Overview of the related Hip Side Cut Angle
and Jack Rafter Side Cut Angle Models


Overview of all Hip-Valley Side Cut Angle Models

Tetrahedra extracted from the Hip Roof
illustrating the Jack Rafter Side Cut Angles


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)

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)
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 ... Triangles of Common Slope and P6

Nested Tetrahedra ... Triangle of Backing Angle
Nested Tetrahedra ... Triangle of Backing Angle

Nested Tetrahedra ... Triangle of Hip Side Cut Angle at the Hip Peak
Nested Tetrahedra ... Triangle of Backing Angle


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

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)
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 Common Slope and P6

Juxtaposed Tetrahedra ... Triangles of Backing Angle
Juxtaposed Tetrahedra ... Triangles of Backing Angle

Juxtaposed Tetrahedra ... Triangle of Hip Side Cut Angle at the Hip Peak
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
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
Model of Nonagonal Footprint Pyramid

Developments of the Juxtaposed Tetrahedra
Developments of Juxtaposed Tetrahedra

Development of the Beam
Development of Square Beam intersected by Hip Rafter

Model of Beam ... Oblique View
Model of Beam ... Oblique View

Model of Beam ... View from Hip Rafter Foot
Model of Beam ... View from Hip Rafter Foot

Hip Rafter intersects Beam ... View of Upper Surfaces (Roof Planes)
Hip Rafter intersects Beam ... View of Upper Surfaces (Roof Planes)

Hip Rafter intersects Beam ... View of Side Faces
Hip Rafter intersects Beam ... View of Side Faces

Tetrahedron representing Roof Surface Angles
juxtaposed with Model of Hip Rafter intersects Beam

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

Tetrahedra modeling all angles juxtaposed with Model of Hip Rafter intersects Beam

Joe Bartok