R4 Timber Framing Angle

Timber Framing Angle: R4
R4 = Hip-Valley Rafter side cut bevel angle on top or bottom of an unbacked hip-valley rafter. Using a Saw Blade Bevel Angle set to the plan angle and cutting along the plumb line on the hip-valley rafter will produce angle R4 on the top and bottom of the unbacked hip rafter. Angle R4 is parallel to the common rafter run.
Use R4B for the hip rafter side cut angles at the foot of the hip rafter for eave angles greater than 90° with unequal roof slopes.

R4 = arctan (tan P2 ÷ cos C5)

R4 = arctan( cos R1 ÷ tan DD)
R4 = arctan( cos R1 x tan D)
R4 = arctan( sin P2 ÷ sin DD)
R4 = arctan( tan P2 ÷ cos C5)
R4 = arctan( tan 90 - DD x sin 90 - R1)

R4 = arctan( cos Hip-Vally Pitch Angle ÷ tan Plan Angle)
R4 = arctan( cos Hip-Vally Pitch Angle x tan Adjacent Plan Angle)
R4 = arctan( sin Jack Rafter Side Cut Angle ÷ sin Plan Angle)
R4 = arctan( tan Jack Rafter Side Cut Angle ÷ cos Backing Angle)
R4 = arctan( tan 90 - Plan Angle x sin 90 - Hip-Vally Pitch Angle)
Hip Rafter Side Cut Angle = arctan( cos( Hip Rafter Pitch Angle ) ÷ tan( Plan 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.