Package Geometry The frustum, outside and inside

Small End Diameter mm

Large End Diameter mm

Package Height mm

Tube Small Diameter mm

Tube Large Diameter mm

Yarn & Dyeing What is wound and what it is for

Yarn Mass on the Package kg

Excluding the tube

Yarn Linear Density tex

Maximum Density for Package Dyeing kg/m3

Package Density

— kg/m3

Wound mass over the frustum volume it occupies

Volume, Length & Dyeability

Yarn Volume: — dm3
Yarn on the Package: — km
Margin to the Dyeing Limit: — %
Build Thickness: — mm
Cone Taper Angle: — deg
Specific Volume: — dm3/kg
Gross Envelope Volume: — dm3
Tube Volume Displaced: — dm3

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.

Cone Package Density, Volume & Dye Penetration Margin — free, with the formula and a worked example, at Textile School.