P3 Timber Framing Angle

Timber Framing Angle: P3
P3 = Clip angle on the bottom of the purlin for the Hip or Valley rafter housing seat. Claw angle, purlin lip cut angle.

P3 = arctan (cos D x sin R1 x cos R1 ÷ cos S)

P3 = arctan (cos D x sin R1 x cos R1 ÷ cos S)
P3 = arccos( sin ( R3 ) ÷ sin ( P2 ))
P3 = arctan (tan C5 x cos P2)

P3 = arctan (cos(plan angle) x sin(hip rafter slope angle) x cos(hip rafter slope angle) ÷ cos(common rafte slope angle))
P3 = arccos( sin ( Saw Miter Angle on upper shoulder of Hip-Valley ) ÷ sin ( Jack Rafter Side Cut Angle ))
P3 = arctan (tan (Backing Angle) x cos (Jack Rafter Side Cut Angle))
Purlin Lip Cut Angle = arctan( tan (Hip Rafter Backing Angle) * cos( Jack Rafter Side Cut 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.