Cutting Room
Life is metres cut through a depth of a cloth. Abrasiveness scales it directly and ply height scales it too.
— m
Cut length between sharpenings on this cloth at this lay height
The reference life is a fitted number and the whole model hangs on it, so take it from the cutting room record on a known cloth at a known lay height rather than from a supplier figure - a blade is quoted under conditions no production room reproduces. Once fitted, the scaling is what the tool is for: it compares a change of cloth or lay height against the baseline reliably, and predicts an absolute life only as well as its anchor. Ply height is given a sub-linear exponent because the blade is doing work along its whole edge whatever the depth, and the marginal ply costs less than the first one; the exponent is nonetheless a fit, and a lay tall enough to deflect the blade behaves much worse than any power law predicts. Blade cost is almost always the smallest term here. The sharpening stops matter more, and the quality consequence matters most of all: a blade allowed to run past its interval does not stop cutting, it starts fusing thermoplastic plies, dragging the lay and cutting inaccurately, and the panels that result are found much later. Read the sharpening interval as a quality control, not a consumable schedule.
Straight-Knife Blade Life, Sharpening & Cost — free, with the formula and a worked example, at Textile School.