Blue Wool Lightfastness Rating from Exposure

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 4 inputs are read from the form on every keystroke: Hours to Reach the Contrast, Hours for Blue Wool 1, Target Rating and Hours per AATCC Fading Unit.
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 Achieved Rating together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Exposure Relative to BW1, Reported Standard, Hours the Target Requires, Margin in Hours, Margin in Grades, Hours for the Next Whole Grade, Extra Exposure that Needs, Equivalent AATCC Fading Units and AFU the Target Requires — 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 Achieved Rating 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 — Exposure and Specification. 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 Achieved Rating in the dark results panel — that is the headline figure, expressed in BW.
4. Check the supporting rows underneath (Exposure Relative to BW1, Reported Standard, Hours the Target Requires, Margin in Hours, Margin in Grades, Hours for the Next Whole Grade, Extra Exposure that Needs, Equivalent AATCC Fading Units and AFU the Target Requires) 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 Achieved Rating before a trial is booked, so machine time and material in Textile Testing & Quality Control are committed against a calculated figure rather than an estimate.
• Costing and quotation — Achieved Rating 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 Hours to Reach the Contrast) shows how much of the gap in Achieved Rating each variable explains.
• Teaching and study — the accepted ranges bracket normal Textile Testing & Quality Control practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.

Assumptions and limits

• The doubling rule is an idealisation of a scale whose real intervals are not exactly a factor of two and are not uniform across it - the gap between standards 6 and 7 is wider in practice than the gap between 2 and 3 - so a fractional rating computed this way is an interpolation for comparing samples rather than a reportable result. What gets reported is always the whole standard the sample matches, which is why the rounded figure is given beside it. The anchor matters more than anything else here: hours for blue wool 1 depend on the cabinet, the lamp, the filter, the irradiance setpoint and the black panel temperature, so the figure must come from the blue wool standards exposed ALONGSIDE the specimen in the same run, never from a table. That is the whole reason the standards are exposed together rather than a time being specified. Humidity is the variable most often left uncontrolled and it moves lightfastness substantially for many dye classes, which is why the effective humidity control standard is exposed as well. The AFU conversion is a convenience for translating between conventions and is approximate; ISO and AATCC do not define the endpoint identically, so a sample at the boundary can be reported differently under the two methods with nothing wrong in either.
• Every input is bounded to the range normal practice occupies (Hours to Reach the Contrast 0.5 to 5000 h, Hours for Blue Wool 1 0.5 to 100 h and Target Rating 1 to 8 BW, 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