Main Slope = 10/12 Adjoining Slope = 7/12
Corner Angle measured between Eaves in Plan View = 90°
Wireframe Sketckes of Tetrahedra modeling the
backed and unbacked Upper Shoulder of a Hip Rafter
Developments of the Tetrahedra
modeling the Fundamental Roof Angles
Tetrahedra modeling the Fundamental Hip Roof Angles
Juxtaposed Tetrahedra in position on Plan Angles
Wireframe Sketch of Post-Type Model
superimposed on the Juxtaposed Tetrahedra
Development of Post Type Model
Oblique View of the Post Type Model
Tetrahedron relating the Hip Side Cut Angle at the Hip Peak (R4P)
the Backing Angle (C5), and the Jack Rafter Side Cut Angle (P2)
tan R4P = tan P2 ÷ cos C5
Comparison of nested Tetrahedra (right)
extracted from the Post Type Model (left)
Development of the Tetrahedron extracted from the
Post Type Model of the Hip Rafter Side Cut Angles
(Trigonometric Scale)
Nested Tetrahedra ... Triangles of Common Slope and P6
Nested Tetrahedra ... Triangle of Backing Angle
Nested Tetrahedra ... Triangle of Hip Side Cut Angle at the Hip Peak
Tetrahedron relating the Principal Purlin Housing Angle (P3)
the Backing Angle (C5), and the Jack Rafter Side Cut Angle (P2)
tan P3 = tan C5 × cos P2
Development of the Tetrahedron extracted from the
Post Type Model of the Hip Rafter Side Cut Angles
(Trigonometric Scale)
Nested Tetrahedra juxtaposed along the Triangle of Backing Angle
Upper Shoulder of unbacked Hip Rafter ... Triangle of R3
Nested Tetrahedra ... Triangle of P3
Proof of Formula for Angle P3
3D models ... Underpurlin intersects Valley Rafter
Main Slope = 16/12 Adjoining Slope = 12/12
Corner Angle measured between Eaves in Plan View = 90°
Valley Rafter viewed from 12/12 (Adjoining) Side
Valley Rafter viewed from 16/12 (Main) Side
Bottom View of intersecting Valley Rafter and Underpurlin
Bottom View of Valley Rafter, notched to accommodated the Underpurlin
Traces created on the Underpurlin by the intersecting Valley Rafter
