Fluorescent Brightener Whiteness Index Saturation Limit

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: Whiteness Before Brightening, Maximum Fluorescent Gain, Saturation Dose Constant, Greening Penalty, Brightener Dose and Fabric 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 CIE Whiteness Index together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Whiteness-Maximising Dose, Peak Whiteness Available, Whiteness Given Away, Dose Above Optimum and Reagent Wasted per Batch — 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 CIE Whiteness Index 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 — Brightener Response and Application. 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 CIE Whiteness Index in the dark results panel — that is the headline figure, expressed in W.
4. Check the supporting rows underneath (Whiteness-Maximising Dose, Peak Whiteness Available, Whiteness Given Away, Dose Above Optimum and Reagent Wasted per Batch) 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 CIE Whiteness Index before a trial is booked, so machine time and material in Specialized Chemistry & Advanced Dye Physics are committed against a calculated figure rather than an estimate.
• Costing and quotation — CIE Whiteness Index 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 Whiteness Before Brightening) shows how much of the gap in CIE Whiteness Index each variable explains.
• Teaching and study — the accepted ranges bracket normal Specialized Chemistry & Advanced Dye Physics practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.

Assumptions and limits

• Both the saturation constant and the greening penalty are fitted to a specific brightener on a specific substrate and must be recovered by running a dose ladder and measuring CIE whiteness and tint on your own goods — they are not transferable between brightener classes or between cotton and polyester. The single whiteness number also hides the tint deviation, which is what an observer actually objects to; a fabric can hold its whiteness index and still look visibly green, so judge a ladder on tint as well. Whiteness measurement is itself illuminant-dependent, since the fluorescence needs UV in the source, and a result read under one instrument condition will not reproduce under another.
• Every input is bounded to the range normal practice occupies (Whiteness Before Brightening 20 to 120 W, Maximum Fluorescent Gain 5 to 150 W and Saturation Dose Constant 0.02 to 2 % owf, 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