R5 Timber Framing Angle

Timber Framing Angle: R5
R5 = Hip-Valley Rafter ridge or plumb header miter housing angle following the bottom of the hip-valley rafter.

R5 = arctan (tan R1 x Cos D)

R5 = arctan( tan( R1 ) x cos (D))
R5 = arcsin( sin( R1 ) x cos (R4))
R5 = arctan( sin( A5 ) ÷ tan (R4))

R5 = arctan( tan( hip rafter slope angle ) x cos (plan angle))
R5 = arcsin( sin( hip rafter slope angle ) x cos ( hip rafter side cut angle))
R5 = arctan( sin( saw blade bevel angle on the side of the housing miter angle) ÷ tan (hip 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.