P4 Timber Framing Angle

Timber Framing Angle: P4
P4 = Square Cut Layout Angle on the Jack Purlin. The angle of the square end of the tenon and its square shoulder on the long (uphill) side of a jack purlin as seen on the top (roof) surface of the purlin. This angle is also called the clip angle down the nose. The angle P4 is used with A8 on the hip rafter for the jack purlin mortise.

P4 = P2 - arctan (tan R2 x tan C5 x cos C5)

P4 = P2 - arctan (tan R2 x tan C5 x cos C5)
P4 = P2 - arctan (tan R2 x sin C5)
P4 = arctan (tan C1 x cos P1)

P4 = Jack Rafter Side Cut Angle - arctan(tan(Hip Rafter Purlin Housing Angle) x tan(Hip Rafter Backing Angle) x cos(Hip Rafter Backing Angle))
P4 = arctan (tan Hip Rafter Purlin Housing Angle Saw Blade Bevel Angle x cos Purlin Saw Blade Bevel Angle)
P4 = Jack Rafter Side Cut Angle - arctan(tan(Hip Rafter Purlin Housing Angle) x sin(Hip Rafter 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.