Size Box Concentration & Stock Make-Up

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: Yarn Count, Ends in the Sheet, Sizing Speed, Size Add-On, Wet Pick-Up, Cooked Stock Concentration and Size Box Volume.
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 Required Box Concentration together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Yarn per Metre per End, Sheet per Metre, Warp Throughput, Dry Size Consumed, Liquor Carried Out, Cooked Stock Required, Dilution Water Required, Stock to Water Ratio, Box Turnover Time and Size per Tonne of Warp — 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 Required Box Concentration 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 — Warp Sheet and Size. 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 Required Box Concentration in the dark results panel — that is the headline figure, expressed in %.
4. Check the supporting rows underneath (Yarn per Metre per End, Sheet per Metre, Warp Throughput, Dry Size Consumed, Liquor Carried Out, Cooked Stock Required, Dilution Water Required, Stock to Water Ratio, Box Turnover Time and Size per Tonne of Warp) 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 Required Box Concentration before a trial is booked, so machine time and material in Warping, Sizing, Weaving & Fabric Formation Control are committed against a calculated figure rather than an estimate.
• Costing and quotation — Required Box Concentration 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 Yarn Count) shows how much of the gap in Required Box Concentration each variable explains.
• Teaching and study — the accepted ranges bracket normal Warping, Sizing, Weaving & Fabric Formation Control practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.

Assumptions and limits

• Wet pick-up is taken as litres per kilogram of yarn on the assumption that the size liquor is close enough to water in density for the two to be interchangeable, which holds at ordinary concentrations and drifts at high solids or with heavy filler loadings. The add-on this delivers is the add-on at the squeeze rolls, not the add-on on the beam: some size is lost at the drying cylinders as the sheet separates, and a little is carried back at the split rods, so the beam figure is usually a fraction of a point below what the box arithmetic predicts. Box turnover time is worth watching as much as concentration; a long turnover means size sitting hot for hours, and starch that has been held at temperature loses viscosity and film strength in a way that no addition of solids recovers. Where the turnover exceeds an hour or two the answer is a smaller box or a higher speed rather than a stronger cook. The concentration derived here assumes the box is at steady state with a constant feed; on start-up and after a stop the box is at whatever it drifted to, and the first hundred metres of warp are sized to a recipe nobody wrote.
• Every input is bounded to the range normal practice occupies (Yarn Count 4 to 120 Ne, Ends in the Sheet 100 to 20000 nos and Sizing Speed 5 to 150 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.

Questions people ask