Sunday, September 2, 2018

Holy Grail of Roof Framing Geometry & Trigonometry Book

Book I & Book II

With all the 3D drawings we use today, a craftsman who spends his whole life doing a few simple operations has little chance of exercising his intelligence and thus corrupts the spirit of his mind. These books are for anyone interested in learning the geometric process to roof framing that can be used on the job site. As well as the trigonometric formulas that have evolved from the geometry. A lot of the geometry in the books will be the first time there’s an English explanation to the geometric drawings. French Art du Trait and German Shiften drawings are intellectual exercises in three-dimensional lines. However, precise rafter layout can only be accomplished with knowledge of the geometry that develops the parallelogram in the compound joint.

Most roofs can be calculated with a CMC calculator. For complex roof framing, trigonometry or geometry must be used. There is more trigonometry in this book than all of the roof framing books written in English combined. However, it has over 800 geometric roof framing drawings in the book as well, for carpenters that are not comfortable using trigonometry.

This book does not fit in your sisters' lunch pail. It was written to make complex roof framing simple.

Link to buy the book:


Precise rafter layout can only be accomplished with knowledge of the geometry that develops the parallelogram in the compound joint. Take away the carpenters Framing Square, CMC calculator, and circular saw to show you what they really know about cutting rafters. Can they still layout and cut a hip rafter without the use of these tools? These books will help you acquire the knowledge that has been passed down by the builders of the past.

The information shown in some roof framing books can be overwhelming. My primary objective in writing these books is to share the knowledge I've gained from reading and studying books on roof framing. It's easy to think you know everything about roof framing, big fish in a little pond syndrome until you see or examine the roof framing from around the world and from the builders of the past. I'm as guilty as anyone on the big fish in a little pond syndrome, roof framing in the San Francisco Bay area during the height of conventional roof stick frame era, before roof trusses. Now that I've studied a lot of geometry and trigonometry, I know that using the Pythagorean theorem in the 1980's was like taking bunny steps compared to what I know and can do now.
The king, queen, and knight of roof framing are
1: Hip Rafter Backing Angle
2: Valley Sleeper Layover Bevel Angle
3: Roof Surface - Sheathing Angles.

All of the roof framing angles we use are based on these three angles. For plumb hip rafters, the hip rafter backing angle and roof sheathing angles define the cut on the timber. For canted rafters, the valley sleeper layover bevel angle and roof sheathing angles define the rafter cuts for canted rafters.

Hip rafter shift - offset, plumb line shift, DP-shadow line, and roof averaging design are the other four techniques that need to be studied-learned to graduate from the big fish in a little pond to compete in the world skills of roof framing. There are other areas in the roof that need to be studied, but these seven angles-techniques should be the base for all roof framers.

Don't re-invent the wheel, like I've been guilty of, learn these seven angles - techniques. That has been passed down through the centuries. The builders of the past have made it pretty easy for us. All we have to do is study the techniques that they used from the middle ages to the present day. And we get to use circular saws, instead of broad axes, handsaws, draw knives, chisels, Bisaiguë, etc... to cut our rafters.

Pages from the book:
Book Table of Contents

    Book I
  • Unit Circle Basics for developing Trigonometric Functions
  • The "Unit Circle" is a circle with a radius of 1
  • Tetrahedron Trigonometric Identity Formulas by Joe Bartok
  • Fundamental Hip-Valley Roof Ratios by Joe Bartok
  • Trigonometric Identities
  • Law of Sines Formulas
  • Law of Cosines Formulas
  • Roof Framing Angles in an Unfolded Tetrahedron
  • Canadian & American Geometric Roof Framing
  • Development using a Steel Framing Square
  • Definitions of Roof Framing Angles by Joe Bartok
  • Timber Framing Trigonometric Identity Formulas by Joe Bartok
  • Timber Framing Hawkindale Angle Formulas
  • Frank L. Martindale - H. L. McKibben - L. E. Gray
  • Rees Hawkins Acheson
  • Ed Levin
  • Curtis Milton
  • Timber Framing Angles: S, D , R1 , R2 , R3 , R4 , R5 , R6 , R7
  • P1 , P2 , P3 , P4 , P5 , P6 , P7
  • C1 , C2 , C3 , C4 , C5 , C6, C7 , C8 ,
  • Timber Framing Angles: A5 , A7 , A8 , A9
  • R5B , A5B , R5P , A5P , R4B , R4P ,
  • P4BV , P5BV , R6P , R6PBV , R7BV , VSB ,
  • Roof Averaging Formula: RA
  • Saw Blade Bevel Angle Trigonometric Formulas
  • Tréteaux Angles, tréteau à devers
  • Tetrahedron Slice for Trigonometric Formulas
  • Platonic Solids Trigonometric Formulas
  • Platonic Solid Tetrahedron Trigonometric Formulas
  • Platonic Solid Hexahedron Trigonometric Formulas
  • Platonic Solid Octahedron Trigonometric Formulas
  • Platonic Solid Dodecahedron Trigonometric Formulas
  • Platonic Solid Icosahedron Trigonometric Formulas
  • Auxiliary Drawings for Platonic and Archimedean Solids
  • Archimedean Solids with Jack Rafter Side Cut Angles
  • Archimedean Solids Compound Joinery
  • Archimedean Solid Truncated Tetrahedron
  • Archimedean Solid Rhombicuboctahedron
  • Archimedean Solid Cuboctahedron
  • Archimedean Solid Truncated Hexahedron
  • Archimedean Solid Truncated Octahedron
  • Archimedean Solid Truncated Cuboctahedron
  • Trigonometric Formulas Quick Reference
    Book II
  • Treatise On Those Parts of Geometry Needed by Craftsmen
  • A lesson in Applied Geometry and Euclidean Geometry
  • Pentagon Developed from 5 Circles
  • daisy - stumpEnNailen Test
  • Glossary - Vocabulary
  • Folding Roof Planes
  • Démaigrissement Method
  • Irregular Hip Roof Development - Billy Dillon
  • When Roofs Collide - Will Beemer
  • Hip and Valley Roof Compound Angle Formulas and Geometry
  • Fundamental Hip-Valley Roof Ratios by Joe Bartok
  • Bunny - Grasshopper Test
  • Snake - Two Headed Serpent Test
  • Warlock Cut and the Secret Line
  • Prism Planes in Roof Framing
  • Pythagorean Theorem
  • Hip Rafter Backing Angles
  • Basic Hip Rafter Shift
  • Basic Hip Rafter Shift On The Job Site
  • Hip Rafter Plumb Line Shift
  • Jack Rafter Board
  • Hip Rafter Plumb Line Shift Example
  • Equal Overhang for Unequal Sloped Roofs
  • Steel Framing Square Usage for Top Bevel Cuts
  • Jack Rafter Plumb Line Shift With Framing Square
  • Jack Rafter Plumb Line Shift
  • Trigonometric Formulas Quick Reference
  • Hip Rafter Plumb Line Shift On The Job Site
  • Basic Rafter Lengths
  • Rafter Lengths
  • Purlin Rafters - Frieze Blocks - Panne - Pfetten
  • Purlin - Roof Sheathing Cuts in the Roof Surface
  • Purlin Lip-Cut - Seat Cut- Lower Claw Angle
  • Shadow Line - Purlin Rafters - Geometrically
  • Saw Blade Bevel Angles
  • Purlin Rafters Geometrically
  • Jack Rafter Lower Claw Angle
  • 4 Hits of the Square for Lower Claw Angles
  • Witches Cut - Hexenschnitt
  • Square Tail Fascia
  • Roof Averaging - Roof Design - Dachausmittlung
  • Sloping Ridge and Roof Averaging - Roof Design
  • Roof Design - Roof Surface - Dachausmittlung
  • Polygonal Roof Framing
  • Polygonal Roof Framing Octagonal
  • Octagon Roof Framing Geometric Development
  • Octagonal 4 Butt Roof Framing
  • Octagonal Roof Framing Head Cuts
  • Octagonal Roof Framing Example
  • Polygonal Roof Framing Hexagon
  • Hexagon Roof Framing Geometric Development
  • Polygonal Roof Framing Pentagon
  • Pentagon Roof Framing Geometric Development
  • Round Tower Roof Framing
  • Round Tower 4 Butt Head Cuts Roof Framing
  • Round Tower Mitered Head Cuts Roof Framing
  • Round Tower Rafter Layout Roof Framing
  • Pyramid Roof Framing
  • Pyramid Square Equal Sloped Roof Framing
  • Pyramid Rectangular Unequal Sloped Roof Framing
  • Bay Window Roof Framing
  • Bay Window Roof Framing Example
  • Bay Window Match Gable Roof Framing
  • Bowed Bay Window Roof Framing
  • Unequal Side Length Bay Window Roof Framing
  • Equal Overhang Bay Window Roof Framing
  • Unequal Sided Octagon Geometric & Trigonometric
  • Layover Valley Sleeper Roof Framing
  • Valley Rafter Roof Framing - de noue - Kehlsparren
  • Irregular Valley Rafter Roof Framing
  • Bisecting Hip & Valley Rafters Roof Framing
  • Cripple Hip Rafter Roof Framing
  • Valley Rafter to Hip Rafter Jack Sliders Roof Framing
  • Valley Sleeper Roof Framing
  • Valley Layover Rafter Geometrically
  • Off Angle Lay-Over California Valley Roof Framing
  • Snub Nose Hip Roof Framing
  • Clipped Hip Roof Framing
  • Alhambra Granada Hip Roof Framing
  • Rake Wall Roof Framing
  • Exterior Hip Roof Rake Wall Framing
  • Rake Walls Rotated into Roof Surface
  • Hopper Angles
  • Crown Molding Angles
  • Shed Dormer - Pitch Break Roof Framing
  • CutIn Dormer Shed Roof Framing
  • Vaulted Ceiling Dormer Roof Framing
  • Unequal Slope Vaulted Ceiling Dormer Roof Framing
  • Trapezoid With Unequal Overhang
  • Trapezoid With Equal Overhang
  • Prow Roof Framing Angles
  • Prow Rafter Perpendicular Framing Angles
  • Unequal Pitched Roofs using The Law of Sines
  • Unequal Pitch Roof With Unequal Height Plate Line Trigonometry
  • Unequal Pitched Gable Rafters with Unequal Plate Heights Example
  • Hip Rafter Diamond Post Angles
  • Chanlattée Hip Rafter Roof Framing
  • Saint Andrews Cross Roof on Plumb Hip Rafter Framing
  • Devers Hip Rafters
  • Devers Hip Rafter Tables for Equal Sloped Roofs
  • English, French, German, Russian Translations
  • Equal Pitched Roof Steel Framing Square Usage
  • Rafter Tables for Equal Sloped Roofs
  • Book List - Reference
  • Book III - Book IV Reference
  • Trigonometric Formulas Quick Reference TFG - Roof Framing Kernel
  • Level 1 Roof Cutter's Exam, Equal Pitched 90° Deck Angle
  • Level 2 Roof Cutter's Exam, Unequal Pitched 90° Deck Angle
  • Level 3 Roof Cutter's Exam, Pentagon with 75° Rafter Tails
  • Level 4 Roof Cutter's Exam, Fan Tail Rafters with Square Rafter Tails
  • Level 5 Roof Cutter's Exam, Unequal Pitched Gable
  • Level 6 Roof Cutter's Exam, Multi-Gon Equal Pitched
  • Level 7 Roof Cutter's Exam, Unequal Pitched with Deck Angles Not at 90°

Monday, March 12, 2018

Holy Grail for Roof Framing Geometry

There are no decimal points in Euclidean Geometry using a straightedge and Compass.

I deciphered what Euclid was drawing on the plaster tablet in 200 BC.  
The Euclidean Geometry for the Devers-canted hip rafter head cuts. 
Using the roof surface angles, the profile rafter slope angle and the valley rafter sleeper angle you can draw out the Devers hip rafter head cut and foot cut angles. As well as the jack rafter and purlin rafter head cuts.