Fibre Length Distribution & Short Fibre Content

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: Mean Fibre Length, Length Coefficient of Variation, Short Fibre Threshold and Long Fibre Threshold.
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 Upper Half Mean Length together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Uniformity Index, Median Length, Short Fibre Content (by Number), Short Fibre Content (by Weight), Fibres Above Long Threshold (by Number) and Log-Normal Shape Parameter σ — 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 Upper Half Mean Length 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 — Measured Distribution and Thresholds. 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 Upper Half Mean Length in the dark results panel — that is the headline figure, expressed in mm.
4. Check the supporting rows underneath (Uniformity Index, Median Length, Short Fibre Content (by Number), Short Fibre Content (by Weight), Fibres Above Long Threshold (by Number) and Log-Normal Shape Parameter σ) 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 Upper Half Mean Length before a trial is booked, so machine time and material in Fiber Testing, Bale Management & Laboratory Sampling are committed against a calculated figure rather than an estimate.
• Costing and quotation — Upper Half Mean Length 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 Mean Fibre Length) shows how much of the gap in Upper Half Mean Length each variable explains.
• Teaching and study — the accepted ranges bracket normal Fiber Testing, Bale Management & Laboratory Sampling practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.

Assumptions and limits

• Everything here rests on one stated assumption: that the by-number length distribution is log-normal. Real cotton is close to that but not equal to it, and the tails — which is exactly where short fibre content lives — are where the fit is worst. Ginning damage in particular produces a broken-fibre population the single-mode model cannot represent, so a heavily ginned lot will have more short fibre than this predicts. The by-number and by-weight figures are the same fibres counted two ways: a fibre contributes mass in proportion to its length, so short fibres are numerous and light and the by-number figure is always the larger. AFIS reports both, HVI infers neither directly, and a specification naming "short fibre content" without a basis and a threshold cannot be enforced against either instrument. Treat the shape parameter as a fitted constant, not a measurement, and prefer a real length array when one is available.
• Every input is bounded to the range normal practice occupies (Mean Fibre Length 1 to 200 mm, Length Coefficient of Variation 1 to 120 % and Short Fibre Threshold 1 to 100 mm, 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