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

The single sided hip sprocket

The single sided hip sprocket
Der einseitige Grataufschiebling

This task model for the single sided hip sprocket presented some new techniques for developing the transition surface triangle of the sprocket hip rafters at the main pitch hip rafter. The right side hip rafter has a lower left edge that's not edge beveled, with the surface plane intersection edge beveled and the standard hip rafter edge bevel above the pitch break of the sprocket rafter plane.   It also has the left sprocket hip rafter with a rafter claw at the intersection of the main hip rafter.

Base drawing of the task model in ground view.

Fully developed drawing for the task model. Well almost. I left out some lines for clarity.

Drawing showing the roof planes of the pitch break for the sprocket rafters.

Drawing with the transition base triangle developed from the foot of the main hip rafter and the transition  surface triangle developed for the intersection of the hip rafter at the pitch break.

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

Valley Sleeper on oblique adjacent roof

Valley Sleeper on oblique adjacent roof
Der schräge Anbau auf Kehlbohlen

This task model was challenging. Keeping track of the geometric lines to develop the valley sleeper rafter lines on the roof surface was confusing. However, I just needed to remember to draw perpendicular lines to the valley rafter in ground plan to the valley rafter on the roof surface plane to develop the correct valley sleeper plane lines. The witches cut is develop two different ways in the task model, by using two different elevation line heights.

Basic ground plan for the Valley Sleeper on oblique adjacent roof.

Drawing with the roof surface plane developed and some of the valley lines on the roof surface plane.

Zoomed in view of the valley lines, including the hidden bottom edge of the valley sleeper on the roof surface plane.

Drawing with the valley sleeper bird mouths lines developed.

Witches cut lines for the ground view of the valley sleeper rafters.

Witches cut lines for the valley sleeper rafters on the roof surface plane.

Method #two for developing the witches cut lines  and the lines for the valley rafter bevel on the roof surface at the peak of the valley sleeper rafters.

Checking my drawing with the 3D valley sleeper rafters.

Roof Planes.

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