Winding
The wind ratio falls as the package grows, so every package passes through every patterning band on its way up.
— x
Coils laid per double traverse at this diameter
Wind ratio is derived on the assumption that the package is driven purely by friction from the drum at matched surface speeds, which is what a drum winder does when the cradle pressure is right and slip is negligible; a slipping package winds at a different ratio than this calculates and, more importantly, at a varying one, which is a different fault presenting as a soft package rather than a ribboned one. Low-order ratios are more damaging than high-order ones because the coils coincide more often per unit of build, so the pattern order limit is doing real work here - a ratio near 1/2 or 2/3 will ribbon in a way that a ratio near 7/8 will not, even at the same distance. The risk figure is a linear ramp inside a declared band rather than a measured probability; it is there to rank diameters, not to predict a defect. Nothing here models what a ribbon breaker actually does, which is to disturb the ratio deliberately by modulating drum speed or by shifting the package axially, and a winder with an effective breaker will pass through these bands without consequence. Anti-patterning behaviour is also why the ratio on a real machine is never quite the clean geometric value this computes.
Wind Ratio & Patterning Risk on a Drum Winder — free, with the formula and a worked example, at Textile School.