Ballnose Milling Scallop Height from Stepover

a ballnose of radius R stepping over by s leaves a scallop h = R - sqrt(R^2 - (s/2)^2), or the inverse for the stepover that holds a target scallop. A 0.5 in ballnose at 0.030 in stepover leaves 0.45 mil; double the stepover and the scallop quadruples (the s^2 law) - a tighter stepover buys a finer finish at the cost of cycle time. Theoretical flat-surface cusp, not Ra. A shop aid; the real finish depends on the tool, deflection, and slope.

scallop mode: h = R - sqrt(R^2 - (s/2)^2); stepover mode: s = 2 sqrt(R^2 - (R - h)^2); approx h ~ s^2/(8R).

The ballnose scallop (cusp) height geometry and its inverse, with the small-scallop approximation, as compiled in the CAM and mold-machining references, by name.

The ballnose scallop-height geometry is a public CAM/milling result in the standard machining references.

Estimate. AHJ and licensed professional govern.

Field names used by the API: r_in, mode, s_in, out_in

• Scallop geometry h = R - sqrt(R^2 - (s/2)^2) between parallel passes of a ballnose radius RCAM geometry
• s^2 scaling near the bottom h ~ s^2/(8R), so doubling the stepover quadruples the scallopscallop approximation
• Flat, geometric theoretical cusp on a flat surface; slope, deflection, and runout change the real finishscope of this tile