Core-Spun Yarn Core Ratio, Sheath Cover & Stretch Potential

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 5 inputs are read from the form on every keystroke: Core Supply Linear Density, Core Draft, Core Fibre Density, Finished Yarn Linear Density and Yarn Bulk Density.
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 Core Ratio by Mass together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Core Inside the Yarn, Sheath Linear Density, Sheath Wall Thickness, Core Diameter, Yarn Diameter, Cover as a Share of Yarn Radius, Core Stretch Held in the Yarn and Sheath to Core Mass Ratio — 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

Seventy-two micrometres of sheath is thinner than a human hair, and that is the nominal figure with the core perfectly centred. Real core-spun yarn is never perfectly centred, which is why grin-through is a concentricity problem rather than a coverage problem, and why it appears at the ring frame rather than in the recipe.

How to use it

1. Work through the input groups in order — Core and Yarn. 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 Core Ratio by Mass in the dark results panel — that is the headline figure, expressed in %.
4. Check the supporting rows underneath (Core Inside the Yarn, Sheath Linear Density, Sheath Wall Thickness, Core Diameter, Yarn Diameter, Cover as a Share of Yarn Radius, Core Stretch Held in the Yarn and Sheath to Core Mass Ratio) 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 Core Ratio by Mass 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 — Core Ratio by Mass 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 Core Supply Linear Density) shows how much of the gap in Core Ratio by Mass 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

• Both strands are treated as solid circular sections, which is reasonable for the elastane monofilament and only nominal for the spun yarn - a real spun yarn is neither circular nor uniform along its length. The cover thickness is therefore a design figure for comparing constructions, not a measurable wall. Core concentricity is not modelled at all and is the dominant real-world variable: an eccentric core can reduce the local wall to near zero while every figure here is unchanged. The stretch potential shown is the core draft expressed as a percentage and represents the extension stored in the core, not the stretch the finished fabric will exhibit, which depends on the construction and on the finishing. Elastane linear density is nominal and drifts with package build as the feed tension changes.
• Every input is bounded to the range normal practice occupies (Core Supply Linear Density 1 to 100 tex, Core Draft 1 to 6 x and Core Fibre Density 0.8 to 2 g/cm3, 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

• ASTM D2731 - Elastic Properties of Elastomeric Yarns.
• ISO 2062 / ASTM D2256 - tensile properties of the finished yarn.
• ISO 1833 - quantitative analysis, the method that verifies the core ratio on the finished product.
• AATCC 66 - Wrinkle Recovery, and ASTM D3107 for stretch fabric properties the core produces.

Questions people ask