FR Add-On Durability & Initial Loading Required

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 4 inputs are read from the form on every keystroke: Initial Add-On, Effective Minimum Add-On, Loss per Wash and Washes Claimed.
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 Add-On at Target Wash Count together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Retained per Wash, Share of Original Retained, Margin over Minimum at Target, Washes Until Minimum is Crossed, Half-Life of the Finish, Initial Add-On the Claim Requires, Shortfall in Loading and Chemical for the Required Loading — 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 Add-On at Target Wash Count 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 — Finish and Laundering. 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 Add-On at Target Wash Count in the dark results panel — that is the headline figure, expressed in % owf.
4. Check the supporting rows underneath (Retained per Wash, Share of Original Retained, Margin over Minimum at Target, Washes Until Minimum is Crossed, Half-Life of the Finish, Initial Add-On the Claim Requires, Shortfall in Loading and Chemical for the Required Loading) 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 Add-On at Target Wash Count before a trial is booked, so machine time and material in Finishing, Coating, Lamination & Functional Performance are committed against a calculated figure rather than an estimate.
• Costing and quotation — Add-On at Target Wash Count 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 Initial Add-On) shows how much of the gap in Add-On at Target Wash Count each variable explains.
• Teaching and study — the accepted ranges bracket normal Finishing, Coating, Lamination & Functional Performance practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.

Assumptions and limits

• A constant fractional loss is the simplest defensible model and it is not exactly what happens: real finishes lose a disproportionate amount in the first few washes as unbound and loosely held material leaves, then settle to a slower rate, so a rate fitted on a five-wash result will be pessimistic at fifty and one fitted on the tail will be optimistic early. Fit the rate across the range the claim covers. Add-on is a proxy for performance rather than performance itself; the specification is a flame test, and char length depends on fabric construction and areal weight as much as on the quantity of retained phosphorus, which is why two fabrics at the same residual add-on can behave differently. Laundering conditions dominate the loss rate and are part of the claim: temperature, alkalinity, chlorine and the presence of a tumble dry step all move it, and a domestic-wash figure does not transfer to industrial laundering, which is far more aggressive. The required loading this returns should be checked against what the fabric can physically carry and still meet its hand and tensile specification - above roughly a quarter of fabric weight most durable systems begin to stiffen the cloth beyond what the end use will accept, and the honest conclusion is often that the claim needs a different chemistry rather than more of this one.
• Every input is bounded to the range normal practice occupies (Initial Add-On 0.5 to 60 % owf, Effective Minimum Add-On 0.5 to 60 % owf and Loss per Wash 0.05 to 25 %, 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