Casting a dome oven Other Oven Types Discuss Casting a dome oven in the Pizza Oven Design and Installation forums; I am casting a dome out of castable refractoy product, I am finding it hard to calculate how much to ...

[casa de Hoadley]

I am casting a dome out of castable refractoy product, I am finding it hard to calculate how much to buy and what the dome will weigh ? Any suggestions on calculating it correctly ?

[dmun]

The volume of the dome is roughly the volume of the exterior sphere minus the volume of the interior sphere, divided by two. The entry area roughly corrects for the door hole.

You can calculate it exactly using various cad programs, but it won't be any more accurate than the accuracy of your hand built forms.

[casa de Hoadley]

Thanks I found this web site that calculates the surface area of a sphere then divide by 2 and times by wall thickness
http://www.easycalculation.com/area/sphere.php

[pacoast]

You might want to double check your calculation. You didn't give any numbers, but the spheres method that dmun described is more accurate and less susceptible to 'intuitive' errors.

If we ignore the vent (doorway) for the moment, it's easy to visualize that the dome is a sphere that is cut in half. So you can circumscribe half a sphere around the outside of the dome and another half sphere inside the dome. Then the entire space between the two half spheres would be filled by the dome. Ergo, subtracting the volume of the smaller dome from the larger will represent the dome wall volume.

Now contrast that against your method of calculating the area and multiplying by the thickness. Same thing, right? Well, no. If you were pouring a rectangular slab, it would be equivalent. But a dome has a curved surface. So say your dome will have an inside diameter of 100cm (radius = 50cm) & a wall thickness of 10cm. Did you use these numbers in your calculations? Or did you use the outside diameter (120cm) & radius (60cm)? Most people seem to opt for the former, but both approaches are wrong & give substantial errors of about 20%.

Since the dome wall thickness is not zero, as the diameter of the dome increases, so does the surface area. A reasonable approximation of the average dome surface area would be to take the diameter in the middle of the wall. In this case that would be 55cm. But the spheres method is still more accurate.

.

[casa de Hoadley]

Thanks, I understand what you are saying, I didnt allow for the thickness of the wall. I will add 20% to the initail calculation.

[pacoast]

Sounds good. Just would hate to see you start the pour before realizing that you didn't have enough bags on hand.

.

[Lars]

The volume of a sphere is 4/3(pi)r^3...

lets say you have a 40" inside diameter oven....
then, let's say you want your walls to be 4" thick...

so find the volume using r(outside)=24 and r(inside)=20, then subtract the inside volume from the outside volume and you get the volume of the shell.


Like this: V1= 4/3( pi) r^3=4/3(pi)(24)(24)(24) = 57905.8 cubic inches.
V2= 4/3(pi) r^3 = 4/3(pi)(20)(20)(20)= 33510.3 cubic inches.

(V1-V2)/2= 24395.5/2 = 12197.75 cubic inches.

To get cubic feet, there are 12^3 cubic inches in a cubic foot, so
(12)(12)(12)= 1728 cu.in.

The volume will be around V(shell)/1728= 12197/1728= 7.06 cubic ft.


Plug in your own numbers and do some math!

L.

[pacoast]

Exactly right & a good exercise. But I have to admit that the online tool that the OP found also calculates spherical volume correctly.

Cheers.

.

[james]

Hey guys,
I move this to Other Oven Types. That seems like the right place.
James

[RTflorida]

OOOOHHHH... the humanity, and the MATH.
LARS, my head hurts after reading your post...I didn't realize how stupid I have become. Literally took over 5 minutes to comprehend. I think you really do lose it if you don't use it (your mind)

RT