BIZOMAT MAKEOS · Manufacturing
Taper Turning Set-Up (Taper per Foot, Half Angle, Tailstock Offset, Compound Setting)
For a taper of given end diameters and length, what taper per foot and angle is it, how far must I offset the tailstock, and should I use the compound slide instead?
Set-up of a lathe to turn a taper: the taper per unit length and per foot on diameter, the half angle and included angle from the tangent (as the trigonometric functions tool), the tailstock offset for turning between centres over the whole length of the work, and the compound slide setting, against the largest tailstock offset the lathe and centres allow.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Large diameter of the taper | mm | Diameter at the large end of the taper. |
| Small diameter of the taper | mm | Diameter at the small end. |
| Length of the taper | mm | Length of the tapered part along the axis. |
| Length of the work between centres | mm | Overall length of the work between the centre points (the offset method tapers the whole length). |
| Largest tailstock offset | mm | Largest set-over the tailstock and centre holes allow without damage. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Large diameter of the taper
- What it is
- The diameter at the large end of the taper, from the drawing.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the diameter at the end of the tapered portion, not the size of a shoulder beyond it.
What this means: Small diameter of the taper
- What it is
- The diameter at the small end of the taper, from the drawing.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It must be smaller than the large diameter.
What this means: Length of the taper
- What it is
- The length of the tapered portion, measured along the axis of the work between the large and small diameters.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 60 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A longer taper for the same diameters gives a smaller angle and a smaller tailstock offset.
- Get it right
- Measure along the axis, not along the sloping surface.
What this means: Length of the work between centres
- What it is
- The overall length of the work between the centre points. With the offset method the whole length between centres is tapered, so the offset depends on it.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 150 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The tailstock offset rises in proportion to the work length.
- Get it right
- Measure the full length between the centre hole points, not just the tapered part.
What this means: Largest tailstock offset
- What it is
- The largest tailstock set-over the lathe and the centre holes can take without damage, compared with the offset needed.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Take it from the lathe’s tailstock travel and your judgement of the centre holes.
Method and formulas
- Taper = (D − d) ÷ l on diameter; per foot = 12 × that.
- Half angle α = atan ((D − d) ÷ 2l) (as the trigonometric functions tool); included angle 2α; the compound slide is set to α.
- Tailstock offset = (D − d) ÷ 2 × L_w ÷ l.
- Example: 1 per foot, half angle 2.3859°; offset the tailstock 6.25 mm.
Limitations
- Offset method assumes the centres sit in the centre holes at the set-over; large offsets wear the centre holes.
- Taper attachments and CNC turning avoid both limits.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Set over the tailstock for a long gentle taper
- Set the compound for a short steep taper
- Convert a drawing taper to an angle
Who it is for
- Machinists
- Apprentices
- Toolmakers
What you get
- Taper per unit length and per foot
- Half and included angle
- Tailstock offset and compound setting
Interpreting the result
- The tailstock offset suits long gentle tapers; the compound suits short steep ones because its travel is short.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 95–114, 682–691. Topic reference; no source tables or recommended settings are reproduced.
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