The Cost of Keeping a Working Edge: Stone Wear, Steel Loss, and the Price of One Sharp Hour for a Machete-Class Tool

A sharp edge is not free: each sharpening consumes a small amount of steel, a small amount of stone, and several minutes of a person's time. This paper adds those three costs together for a machete-class tool with a 500 mm edge, sharpened on three kinds of abrasive: a natural stone, a silicon carbide (carborundum) stone, and a diamond plate. A routine sharpening, modelled as a 0.08 mm setback of the apex, removes 46.87 mg of steel. Against a usable stone volume of 75 cubic centimetres, a natural stone lasts 178.6 routine sharpenings and a silicon carbide stone lasts 468.8, while a 50 micrometre diamond layer worn at 0.06 micrometres per sharpening lasts 833.3. Because six minutes of labour valued at 12 dollars per hour costs 1.20 dollars, far more than any stone's wear per sharpening, the total cost of one sharp working hour is nearly the same for all three abrasives: 0.52 dollars on natural stone, 0.49 dollars on silicon carbide, and 0.50 dollars on a diamond plate. The abrasive choice therefore matters much less than whether sharpening time itself is kept short. Repairing damage is a different matter. Steel removal grows with the square of the required setback, so a chip requiring a 1.0 mm setback removes 7.324 g of steel, equal to 156.2 routine sharpenings, and takes 91.6 minutes at the stated removal rate. The total repair cost reaches the 22 dollar replacement price of the tool at a chip depth of 0.99 mm on silicon carbide and 0.80 mm on natural stone. Beyond roughly one millimetre of damage, replacing the tool is cheaper than restoring its edge on a bench stone, under these assumptions.