45 Plan Angle Rake Wall Plates

Yesterday, I was building the rake walls for a corner fire place. I have studied rake wall plates rotated into the roof surface plane quite extensively. However, yesterday I just couldn't remember how to calculate the rake plate miter angles. So this post is a reference for me the next time I'm on the jobsite building rake walls rotated into the roof surface plane.

Here's a drawing of the corner fire place I was building. The roof slope angle was 26.56505°, 6:12, with a 135° eave angle for the wall rake plate rotated into the roof surface.

Saw Miter Angle for Common Rafter Pitch Rake Wall = arctan ( tan (Direction Of Saw Travel ) ÷ cos (Roof Slope ))

R2 = Saw Miter Angle for Common Rafter Pitch Rake Wall = arctan ( tan (22.5° ) ÷ cos (26.56505° )) = 24.84908°

R2 = Saw Blade Bevel Angle = arcsin ( sin (26.56505° ) × cos (22.5° )) = 24.40422°

Saw Miter Angle = 180° - Real Roof Surface Angle - Saw Miter Angle for Common Rafter Pitch Rake Wall
H2 = Saw Miter Angle = 180° - 138.18969 - 24.84908= 16.96123°
H2 = Saw Blade Bevel Angle = arcsin ( sin (26.56505° ) × cos (22.5° )) = 24.40422°

A1 = Saw Miter Angle = arctan ( cos (26.56° ) ÷ tan (67.5° )) = 20.32886°

A1 = Saw Blade Bevel Angle = arcsin ( sin (26.56° ) × cos (22.5° )) = 24.3996°

Saw Miter Angle = 180° - Real Roof Surface Angle - Saw Miter Angle for Common Rafter Pitch Rake Wall

H1 = Saw Miter Angle = 180° - 131.81031 - 20.32886= 27.86083°

H1 = Saw Blade Bevel Angle = arcsin ( sin (26.56° ) × cos (67.5° )) = 9.85418° 

Hip Rake Wall Studs
Hip Rafter Pitch Angle = arctan( tan( Pitch Angle ) * sin( Plan Angle ))
Hip Rafter Backing Angle = arctan( sin( Hip Rafter Pitch Angle) ÷ tan( Plan Angle ) ) 
Hip Rafter Plumb Backing Angle = arctan( tan( Pitch Angle ) * cos( Plan Angle ))

Hip Rake Wall Pitch Angle = arctan( tan( Rafter Pitch Angle ) * sin( Working Angle ))
Hip Rake Wall Pitch Angle = arctan( tan( 26.56505.69 ) * sin( 45 )) = 19.47121°
Rake Stud Saw Miter Angle = Hip Rafter Plumb Backing Angle = 19.47121°
Rake Stud Saw Blade Bevel Angle = arctan(cos(Hip Rafter Plumb Backing Angle)* tan(Hip Rafter Pitch Angle))
Rake Stud Saw Blade Bevel Angle = arctan(cos(19.47121)* tan(19.47121)) = 18.4349°

Hip Rafter Rake Wall Calculator

Hip Rake Wall Calculator Plan A

Hip Rake Wall Calculator Plan B

Hip Rafter Wall Calculator Plan C