Compound mitre cuts are required when making many types of decorative wood projects. For example, compound mitres are used when installing crown moulding around the perimeter of a room, between a wall and ceiling. Compound mitre cuts are also used when making multi-sided bevelled planter boxes and gazebos. In most cases, a table of values is the simplest way to obtain these settings. For custom applications, compound mitre settings can be calculated in a few steps.
- Skill level:
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Things you need
- Carpenter's square
- Carpenter's bevel or similar angle measuring device
- Table saw
- Table saw mitre slide
- Scientific calculator
Determine the three dimensions -- drop, projection and slope -- involved in your wood project. The drop is total vertical distance, or the height of the piece. The projection is the total distance the piece of wood will project from a vertical line. The slope is the angle at which a piece of wood will descend from a horizontal plane lying along the top edge of the wood piece.
Determine the fourth dimension needed for these calculations, which is the flat mitre dimension. The flat mitre dimension is the angle at which a saw would be set if cutting a perpendicular cut along the edge of the wood board or moulding. For example, if cutting the mitres to make a square four-sided box, the flat mitre dimension would be 45 degrees for each edge of each board. In general, the flat mitre would be one-half of the total angle to be achieved when joining the two boards.
Apply the following equation to determine the mitre angle for the piece of wood: Mitre = ArcTan [ Tan [flat mitre] x projection / width]. Determine the angle setting for this miter with the scientific calculator. Set this miter angle on the table saw's miter gauge guide.
Apply the following equation to determine the bevel angle for the piece of wood: Bevel = ArcSin [sin [flat mitre] x drop / width]. Determine the angle setting for this bevel cut with the scientific calculator. Set the table saw's blade to this angle.
Remove the table saw's rip fence. Carefully cut each piece of wood needed for the project with the mitre saw slide gauge.
Test fit each piece of wood after every cut. Small adjustments can be made to either the bevel or the mitre angles to ensure a perfect fit for each piece.
Tips and warnings
- Always use caution when operating power equipment. Wear safety glasses and make sure to not wear loosefitting or baggy clothing, which can become entangled during the table saw's operation.
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