Formulas arise from the geometry #2

1980’s version of the hip rafter backing angle formula I used. It was developed from the book 

Full Length Roof Framer by A.F.J Riechers

One triangle at a time type of formula

Hip rafter backing angle = arctan( ((hip rafter thickness * 0.5) * sin(hip rafter slope angle)) / (hip rafter thickness * 0.5))

It wasn't very efficient, but at least it was correct for equal pitched roofs.

Roof framing is the Ph.D. of carpentry, it's apparent that  Marshall Gross never got his Ph.D. of carpentry.

I was thumbing through Marshall Gross's book "Roof Framing", 1984, and on page 135 he said to use the hip rafter slope angle as the hip rafter backing angle to cut the hip rafter edge bevels. Not only was the hip rafter backing angle wrong, his hip rafter backing depth on the side of the hip rafter was also incorrect. No way was he ever taught by a German Master carpenter. A German Master Carpenter would have taught him how to layout the backing angles correctly for any roof by using geometry that was developed centuries ago. Hip Rafter Backing Angle Formulas are developed from geometry, not from sketches of what you think are correct.

Hip Rafter Backing Angles for Edge Bevel Formulas