There are several methods of turning a taper on a lathe: the
compound slide method, the offset tailstock method,
the taper attachment method, the use of a form tool, and
the use of a tracer or CNC lathe. Each method has its advan-
Both internal and external short, steep tapers can be turned on
a lathe by hand feeding the compound slide (Figure I-347).
The swivel base of the compound is divided in to degrees.
When the compound slide is in line with the ways of the
lathe, the 0-degree line will align with the index line on the
cross slide (Figure I-348). When the compound is swiveled
off the index, which is parallel to the centerline of the lathe,
a direct reading may be taken for the half-angle or angle to
the centerline of the machined part (Figure I-349). When a
taper is machined off the lathe centerline, its included angle
will be twice the angle that is set on the compound. Not all
lathes are indexed in this manner.
When the compound slide is aligned with the axis of
the cross slide and swiveled off the index in either direction,
an angle is directly read off the cross-slide centerline
(Figure I-350). Because the lathe centerline is 90 degrees
from the cross-slide centerline, the reading on the lathe
centerline index is the complementary angle. So, if the
compound is set off the axis of the cross slide degrees,
the lathe centerline index reading is
degrees, as seen in Figure I-350.
Tapers of any angle may be cut by this method, but the
length is limited to the stroke of the compound slide. Since
tapers are often given in tpf, it is sometimes convenient
to consult a tpf-to-angle conversion table, like Table I-8.
A more complete table may be found in Machinery’s
If a more precise conversion is desired, the following
formula may be used to find the included angle: Divide the
taper in inches per foot by 24, find the angle that corresponds
to the quotient in a table of tangents, and double this
angle. If the angle with centerline is desired, do not double
The angle of this tangent is 8 degrees 18 minutes, and the
included angle is twice this, or 16 degrees 36 minutes.
When either an internal or external taper is turned by
any method on a lathe, the cutting tool must be on the exact
centerline of the lathe. If the tool is either too high or too
low, the taper will not correspond to any calculations and
will be in error.