Braid Extension, Diameter Change & the Neutral Angle

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.