This is fascinating - the catenary arch
There may be an "ideal" dome profile for baking pizza in a pompeii oven, but that does not necessarily correspond to what is an "ideal" dome shape for structural stability.
The "catenary arch" is an arch profile which is essentially the inverted profile of a suspended chain. I'm not an engineer (someone who is please chime in and correct me), but as I understand it, when you take a lenth of chain and suspend it upside down, like a "U," it will naturally form a shape which reflects the varying gravitational stresses on the chain. Invert that profile, and this will provide a dome profile which is structually balanced.
Wikipedia says that the catenary arch is used to design kilns made of firebrick:
A kiln, a kind of oven for firing pottery, may be made from firebricks with a body in the shape of a catenary arch, usually nearly as wide as it is high, with the ends closed off with a permanent wall in the back and a temporary wall in the front. The bricks (mortared with fireclay) are stacked upon a temporary form in the shape of an inverted catenary, which is removed upon completion. The form is designed with a simple length of light chain, whose shape is traced onto an end panel of the form, which is inverted for assembly. A particular advantage of this shape is that it does not tend to dismantle itself over repeated heating and cooling cycles — most other forms such as the vertical cylinder must be held together with steel bands.
The "flattened dome" used for cooking pizza is thus not a proper catenary arch. The issue is thus, whether you want long structural integrity or good pizza. I'll choose the latter.
Am I speaking in hyperbole?
(M) You must have gone to:
n., pl. -ies.
catenary cat'e·nar'y adj
(M) You can create various arches that still qualify as "catenary" by varying the distance between the end points of the chain.
(M) This variability suggests that, regarding strength versus "bakeability", you can have your arch and eat it, too. James offers both a low and a high profile oven and they could both be catenary arches in the same way that Isoceles triangles can vary depending upon the width of the base.
I'd like to try this. . .
Use a chain tacked to a wall to draw your arch profile. Here's how I'd try it:
1) Obtain a LONG piece of fine chain - watch chain, inexpensive necklace chain, etc. It should be at least twice as long as your desired oven diameter.
2) Tack up a large piece of cardboard in the wall. Draw a perfectly level line on this board the length of your desired oven diameter, e.g. 42".
3) From the center point of this line, draw a plumb line down toward the floor, the length of which is your desired dome height. E.G. 20" The bottom point of this center line represents the peak of your dome.
4) Tack one end of the chain to one end (Point "A") of the line. Drive a nail in the other end (Point "B").
5). Drape the free end of the chain over the nail in point B and pull on it until the center (nadir) of the chain just hits the bottom of the center line.
6) Tie off/tack or affix the free end of the chain to the nail in point B. Trace the line formed by the chain (If you're lazy, you can use spray paint as long as you don't move the chain).
7) Remove the chain and nails. The chain now constitutes a catenary arch to provide a stable dome with the dimensions you prefer. You have a perfect dome form.
Don't forget to turn it upside down before you actually build the oven.
QUESTION: Does this line represent the inside, outside, or center line of the brick dome profile? You will have adjust the dimensions to fit (I don't know the answer but I suspect it's the center line of the bricks, so you have to adjust your endpoints accordingly.).
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