DD Timber Framing Angle

Timber Framing Angle: DD or D
DD = Main or Adjacent side Plan Angle. Saw Blade Bevel Angle to cut along the plumb lines on a Jack Rafter or Hip Rafter.
DD = Main Side Plan Angle
D = Adjacent Side Plan Angle
SS = Main Side Common Rafter Slope Angle
S = Adjacent Side Common Rafter Slope Angle

DD = arctan (tan S ÷ tan SS)
D = arctan (tan SS ÷ tan S)

DD = arctan (cos SS ÷ tan P2)
DD = arctan (cos SS x tan 90 - P2)
DD = arccos (sin P2 ÷ cos R1)
DD = arccos (cos 90 - P2 ÷ cos R1)
DD = arccos (sin C5 ÷ sin SS)
DD = arcsin (tan R1 ÷ tan SS)
DD = arctan (sin R1 ÷ tan C5)
DD = arcsin (cos C5 x cos P2)
DD = arcsin (cos C5 x sin 90 - P2)

DD = arctan (cos Common Rafter Pitch Angle ÷ tan Jack Rafter Side Cut Angle)
DD = arctan (cos Common Rafter Pitch Angle x tan Sheathing Angle)
DD = arccos (sin Jack Rafter Side Cut Angle ÷ cos Hip-Valley Pitch Angle)
DD = arccos (cos Sheathing Angle ÷ cos Hip-Valley Pitch Angle)
DD = arccos (sin Backing Angle ÷ sin Common Rafter Pitch Angle)
DD = arcsin (tan Hip-Valley Pitch Angle ÷ tan Common Rafter Pitch Angle)
DD = arctan (sin Hip-Valley Pitch Angle ÷ tan Backing Angle)
DD = arcsin (cos Backing Angle x cos Jack Rafter Side Cut Angle)
DD = arcsin (cos Backing Angle x sin Sheathing Angle)

The Hip-Valley Roof Ratios Angle Formulas were developed by Joe Bartok.

The Timber Framing Hawkindale Angle Formulas were developed by Rees Hawkins Acheson from the Martindale Hip and Valley Roof Angles and Hawkindale angle drawings by Ed Levin of the Timber Framers Guild.

The Hawkindale angles were based on the book by Frank L. Martindale "Bevel Angles for Three Dimensional Connections" 1948 that was based on the book "Hip and Valley Design" by H. L. McKibben and L. E. Gray published in 1912.