Timber Framing Angle: R2
R2 = Hip-Valley Rafter Purlin Housing Miter Angle on the side of hip rafter perpendicular to roof surface plane. Also, the Hip rafter square tail fascia miter angle. Hexenschnitt, the Witches Cut.
HawkinDale Formula
- R2 = arctan (sin S x cos S x cos D ÷ tan D)
Hip-Valley Roof Ratios Angle Formulas
- R2 = 90° - (arctan(sin(DD) x tan(90° - SS) + R1)
- R2 = 90° - (arctan(cos(D) x tan(90° - SS) + R1)
- R2 = 90° - arctan(sin(plan angle) x tan(purlin rotation angle - roof slope angle) + hip slope 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.