I call it modified because I intend the vault to rise directly from the oven floor in a semicircular arch. 36" oven floor will yield an 18" high dome height. I did the math and worked the numbers around the dimensions of a standard (at least locally in Corpus Christi) fire brick (9"x4.5"x2.5"). The physics is actually better as well as the vault transfers its weight directly to the floor rather than the walls of the traditional barrel vault which then have to resist the outward thrust of the vault dome. So I have a 36"x36" nominal, 31"x31" actual oven floor. I cut 7.5 degree bevels on the side of each brick (48 bricks in the dome, 96 cuts, not counting the two I screwed up- currently researching the toxicity of fire brick dust) so that they would produce a natural semicircle when stacked and mortared.
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My Modified Barrel Vault in Texas