Timber Framing Angle: R3
R3 = Line traced on the top or bottom of unbacked hip rafter following the perpendicular plane of the purlin. The bevel angle at the foot of the hip rafter for square tail fascia.
HawkinDale Formula
- R3 = arctan (Sin S x Cos S x Cos D ÷ Sin R1)
Hip-Valley Roof Ratios Angle Formulas
- R3 = arctan( tan( P2 ) x cos (C5))
- R3 = arctan( cos( P2 ) x cos (C5))
- R3 = arccos( sin( P3 ) ÷ sin (C5))
- R3 = arctan( cos(C5) ÷ tan(90° - P2)
- R3 = arctan( cos (C5) x tan(P2))
- R3 = arcsin( cos( P3 ) x sin (P2)
- R3 = arctan(sin(roof slope angle) x cos(roof slope angle) x cos(plan angle) ÷ sin(hip rafter slope angle)
- R3 = arctan(tan(jack rafter sidecut angle) x cos(hip rafter backing angle)
- R3 = arccos(sin(purlin lip cut angle) ÷ sin(hip rafter backing angle)
- R3 = arctan( cos(hip rafter backing angle) ÷ tan(90° - jack rafter side cut angle)
- R3 = arctan( cos ( Hip Rafter Backing Angle ) x tan( Jack Rafter Side Cut Angle ))
- R3 = arcsin( cos(Purlin Lip Cut Angle) x sin ( 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.