Thermosol Fixation Dose & Line Speed Limit

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 7 inputs are read from the form on every keystroke: Heated Oven Length, Line Speed, Fabric Heat-Up Time, Curing Temperature, Reference Temperature, Reference Time and Halving Interval.
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 Fixation Dose Delivered together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Total Dwell in Oven, Dwell at Temperature, Dwell Lost to Heat-Up, Temperature Factor, Equivalent Time at Reference, Dwell Required at this Temperature, Total Oven Time Required, Maximum Line Speed and Speed Margin — 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 Fixation Dose Delivered 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 — Oven & Line and Reference Point. 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 Fixation Dose Delivered in the dark results panel — that is the headline figure, expressed in %.
4. Check the supporting rows underneath (Total Dwell in Oven, Dwell at Temperature, Dwell Lost to Heat-Up, Temperature Factor, Equivalent Time at Reference, Dwell Required at this Temperature, Total Oven Time Required, Maximum Line Speed and Speed Margin) 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 Fixation Dose Delivered before a trial is booked, so machine time and material in Dyeing, Printing, Color Management & Chemical Control are committed against a calculated figure rather than an estimate.
• Costing and quotation — Fixation Dose Delivered 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 Heated Oven Length) shows how much of the gap in Fixation Dose Delivered each variable explains.
• Teaching and study — the accepted ranges bracket normal Dyeing, Printing, Color Management & Chemical Control practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.

Assumptions and limits

• The halving rule is an engineering approximation to Arrhenius behaviour and holds only across the working thermosol window of roughly 190 to 215 degrees; extrapolated far outside it the factor becomes meaningless, and above about 220 degrees polyester begins to change in ways that no amount of dwell compensates for. Curing temperature means the temperature of the cloth, which is not the air set point and not the controller reading - a heavy construction entering wet runs cooler than the zone it is in for longer than most operators allow, and the honest way to get this number is a temperature-recording device through the oven rather than off the panel. Heat-up time is treated as wholly unproductive, which is slightly pessimistic because some fixation occurs on the way up; the error is in the safe direction. The dose figure says whether fixation completes, not what shade results: migration, sublimation of the lighter disperse fractions and thermomigration of the fixed dye into finish films all move the shade at constant dose, which is why a line held at exactly the same dose by a different time-temperature pair can still need a shade correction.
• Every input is bounded to the range normal practice occupies (Heated Oven Length 1 to 80 m, Line Speed 1 to 200 m/min and Fabric Heat-Up Time 0 to 120 s, 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