Filament Denier, Spinneret Hole Throughput & Spin Draw Ratio

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 6 inputs are read from the form on every keystroke: Polymer Throughput, Spinneret Holes, Take-Up Speed, Capillary Diameter, Melt Density at the Die and Solid Fibre 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 Denier per Filament together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Dtex per Filament, Total Yarn Denier, Solid Filament Diameter, Die Exit Velocity, Spin Draw Ratio, Capillary Wall Shear Rate, Throughput per Hole and Hole to Filament Diameter 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

The attenuation ratio of 11 against a spin draw ratio of 106 is the check that the two are consistent: area scales as diameter squared, and 11.04 squared is 122, against 106 once the density change from melt to solid is taken out. The spinline stretches the filament by two orders of magnitude in a metre of free air.

How to use it

1. Work through the input groups in order — Mass Balance and Capillary & Polymer. 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 Denier per Filament in the dark results panel — that is the headline figure, expressed in den.
4. Check the supporting rows underneath (Dtex per Filament, Total Yarn Denier, Solid Filament Diameter, Die Exit Velocity, Spin Draw Ratio, Capillary Wall Shear Rate, Throughput per Hole and Hole to Filament Diameter 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 Denier per Filament before a trial is booked, so machine time and material in Polymer Rheology & Synthetic Extrusion are committed against a calculated figure rather than an estimate.
• Costing and quotation — Denier per Filament 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 Polymer Throughput) shows how much of the gap in Denier per Filament each variable explains.
• Teaching and study — the accepted ranges bracket normal Polymer Rheology & Synthetic Extrusion 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

• Denier here is the nominal spun value from mass balance; the wound package will read slightly lower after any relaxation and slightly different again after drawing or texturing, so a measured skein count will not match this exactly. The filament diameter assumes a solid circular section - it is wrong for hollow, trilobal or other profiled spinnerets, where the same linear density corresponds to a larger circumscribed dimension. Die swell is not modelled: the extrudate expands on leaving the capillary before it attenuates, so the true maximum diameter exceeds the hole and the effective draw is greater than the ratio shown. The shear rate is the apparent Newtonian wall value and takes no account of entrance pressure losses, which for a short capillary can exceed the capillary loss itself.
• Every input is bounded to the range normal practice occupies (Polymer Throughput 0.5 to 3000 kg/h, Spinneret Holes 1 to 200000 and Take-Up Speed 50 to 8000 m/min, 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 1144 and ISO 2060 - linear density designation and determination, which define denier and dtex.
• ASTM D1907 - Linear Density of Yarn by the Skein Method, for verifying the computed denier on the wound product.
• ISO 11443 - Determination of the fluidity of plastics using capillary rheometers, the reference for the apparent shear rate used here.

Questions people ask