Fibre Length Distribution & Short Fibre Content

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.