Advanced Timber Framing by Steve Chappell

Advanced Timber Framing by Steve Chappell ."Exploring the Seven Planes of Compound Joinery"

I started reading through the book Advanced Timber Framing by Steve Chappell http://chappellsquare.com/product/advanced-timber-framing/ 

and will add notes to my roof framing geometry blog on concepts covered in the book.


First up is the valley rafter foot to principal rafter joinery. Steve takes you through the process of laying out the geometry on the valley rafter foot and discuses the working plane. This got me to thinking about all the roof framing angles rotated into different planes.

Rotated Angle = arctan(tan (of angle to be rotated) * cos( rotation angle))
or
Rotated Angle = arctan(tan (of angle to be rotated) * sin( rotation angle))

These examples use an 8:12 pitch and a plan angle of 45°

Common Rafter Angle rotated by the plan angle
Hip/Valley Rafter Angle = arctan(tan (common rafter angle ) * cos(rotation angle))
Hip/Valley Rafter Angle = arctan(tan (33.69007° ) * cos(45°)) = 25.2394°


Hip/Valley Rafter Angle rotated by the plan angle
Hip/Valley Housing Angle = arctan(tan (hip rafter angle ) * cos(rotation angle))
Hip/Valley Housing Angle = arctan(tan (25.2394° ) * cos(45°)) = 18.43495°


Hip/Valley Rafter Plumb Backing Angle rotated by the Hip/Valley Rafter Angle
Hip/Valley Backing Angle = arctan(tan (hip rafter angle ) * cos(hip rafter angle))
Hip/Valley Backing Angle = arctan(tan (25.2394° ) * cos(25.2394°)) = 23.09347°

Irregular Hip Roof Example
8:12 main pitch
10:12 adjacent pitch


Common Rafter Angle rotated by the plane rotation angle
Hip/Valley Rafter Angle = arctan(tan (common rafter angle ) * cos( plane rotation angle))
Hip/Valley Rafter Angle = arctan(tan (33.69007° ) * cos(38.65981°)) = 27.50055°


Hip Rafter Angle rotated by the plane rotation angle
Hip/Valley Housing Angle = arctan(tan (hip rafter angle ) * cos( plane rotation angle))
Hip/Valley Housing Angle = arctan(tan (27.50055° ) * cos(51.34019°)) = 18.01470°
or
Hip/Valley Housing Angle = arctan(tan (27.50055° ) * sin(38.65981°)) = 18.01470°


Hip Rafter Angle rotated by the plane rotation angle
Hip/Valley Housing Angle = arctan(tan (hip rafter angle ) * cos( plane rotation angle))
Hip/Valley Housing Angle = arctan(tan (27.50055° ) * cos(38.65981°)) = 22.12194°
or
Hip/Valley Housing Angle = arctan(tan (27.50055° ) * sin(51.34019°)) = 22.12194°

Hip/Valley Rafter Plumb Backing Angle rotated by the Hip/Valley Rafter Angle
Hip/Valley Backing Angle = arctan(tan (hip rafter angle ) * cos(hip rafter angle))
Hip/Valley Backing Angle = arctan(tan (22.60994° ) * cos(27.50055°)) = 20.27452°

Steve Chappell uses axioms to guide you thru the timber framing angles layout on the actual timbers. When I first looked at his drawing of the Bisected Foot Print Angle, I wondered why he didn't use the word plan angle. However, after reading through the book I realized he was using the adjacent plan angle to calculate some of the angles that were rotated into different planes. The BFA is worth exploring and seems to be the key to laying out the correct rotated angles on the timbers.

Steve does not use tetrahedrons in his book. Using a tetrahedron is just my way of checking the axioms based on a unit circle.

Can't wait to find the time to actually layout out the valley to principal rafter joinery on real timbers, following Steve's examples in his book.