Spunbond Spinline Draw-Down & Aerodynamic Drag

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: Throughput per Hole, Target Filament Denier, Capillary Diameter, Polymer Density, Air Velocity, Air Density, Skin Friction Coefficient and Effective Drag Length.
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 Draw-Down Ratio together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Mass per Metre of Filament, Extrusion Velocity, Final Filament Velocity, Final Filament Diameter, Slip Velocity, Slip as Share of Air Speed, Drag per Metre of Filament, Total Drag Force, Spinline Stress and Throughput per Hole — 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

The tool loads with this case already solved — the Draw-Down Ratio shown above is its answer. Change one value and the difference from this baseline is the sensitivity of the result to that variable.

How to use it

1. Work through the input groups in order — Spinneret & Polymer and Aspirator Air. 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 Draw-Down Ratio in the dark results panel — that is the headline figure, expressed in x.
4. Check the supporting rows underneath (Mass per Metre of Filament, Extrusion Velocity, Final Filament Velocity, Final Filament Diameter, Slip Velocity, Slip as Share of Air Speed, Drag per Metre of Filament, Total Drag Force, Spinline Stress and Throughput per Hole) 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 Draw-Down Ratio before a trial is booked, so machine time and material in Nonwovens, Filtration, Hygiene & Technical Webs are committed against a calculated figure rather than an estimate.
• Costing and quotation — Draw-Down Ratio 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 Throughput per Hole) shows how much of the gap in Draw-Down Ratio each variable explains.
• Teaching and study — the accepted ranges bracket normal Nonwovens, Filtration, Hygiene & Technical Webs practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.

Assumptions and limits

• This is a lumped balance at the end of the spinline, not a solution of the coupled momentum, energy and crystallisation equations that actually govern it: the real filament accelerates, cools and crystallises together, the drag coefficient varies along its length with local Reynolds number, and stress-induced crystallisation eventually arrests the draw entirely. Treat the stress figure as an order-of-magnitude check on whether the aspirator can plausibly deliver the draw-down being asked of it, not as a design value. Final velocity is derived from mass conservation and the target denier, which means it is the velocity the process MUST reach to make that denier rather than a prediction that it will; where the computed drag looks small against the stress required, the honest reading is that the denier is not achievable at that air setting. The skin friction coefficient is the least certain input and depends strongly on filament Reynolds number and on whether neighbouring filaments are shielding each other, which they are in any real spinneret. Nothing here treats filament-to-filament interaction, drag-induced whipping instability, or the quench that sets the crystalline structure and therefore the tenacity of the finished web.
• Every input is bounded to the range normal practice occupies (Throughput per Hole 0.02 to 5 g/hole/min, Target Filament Denier 0.3 to 20 dpf and Capillary Diameter 0.1 to 2 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.

Questions people ask