P2 Timber Framing Angle

Timber Framing Angle: P2
P2 = Jack Rafter Side Cut Angle located on the uphill side of the jack rafter shoulder set in the surface of the roof.

P2 = arctan (cos S ÷ tan D)

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

P2 = arccos (sin Plan Angle ÷ cos Backing Angle)
P2 = arcsin (cos Plan Angle x cos Hip-Valley Pitch Angle)
P2 = arctan (cos Common Rafter Pitch Angle ÷ tan Plan Angle)
P2 = arctan (cos Common Rafter Pitch Angle x tan Adjacent Plan Angle)
P2 = arccos (sin Hip-Valley Pitch Angle ÷ sin Common Rafter Pitch Angle)
P2 = arcsin (tan Backing Angle ÷ tan Common Rafter Pitch Angle)
P2 = arctan (sin Backing Angle ÷ tan Hip-Valley Pitch Angle)
Jack Rafter Side Cut = arctan( cos( Pitch Angle ) ÷ tan( Plan Angle ))

Timber Framing Angle: 90 - P2
90 - P2 = Roof Sheathing Angle.

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

90 - P2 = arccos (cos Plan Angle x cos Hip-Valley Pitch Angle)
90 - P2 = arctan (tan Plan Angle ÷ cos Common Rafter Pitch Angle)
90 - P2 = arcsin (sin Plan Angle ÷ cos Backing Angle)
90 - P2 = arccos (tan Backing Angle ÷ tan Common Rafter Pitch Angle)
90 - P2 = arcsin (sin Hip-Valley Pitch Angle ÷ sin Common Rafter Pitch Angle)
90 - P2 = arctan (tan Hip-Valley Pitch Angle ÷ sin Backing 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.