Braid Extension, Diameter Change & the Neutral Angle

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: Braid Angle as Made, Diameter as Made, Length as Made and Braid Angle Under Load.
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 Extension together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Length Under Load, Diameter Under Load, Diameter Change, Length Ratio, Enclosed Volume Change, Geometric Limit of Extension, Neutral Angle and Distance from Neutral — 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 Extension 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 — As Braided and As Pulled. 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 Extension in the dark results panel — that is the headline figure, expressed in %.
4. Check the supporting rows underneath (Length Under Load, Diameter Under Load, Diameter Change, Length Ratio, Enclosed Volume Change, Geometric Limit of Extension, Neutral Angle and Distance from Neutral) 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 Extension before a trial is booked, so machine time and material in Narrow Fabrics, Tapes & 3D Weaving are committed against a calculated figure rather than an estimate.
• Costing and quotation — Extension 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 Braid Angle as Made) shows how much of the gap in Extension each variable explains.
• Teaching and study — the accepted ranges bracket normal Narrow Fabrics, Tapes & 3D Weaving practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.

Assumptions and limits

• The yarns are taken as inextensible, which is the assumption that makes all of this exact rather than approximate - and it is a good assumption for aramid, glass, carbon and steel, a fair one for polyester, and a poor one for a nylon or elastane braid where a real part of the extension is the yarn itself and this arithmetic will understate it. There is no jamming limit here: as the angle closes the yarns crowd together and at some construction-dependent angle they lock and the braid stops extending long before the geometric limit this tool reports, so treat that figure as the ceiling geometry allows rather than the extension a braid will give. Friction is absent too, so nothing here says what force is needed to reach a given angle, only what the braid looks like when it gets there - which is why the answer to a question like the 22 centimetre cord limit is a measurement under the stated load and this is the shape of the argument rather than the number. Diameter is over the braid: a braid on a mandrel cannot neck down past the mandrel and the geometry stops applying at that point, which is the case in overbraiding and the reason a jammed overbraid is a different problem from a jammed sleeve. The enclosed volume figure is the space inside the tube and not the yarn in it, which does not change.
• Every input is bounded to the range normal practice occupies (Braid Angle as Made 1 to 89 °, Diameter as Made 0.5 to 500 mm and Length as Made 1 to 100000 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