Taper Missing Diameter (Lathe Setup)
Cutting a taper to a spec: given the taper per foot, one known end diameter, and the length.
Example
You enter
- Known diameter (in) 1
- Which end is known large
- Taper per foot (in/ft) 0.6
- Length over taper L (in) 3
You get
- Missing end diameter 0.85 in
- Angle per side (compound set) 1.4321
Details, formula, and sources
The missing end diameter is known -/+ (TPF/12) x L. A 1.000 in large end at 0.600 in/ft over 3 in makes a 0.850 in small end (drops 0.050 in per inch of length); the compound angle per side = atan(TPF/24) = 1.432 deg, which depends only on the TPF so the same setting cuts the taper at any length. First-principles trigonometry; the tool nose radius and setup govern the finished part.
change = (TPF/12) x L; small end = known - change (large end = known + change); angle per side = atan(TPF/24); included = 2 x (angle per side).
Taper setup inverse - the missing end diameter and the compound angle from the taper per foot - first-principles trigonometry as in Machinery's Handbook (Industrial Press), by name; public domain.
Pure trigonometry, public.
Estimate. AHJ and licensed professional govern.
Field names used by the API: known_dia_in, known_end, taper_per_foot, length_in, missing_dia_in, angle_per_side_deg
- Missing diameter missing end = known -/+ (TPF/12) x L (subtract for the small end, add for the large)taper geometry
- Compound angle angle per side = atan(TPF/24), a function of TPF alonetaper geometry