Wind Ratio & Patterning Risk on a Drum Winder

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 7 inputs are read from the form on every keystroke: Grooved Drum Diameter, Drum Speed, Double Traverses per Drum Revolution, Traverse Stroke, Package Diameter, Highest Pattern Order Considered and Risk Band Half-Width.
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 Wind Ratio together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Winding Speed, Package Speed, Double Traverses, Traverse Speed, Coil Angle, Nearest Pattern, Numerator, Nearest Pattern, Denominator, Distance from that Pattern, Patterning Risk and Diameter at that Pattern Band — 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 Wind Ratio 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 — Winder and Package & Risk. 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 Wind Ratio in the dark results panel — that is the headline figure, expressed in x.
4. Check the supporting rows underneath (Winding Speed, Package Speed, Double Traverses, Traverse Speed, Coil Angle, Nearest Pattern, Numerator, Nearest Pattern, Denominator, Distance from that Pattern, Patterning Risk and Diameter at that Pattern Band) 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 Wind Ratio before a trial is booked, so machine time and material in Spinning, Winding & Yarn Package Engineering are committed against a calculated figure rather than an estimate.
• Costing and quotation — Wind Ratio 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 Grooved Drum Diameter) shows how much of the gap in Wind Ratio each variable explains.
• Teaching and study — the accepted ranges bracket normal Spinning, Winding & Yarn Package Engineering practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.

Assumptions and limits

• 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.
• Every input is bounded to the range normal practice occupies (Grooved Drum Diameter 30 to 300 mm, Drum Speed 200 to 12000 rpm and Double Traverses per Drum Revolution 0.25 to 4 nos, 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