Siro Spinning Strand Spacing, Convergence Angle & Twist Balance

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: Finished Yarn Linear Density, Strand Spacing at the Front Roller, Convergence Height, Yarn Twist and Strand 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 Convergence Angle together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Each Strand, Strand Diameter, Spacing to Strand Diameter, Twist about the Strand Axis, Twist Multiplier, Spinning Triangle Width, Ply Balance Index and Yarn Count — 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

Nearly nineteen degrees of convergence over a strand only a tenth of a millimetre thick: the two strands are held far apart relative to their own size, which is exactly what stops them merging into one and what gives the yarn its ply-like character.

How to use it

1. Work through the input groups in order — Strands & Geometry and Twist & Strand. 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 Convergence Angle in the dark results panel — that is the headline figure, expressed in deg.
4. Check the supporting rows underneath (Each Strand, Strand Diameter, Spacing to Strand Diameter, Twist about the Strand Axis, Twist Multiplier, Spinning Triangle Width, Ply Balance Index and Yarn Count) 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 Convergence Angle 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 — Convergence Angle 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 Finished Yarn Linear Density) shows how much of the gap in Convergence Angle 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

• The convergence geometry treats both strands as meeting at a single point in a plane, which is a good approximation for the angle and ignores the twist-driven spiralling that actually occurs above the convergence. Strand tex assumes the two rovings are equal, which is the normal arrangement but not the only one - deliberately unequal strands are used for effect yarns and this calculation does not cover them. Strand diameter uses the bulk density of the drafted strand, which is lower than the finished yarn density since the strand is untwisted at that point, so it is indicative rather than measured. The ply balance index is a comparative figure formed from twist and spacing, with no units and no absolute meaning.
• Every input is bounded to the range normal practice occupies (Finished Yarn Linear Density 5 to 200 tex, Strand Spacing at the Front Roller 2 to 20 mm and Convergence Height 5 to 60 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

• ASTM D1423 / ISO 2061 - twist determination on the finished yarn.
• ASTM D2256 - tensile properties, for comparing siro against true two-ply.
• ASTM D5647 - hairiness measurement, one of the main properties siro improves.

Questions people ask