BIZOMAT MAKEOS · Quality
Taper and Angle Gauges with Discs
What angle or taper do these two discs set, or where must they be placed for a required taper?
Angle and taper per foot set by two discs at a centre distance, the centre distance for a required angle or taper (on the centre-line or from one side), and the disc size for a given angle, using the handbook’s disc gauge rules.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Calculate | choice | What to calculate. |
| Large disc diameter | in | Diameter of the larger disc. |
| Small disc diameter | in | Diameter of the smaller disc. |
| Centre distance | in | Distance between disc centres. |
| Included angle | ° | Required included angle. |
| Taper per foot (on diameter) | in/ft | Required taper per foot (change in diameter over 12 in), measured on the centre-line or from one side as selected. |
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: Calculate
- What it is
- What to work out from the discs: the angle and taper they set, the centre distance needed for a taper or an angle, or the large disc size needed to touch a small one at an angle.
- Units and format
- Choose one of 5 options from the list: Angle and taper from D, d and C; Centre distance for a taper per foot (centre-line); Centre distance for an angle; Centre distance for a taper measured from one side; Large disc to touch a small disc at an angle.
- Example
- The form opens with “Angle and taper from D, d and C” selected as a worked example. Choose the option that matches your case.
- Get it right
- Each mode reads only some inputs: the angle modes ignore taper per foot, the taper modes ignore the angle.
What this means: Large disc diameter
- What it is
- The diameter of the larger of the two discs set between the gauge’s straight edges.
- Units and format
- Enter a number in in: inches. The form accepts 0.000001 in to 10000 in. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.5 in as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Not used when calculating the large disc size, which the tool then works out.
What this means: Small disc diameter
- What it is
- The diameter of the smaller of the two discs set between the gauge’s straight edges.
- Units and format
- Enter a number in in: inches. The form accepts 0.000001 in to 10000 in. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 in as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure the actual disc; size errors change the angle directly.
What this means: Centre distance
- What it is
- The distance between the centres of the two discs, as set with gauge blocks. It is an input only when finding the angle from the discs.
- Units and format
- Enter a number in in: inches. The form accepts 0.000001 in to 100000 in. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 in as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- In angle mode, a longer centre distance gives a smaller angle and taper.
- Get it right
- Measure centre to centre, not edge to edge. In the other modes the tool calculates or ignores it.
What this means: Included angle
- What it is
- The required included angle between the two straight edges touching the discs, used when finding a centre distance or a large disc size for an angle.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0.001° to 179°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Give the full included angle, not the angle of one side to the centre line.
What this means: Taper per foot (on diameter)
- What it is
- The required taper as change in diameter over 12 inches of length, either about the centre line or measured from one side, depending on the mode.
- Units and format
- Enter a number in in/ft: in/ft. The form accepts 0.0001 in/ft to 1000 in/ft. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.75 in/ft as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Taper per foot is on diameter, not per side. Convert a metric taper ratio to inches per foot first.
Method and formulas
- K = (D − d) ÷ 2C; included angle = 2 arcsin K; taper per foot = 24K ÷ √(1 − K²); from one side T = 24K √(1 − K²) ÷ (1 − 2K²).
- Centre distance for taper T: C = (D − d)/2 × √(1 + (T/24)²) ÷ (T/24); for an angle: C = (D − d) ÷ 2 sin(α/2).
- Centre distance for a taper from one side: C = (D − d) ÷ √(2 − 2 ÷ √(1 + (T/12)²)). Disc to touch at an angle: D = d (1 + sin(α/2)) ÷ (1 − sin(α/2)).
- Example (handbook case): 1.5 and 1 in discs at 5 in give 5.732° and 1.2015 in/ft.
Limitations
- Inch units with taper per foot as in the handbook rules; convert metric tapers to the same basis.
- Discs must be round and of known diameter.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Set up a disc gauge for checking tapers
- Find the taper given by a disc set-up
- Size a disc to contact a reference disc at an angle
Who it is for
- Quality inspectors
- Toolmakers
- Metrology technicians
What you get
- Included angle
- Taper per foot (centre-line and from one side)
- Centre distance or disc diameter
Interpreting the result
- Use gauge blocks between disc centres or a sine bar to set the centre distance accurately.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 684–685. Topic reference; no source tables or recommended settings are reproduced.
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