BIZOMAT MAKEOS · Geometry
Compound Angle
What true compound angle results from tilts in two perpendicular planes?
Combine two angles measured in perpendicular planes into the true compound angle and its direction, for compound sine plates, fixtures and hoppers.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Tilt angle in the first plane | ° | Slope of the surface measured in the first vertical plane (e.g. seen from the front). |
| Tilt angle in the perpendicular plane | ° | Slope of the same surface measured in the perpendicular vertical plane (e.g. seen from the side). |
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: Tilt angle in the first plane
- What it is
- The slope of the surface as it appears in a first vertical plane, for example the angle seen from the front view, measured from horizontal.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0° to 89.999°. 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
- Both angles must be slopes of the same flat surface seen in two vertical planes at 90° to each other.
What this means: Tilt angle in the perpendicular plane
- What it is
- The slope of the same surface as it appears in the vertical plane at right angles to the first one, for example the angle seen from the side view.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0° to 89.999°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure from horizontal, like the first angle; an angle measured from vertical gives a wrong result.
Method and formulas
- tan C = √(tan²A + tan²B), where A and B are the slopes seen in two perpendicular planes.
- Direction of the steepest slope from the first plane: tan R = tan B ÷ tan A.
- Example: slopes of 20° and 30° combine to a true angle of 34.314°, 57.772° from the first plane.
Limitations
- Both angles must be apparent slopes of one plane surface, measured in vertical planes at right angles.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Set work on a compound sine plate
- Find the true slope of a surface tilted in two directions
- Check hopper and chute valley angles
Who it is for
- Toolmakers
- Machinists
- Design engineers
What you get
- True compound angle
- Direction of steepest slope
- Equivalent single-plane setting
Interpreting the result
- Set a single-axis sine plate to the compound angle after rotating the part by the direction angle.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 119–121. Topic reference; no source tables or recommended settings are reproduced.
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