Taking the arctan of the result of the formula above returns the equivalent of the Common Rafter Pitch Angle.
This angle will vary with the Framing Point selected on the ellipse.
The Plan Angle is constant for a given pair of intercepting barrels. The purlins in the images are set with their wide faces tangent to the curve of the ellipse. To cut the compound angle from this face: The Saw Miter Angle formula is the same as the Jack Rafter Side Cut Angle formula. The same miter angle is required to cut a purlin intercepting a Valley rafter created by the given combination of Common Rafter Slope and Plan Angle. Saw Miter Angle = arctan (cos Common Rafter Pitch Angle ÷ tan Plan Angle) The formula for the Angle on the Purlin or Angle on the Stick is the same as the formula for the Sheathing Angle or Plywood Angle. The angle is the same as on a purlin intercepting a Valley rafter created by the given combination of Common Rafter Slope and Plan Angle. Angle on the Purlin = arctan (tan Plan Angle ÷ cos Common Rafter Pitch Angle) or Angle on the Purlin = 90° – Saw Miter Angle The Saw Blade Bevel Angle is the equivalent of the Backing Angle. The same blade bevel is required to cut a purlin intercepting a Valley rafter created by the given combination of Common Rafter Slope and Plan Angle. Saw Blade Bevel Angle = arcsin (sin Common Rafter Pitch Angle × cos Plan Angle) |