The arrangement discussed last time allows arches to meet at right angles to each other, and merge into a larger spherical section, or dome. I find it interesting that an endless number of masonry arches have been built, and none (that I can find) show these arches arranged in the way I’ve described. If anyone is aware of such a design, I would be very interested to see one.
In Romanesque and Gothic arch configurations, where arches are placed at right angles, the intersection of orthogonal (right angle) arches is always resolved with a diagonal rib. This diagonal rib does not describe a helical edge. Using triangular block results in a helical edge; this is what steered me toward this arrangement. Traditional masonry units (“voissours”) are made as square-based wedges. A unit triangular block was hardly ever used as the basic masonry shape in traditional masonry construction.
I realized this design through using a Pythagorean approach. Sometimes numbers just jump out at you. I began to see the square root of 2, and realized that a larger hemisphere could fit within this layout. This design allowed for extensive ways to configure the system. Domes and arches, arches at right angles, square corners: all can be combined and configured in a manner that utilizes economy of material while taking advantage of the high compressive strength of concrete or ceramic units.
This arrangement allows for orthogonal arches and larger domes made of triangular blocks to be assembled. The arch terminating in a larger dome resolves the thrusting forces at the “haunch” of the arch, the most vulnerable part of the arch, located just below 45 degrees in the arch. This is also where the larger sphere deviates most from the described surface, as a result of the impossibility of ‘squaring a circle.’ Furthermore, this system still provides the conjugate shear planes at the abutting edges of adjacent interlocking block.
The design flexibility inherent in this system allows for two, three or four arches to merge into a larger dome. The architectural effect is that of hallways or barrel-vaulted ceilings entering into a larger dome. It also lets right angles be introduced into the round geometry of a dome. People are used to right angles, so this provides a comforting conventional aspect to the round dome, sort of a visual anchor.
This configuration seems so fundamental and basic that I have proposed a theory that it may be present in the structure of DNA, at sites called centromeres and telomeres. We’ll take a look at this possibility next time.