Edge Included Angle as a Design Choice: Cutting Force, Chipping Life, and a Test of the Claim That a Thinner Edge Is Always Better

The included angle of a cutting edge is often discussed as if smaller were simply better: a thinner edge cuts with less force, so the thinnest edge that can be ground is treated as the best edge. This paper tests that claim for a machete-class tool in mixed clearing work, by computing both sides of the trade. Cutting force falls as the angle narrows, from 49.8 N at an included angle of 60 degrees to 25.2 N at 15 degrees, following a stated wedging model. Chipping life, however, falls far faster: mean time to first chip is 3.0 hours at 20 degrees, 16.0 hours at 30 degrees, and 54.5 hours at 40 degrees, under a stated survival model in which the impact energy an edge can absorb grows with the square of its supporting wedge. When force and the downtime caused by chip repairs are combined into a daily output index, performance is not monotonic in angle. Output rises from 26.48 at 15 degrees to a maximum of 30.49 at 20 degrees, then falls steadily to 19.44 at 60 degrees. The thinnest edge considered is therefore not the best edge, even though it cuts with the least force: the claim that a thinner edge is always better does not survive the arithmetic. A sizing rule follows from the chipping side alone. To obtain a mean chip life of at least 40 working hours, the required included angle is 25 degrees in gentle work with rare hard contact, 40 degrees in mixed clearing work, and 60 degrees in harsh work with frequent hard contact, at which point no practical clearing edge fully satisfies the requirement and damage must simply be budgeted for.