Fibre Testing & Bale Management
Spread falls with the square root of bale count. Doubling the laydown buys 41%, not 100%.
— bales
The larger of the two constraints — the binding property sets the laydown size
The square-root law assumes the bales in a laydown are drawn independently. They are not: bales from one gin, one field or one arrival lot are correlated, and a laydown built from three trucks behaves like three samples rather than forty-eight. Correlation inflates the true mix-to-mix spread well above what this predicts, which is why laydown rules specify a spread of origins and not just a count. The model also treats micronaire and strength as separate constraints when they covary within a growth, so satisfying both simultaneously can need more bales than either alone. Nothing here addresses the sequence in which bales enter the mixing line — a laydown with the correct mean and a systematic drift from first bale to last produces exactly the barré this calculation was meant to prevent.
Bale Laydown Constraint Window & Minimum Bale Count — free, with the formula and a worked example, at Textile School.