ORIGINAL GEOMETRY EXAMPLE
Ø40 → Ø30 mm over 100 mm
C = 10/100 = 1:10. The radius changes by 5 mm, so tan β = 5/100: β ≈ 2.862° and α ≈ 5.725°. Setting 5.725° relative to the spindle axis would produce the wrong taper.
Use large diameter D, small diameter d and axial taper length L, all in the same unit. The compound-rest setting relative to the spindle axis is the half-angle β, not the full included angle α.
| Quantity | Relationship |
|---|---|
| Taper ratio | C = (D − d) / L = 1 : x; x = L / (D − d) |
| Half-angle | β = arctan((D − d) / (2L)) |
| Included angle | α = 2β |