Management & Chemical Control are committed against a calculated figure rather than an estimate.
• Costing and quotation — Corrected Dose 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 Dye in Stock) shows how much of the gap in Corrected Dose each variable explains.
• Teaching and study — the accepted ranges bracket normal Dyeing, Printing, Color Management & Chemical Control practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.

Assumptions and limits

• Strength correction is linear in the assay, which is a good description over the narrow band a commercial lot varies across and a poor one over a wide range, because depth is not linear in concentration - the Kubelka-Munk relation between concentration and reflectance is, but the visual depth built on it is not, so a correction across a large strength gap should be checked with a lab dip rather than trusted. The assay itself is a comparison against a retained standard, so it is only as good as that standard: a reference sample that has itself aged, absorbed moisture or been decanted repeatedly will drift the whole scale, and the usual symptom is a mill that corrects steadily in one direction over years. Hygroscopic dyes are the common trap, since a powder that has picked up moisture assays low for a reason that has nothing to do with chromophore content and the correction then over-doses; where moisture is suspected the assay should be reported on a dry basis. The stock figures assume the whole drum shares one assay, which is fair for a single lot and wrong for a bin holding several - blending lots without re-assaying is how a store loses track of strength entirely.
• Every input is bounded to the range normal practice occupies (Dye in Stock 1 to 100000 kg, Nominal Strength 10 to 300 % and Assayed Strength 10 to 300 %, 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