Shadow Lines and Witches Cut Plane

Task model

Canted Valley Rafter on Rectangular Ground Plan

Verkanteter Kehlsparren im Rechten Winkel Grund:

Lotrechten --> perpendicular
spitzwinkliges -->acute angled
verkanteter Kehlsparren auf spitzwinkligem Grund --> next task model
Canted Valley Rafter on Acute Angled Ground Plan

Interesting geometry from Bernd Kuppers book, on the Shadow Line Elevation Line, developed from the Light Source Direction, that's perpendicular to the roof surface. That develops the shadow line of the canted valley rafter and the shadow line of the outer edge of the canted valley rafter. Which in turn, develops the claw cutting line direction for the valley jack rafter lower claws. The witches planes for the canted valley rafter is also fairly easy, at this point in the book.  

The shadow line theories are similar to the French DP line. The shadow line of the valley is following the footprint of the valley rafter.

Roof Framing Geometry Proposition – Axioms  # 3:

The intersection of the DP Lines of two rafters define the line for the upper claw angle on the rafter.

Roof Framing Geometry Proposition – Axioms  # 4:

The intersection of the rafter DP Line and the hip rafter foot print line define the line for the lower claw angle on the rafter.

Roof Framing Geometry Proposition – Axioms # 9:
If the hip rafter foot print line is parallel to the jack rafter run line, then the lower claw line for the jack rafter is parallel to the jack rafter run line.

This Axiom will apply to roofs with an eave angle of 90°, with equal or unequal profile roof slope angles.

Verkanteter Gratsparren Axiom # 9

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