Tailstock Setover for Taper Turning
The lathe tailstock offset to turn a taper between centers: S = OAL x (D - d) / (2 L). The step people miss: the setover scales with the OVERALL length between centers, not the taper length, because the whole part pivots about the headstock center. A 12 in part with a 1.500-to-1.000 in taper over 8 in needs 0.375 in of setover; if the taper ran the full length it would be just (D - d)/2 = 0.250 in. Offset the tailstock away from the tool to put the small end at the tailstock. Shallow tapers only -- the method swings the center holes off axis, so steep tapers want a taper attachment or the compound. A setup aid; check the first part.
Formula and source
S = OAL x (D - d) / (2 L); per-inch setover = (D - d) / (2 L). When L = OAL it reduces to S = (D - d) / 2.
Lathe tailstock setover for taper turning between centers - first-principles as in Machinery's Handbook (Industrial Press), by name; public domain.
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