About
I learned to be a carpenter from my father and other carpenters that I worked with during my four-year union apprenticeship in Mountain View California in the 1970’s. With 100+ houses in each tract of houses that we worked on, there were always 4 or 5 roof stacking crews framing the roofs, but only one roof cutter. The roof cutter was always the top dog and earned the most respect.
In 1974 when I did start cutting roofs, like everyone else at that time, I used the book by Augustus Frederick John Reicher’s - Full-Length Roof Framer to cut the roofs. Then in 1980, I started to use a calculator to figure out irregular hip roofs. There were still parts of the roof that I still couldn’t figure out using right triangle trigonometry, so I went back to college and studied geometry, trigonometry, and calculus. I learned how to use the Law of Sines and the Law of Cosines to figure out the angles and dimensions on roofs that I couldn’t calculate by just using right triangle trigonometry.
Fast forward to 2006, after cutting and stacking about 5,000 roofs, I meet Billy Dillon and Joe Bartok online at the JLC forum. Billy introduced me to roof framing geometry, and Joe taught me how to unfold a tetrahedron roof framing kernel to develop trigonometric formulas. I could go on about the other 50+ great roof cutters and roof stackers that influenced me, but I’ll only mention two. Mike Jones of Fremont California and Eric Johnson of Tracy California. Both roof framers made roof framing fun.
After I started studying roof framing geometry, I also learned that roof framing geometry gave me a better understanding of roof framing in general. There are no decimal points in geometry. However trigonometric formulas arise from the geometry. If I can't find the angles I'm looking for in a tetrahedron drawing; I'll take a tetrahedron slice cut from the roof framing joint. Then I'll unfold the tetrahedron slice, and finally, I'll develop the correct tetrahedron showing the relationships of the different roof framing angles that I can use to develop the trigonometric formula.
However, there are times that using geometry for complex roof framing angles and bevel cuts is much easier than trying to find the correct trigonometric formulas. Using the geometric roof averaging drawing technique only takes a couple of minutes to find the hip rafter run lines in plan view for un-equal pitched roofs with eave angles that are not at 90°. It was by studying the unit circle drawing technique and roof averaging geometry that I was able to find the Roof Averaging formula to calculate the plan angles for complex roofs with unequal slopes. So, you need to study Geometry to develop the correct Trigonometry for complex roof framing.
It turns out that the geometry for complex roof framing we use today was developed 1,000+ years ago. It wasn't until about the 18th century that the French Compagnons and German Zimmermann were documenting the methods and techniques in books detailing the geometric layout of complex roof framing. The few architectural drawings that were handed down from the middle ages and the insufficient documents of the building guilds merely hint at geometric methods of roof framing design, either because the philosophy symbolized by their designs was a guild secret, or a knowledge of it was assumed to be the common property of all builders. What mathematical knowledge, and particularly what knowledge of geometry was possessed by the remarkable builders of the great cathedrals.
In these books, we'll explore the trade secrets from ancient Greeks, Euclid, Cistercian monks, French Compagnons, German Zimmermann and the American Carpenters & Builders of centuries past, that only a limited few were allowed to know. Including the Platonic and Archimedean Solids that are the basis of all roof framing geometry. The ancient Greeks developed the Archimedean Solids by adding polygonal roofs on top of other polygonal roofs. With the geometry from the renaissance mathematicians, Luca Pacioli (1445 - 1514) and Leonardo da Vinci who studied and built the Archimedean Solids, we'll draw out complex roofs based on the diagonal of a pentagon.
The Compagnons du Tour de France are a French organization of craftsmen and artisans dating from the Middle Ages, but still active today.
The German Zimmermann journeyman years (Wanderjahre) refer to the tradition of setting out on travel for several years after completing an apprenticeship as a craftsman. This tradition dates back to medieval times and is still alive in German-speaking countries today. The origin of this tradition in the Middle Ages, similar to the French Compagnons, lies in the building of monastic construction, like the fortified Maulbronn Abbey in Germany. Journeyman years or Wanderschaft is also a tradition in Denmark.