Skewed Rafter Footprint & Stereotomic View

Steps to geometrically develop the Trapezoidal Ground Plan Skewed Rafter on page 52 in "Traité Théorique et Pratique de Charpente" by Louis Mazerolle.


Step 1:
Develop the point PT, swing an arc with center point K and radius equal to KZ. This is the rise of the principal rafters. Draw a line from PT to AC. The angle K-PT-AC is the plane tilt of the skewed rafter (8.68257°). Draw a line thru GC, perpendicular to Q - G to K. Swing an arc from center point AC with radius equal to AC-PT, thru point SP. Draw a line from SP to G, to develop the triangle that gives us the miter angle at the skewed rafter foot.

The dark brown triangle is the plane tilt triangle, the red triangle is the horizontal plane rotation of the the tilted plane, the tan triangle is the miter angle at the skewed rafter foot. The green triangle is just part of a tetrahedron and not significant to the skewed rafter miter or bevel angles. 

Then draw some horizontal trace lines thru g1, g2, g3 and g4. Transfer the lines g1-g2 to the stereotomic view of the skewed rafter and then the lines g1-g4, g2-g3. Then draw the sides of the skewed rafter at the skewed rafter angle (44.33393°).

Here's a link to the Google SketchUp file.

Trapezoidal_Timber_Footprint.skp