and Jack Rafter Side Cut Angle Models
Tetrahedra extracted from the Hip Roof
illustrating the Jack Rafter Side Cut Angles
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
Main Slope = 10/12 Adjoining Slope = 7/12
Corner Angle measured between Eaves in Plan View = 90°
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
Juxtaposed Tetrahedra relating the
Hip Side Cut Angle at the Hip Peak (R4P)
the Backing Angle (C5), and the Hip Slope Angle (R1)
tan R4P = tan C5 ÷ tan R1
Main Slope = 10/12 Adjoining Slope = 7/12
Corner Angle measured between Eaves in Plan View = 90°
Juxtaposed Tetrahedra extracted from the
Post Type Model of the Hip Rafter Side Cut Angles
Development of the juxtaposed Tetrahedra extracted
from the Post Type Model of the Hip Rafter Side Cut Angles
(Angular Scale)
Juxtaposed Tetrahedra ... Triangles of Common Slope and P6
Juxtaposed Tetrahedra ... Triangles of Backing Angle
Juxtaposed Tetrahedra ... Triangle of Hip Side Cut Angle at the Hip Peak
Juxtaposed Tetrahedra and the Triangles of Hip Slope
... Plumb Section Plane taken through the line of the Hip Run
Application of Juxtaposed Tetrahedra
... Square Beam intersected by Hip Rafter
Main Slope = 12/12 Adjoining Slope = 12/12
Corner Angle measured between Eaves in Plan View = 140°
Model of Nonagonal Footprint Pyramid
Developments of the Juxtaposed Tetrahedra
Development of the Beam
Model of Beam ... Oblique View
Model of Beam ... View from Hip Rafter Foot
Hip Rafter intersects Beam ... View of Upper Surfaces (Roof Planes)
Hip Rafter intersects Beam ... View of Side Faces
Tetrahedron representing Roof Surface Angles
juxtaposed with Model of Hip Rafter intersects Beam
Tetrahedra modeling all angles
juxtaposed with Model of Hip Rafter intersects Beam
