Cone Package Density, Volume & Dye Penetration Margin

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 8 inputs are read from the form on every keystroke: Small End Diameter, Large End Diameter, Package Height, Tube Small Diameter, Tube Large Diameter, Yarn Mass on the Package, Yarn Linear Density and Maximum Density for Package Dyeing.
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 Package Density together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Yarn Volume, Yarn on the Package, Margin to the Dyeing Limit, Build Thickness, Cone Taper Angle, Specific Volume, Gross Envelope Volume and Tube Volume Displaced — 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

Substituting

The 95 km agrees exactly with the package length the winding calculator derives from mass and count alone, by a completely different route - which is the geometry confirming itself. The negative dye margin is the real finding: this cone is 43% denser than package dyeing tolerates, and it would have to be rewound before it could be dyed.

How to use it

1. Work through the input groups in order — Package Geometry and Yarn & Dyeing. 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 Package Density in the dark results panel — that is the headline figure, expressed in kg/m3.
4. Check the supporting rows underneath (Yarn Volume, Yarn on the Package, Margin to the Dyeing Limit, Build Thickness, Cone Taper Angle, Specific Volume, Gross Envelope Volume and Tube Volume Displaced) 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 Package Density 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 — Package Density 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 Small End Diameter) shows how much of the gap in Package Density 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.

Reading the result

Typical bands and what each one is telling you.

Assumptions and limits

• Density here is the package average. Real packages have a density gradient through the build - the inner layers are compressed by everything wound over them - so the core can be substantially denser than this figure while the surface is looser, which is exactly the gradient that causes uneven package dyeing. Package weight must exclude the tube. The dyeing limit is entered as an input because it depends on the machine, the pump capacity, the yarn and the shade depth; 400 to 420 kg/m3 is a common working figure for cotton but is not a universal constant. The geometry assumes clean frustum surfaces and takes no account of the nose and base profiles a real cone carries.
• Every input is bounded to the range normal practice occupies (Small End Diameter 40 to 400 mm, Large End Diameter 50 to 500 mm and Package Height 50 to 400 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.

Standards and further reading

• ISO 8115 and DIN 61800 - yarn package dimensions and designation.
• AATCC 23 / ISO 105 series - the dyeing uniformity this density governs.
• ASTM D1907 - linear density, for the length derived from mass.

Questions people ask