LOG
and
TIMBER FRAMING
ANGLES

THEORY: Hip and Valley Roof Trigonometry

 The focus is on concise, generic trigonometric methods of resolving the angles required for accurate joinery in a Hip / Valley roof. Diagrams are used extensively to supplement the abstract trigonometry. The following ideas are explored:
 All kernels are equivalent (Cognate kernels) The sine, cosine, and tangent of any kernel angles may be resolved in terms of two other angles Compound angle relationships on the stick The location of right angles on the roof, on the kernel, and on the stick Definition, measurement and relationships between Dihedral, Saw blade, Miter and Bevel angles General solutions of Deck angles Utilizing a unit reference length to determine trig functions of angles Extracting kernels from the stick Extracting kernels from Interlocking kernels Extracting sticks from kernels Superimposing sticks on kernels Models other than tetrahedral kernels
 ANGLE CALCULATORS   contains links to Excel worksheets and Javascript calculators which will solve the complex roof framing and joinery angles based on the theory in this section.

Overview of Tetrahedra and Triangles defining a Hip Roof