The Mandala roof (reciprocal roof)

Task model

The Mandala roof (reciprocal roof)

Das Mandaladach

Drawing a tangent line with a framing square is fairly easy. However, Google SketchUp doesn't have a tangent to circle line function like other CAD programs do. So, I had to use some math to establish the line tangent to the eye of the reciprocal roof.

Here's the math for drawing a line tangent to a circle.

Radius = 400

Center Radius = 50

arcsin(50 ÷ 400) = 7.180755°

Drawing the rest of the Mandala -- Reciprocal roof task model went fairly easy from the drawings and Bernd's instructions, even the witches cuts on the reciprocal rafter. However, I wasn't able to decipher the lines in the task model drawings for developing the seat for the intersection of the reciprocal rafters.

Update: I was able to establish the inclined rafter seat line from the drawings. See below.

I had to develop some drawings to develop the theory on how the geometric seat lines of the reciprocal rafters are established. In these drawings the" Intersecting Point of the top edges of the Reciprocal Rafters" in ground plan are the starting point for establishing the seat lines in ground plan. Then using the intersecting run dimensions of the the two rafters in profile, establishes the plumb heights of the rafters at the intersecting point. Then by drawing a level line from the lower rafter plumb height to the upper rafter plumb height establishes the seat line point for drawing the seat line of the reciprocal rafter.

Update: I was able to establish the inclined rafter seat line from the drawings from the book. 

Here's a drawing showing the ridge height line development for the seat lines.

You can also use this geometric development for drawing the seat lines in profile.

The Intersecting point of the Inclined Rafter & Hip Rafter develop the seat line on the Inclined Rafter.

I tested the seat line theory on a Pentagonal Reciprocal Roof and the theory works as well on this pentagonal roof.

Theory for seat line on Inclined rafter:

The Intersecting point of  the Inclined Rafter & Hip Rafter develop the seat line on the Inclined Rafter.

The new book on the ancient knowledge Roof Framing by Bernd Küppers