Patrick Moore's Historical Carpentry Website
The first time I dimensioned the angle at this location I thought I had the wrong angular dimension. However, after using the trigonometric formula for rotating vertical planes the angular dimension is correct. This is a new angle for me. The notch in the common rafter joist is the angle of the roof slope, 33.69007° in these drawings. Rotating the vertical plane by 45°, or the plan angle results in a vertical plane angle of 43.31386°. This would have been drawn out using traditional layout geometry by the French carpenters and they wouldn't have cared what the actual angle was. As long as the geometry was correct. However, this angle is not present in the Timber Framing Angles.
Maybe, we could call it R8?
Seat cut layout on horizontal timber for purlin rafter following the hip rafter run line.
Timber Framing List of Angles
arctan(tan(33.69007°) ÷ cos(45.00°) = 43.31386°
Geometric development for the notch in the hip rafter run line joist.
Joist with notch for Purlin Plates.
Purlin Plates installed.
The typical purlin rafter angles.
Added some jack rafters with a claw to position the hip rafter.
The rotated purlin wind braces can be drawn out on the roof surface using the fold down or draw down layout technique.
The overlay rafters in position.