Mathematical analysis of dome geometry

[cobblerdave]

Re: Mathematical analysis of dome geometry

G'day
Third man in!
Yep I like the simplicity of the Forno WFO. Oven door, 63 per cent oven of the internal height, a little less than half the internal width for the door.
If its low dome or high doesn't matter, it breaths and regulates itself.
As for the heat it not like a domestic oven and standard recipes, its more like you take you time to cook things as you like. Too high protect it, to low, no such thing just leave it a little longer.
What's with the radiant heat from a brick/caste oven? Its about as different as possible from that from a microwave as you can get. More forgiving I suppose.
The saying goes "don't over think it" it true with a WFO , it follows the laws of nature so don't muck with the ultimate law...
Regards dave

[Greenman]

Re: Mathematical analysis of dome geometry

We all look for something of substance to hitch our wagon to when planning and building a project as significant as a WFO. I am no engineer so I was impressed with the theories put forward by those with technical skills but the things that sold me on the Pompeii design was the Golden Ratio, the fact that they have been doing the job for 1000's of years and the apparent success of the design.

Add to that the magic of a flickering fire, the smells of good food and the good company it attracts and that's it for me.

It is the nature of man to complicate the simple things and I am sure that there will be tweaking of design and construction methods for as long as mankind draws breath.

[jeeppiper]

Re: Mathematical analysis of dome geometry

I read through this thread and I sit back and shake my head...and one word comes to mind: "REALLY????"

Radiant heat from the ccurved ceiling (elliptical, circular, cylindrical, parabolic.)....conductive heat from he floor....there is also a large convective heat component and complex flow patterns that aren't being discussed. Now throw an active fire into the mix....????

This is just my opinion, but rather than trying to boil our wood fired oven designs down to some engineering formula, I think we should all simply marvel in the creativity, ingenuity, and practicality of the ancient ones who developed them in the first place and the FB folks who brought this to the fore-front. RELAX and ENJOY, people!!! Each oven is going to be different....each design is optimum in its own way. When you combine the uniqueness of the oven with the imagination creativity of its chef.....

I've said enough and I hope I didn't offend anyone. Im probably going to get a lot of flack from this one.

[di11on]

Re: Mathematical analysis of dome geometry

With all that in mind, does anyone have any thoughts on what the optimal shape would be for a 26" oven using a grog based castable?

[stonecutter]

Re: Mathematical analysis of dome geometry

To be clear, I was talking about the temperature of the masonry, not the air.

[Tscarborough]

Re: Mathematical analysis of dome geometry

Wood fired ovens do not cook by air temp, they cook via conductive heat (the floor) and radiant heat (the walls, ceiling, and active fire). Radiant heat is squared by the distance, so it has to be balanced with the conductive properties of the floor. Italian ovens using volcanic based materials have very different properties than medium or low duty firebrick floors, thus the ceiling height will be different for an oven using them. The Pompeii oven is not a Neapolitan oven, and the dimensions are different as is the shape of the dome.

All of that is splitting of very fine hairs in reality, but the 62% ratio applies across the range.

[stonecutter]

Re: Mathematical analysis of dome geometry

According to mklingle's analysis, 42" domes with 21"H and 18"H have virtually identical heat signatures on the floor. Given the intensity of live pizza flames, I'm not sure even a parabolic dome shape would behave any different than a flatter Neapolitan dome.

Little temperature variables makes sense when your talking hemispherical domes, but there is no way that a flatter dome or more elliptical shape will perform the same, even at lower temps.

A pound of feathers is the same as a pound of lead, like 1000 degrees is a 1000 degrees in an oven.

But whether through convection or radiant heat, the source of the heat is closer to what is being baked, roasted or cooked in an elliptical (Neapolitian) dome. That will translate into much faster cook times, as far as finished product. So that is something to consider when designing an oven shape.

[GianniFocaccia]

Re: Mathematical analysis of dome geometry

You might build a dome that is optimal for distributing the heat for a particular purpose, but if it doesn't work from an airflow heat generation point of view, you might not get the heat to distribute in the first place???

I believe the 63% golden door-height rule has to be the least-flexible 'variable' in proper dome design. Like StoneCutter said, just look at thousand-year-old ovens to see what good-breathing ovens look like.

According to mklingle's analysis, 42" domes with 21"H and 18"H have virtually identical heat signatures on the floor. Given the intensity of live pizza flames, I'm not sure even a parabolic dome shape would behave any different than a flatter Neapolitan dome.

Although pizza is a main fare at home, I built my oven with a 12" door-height to accommodate taller pots. Working with an 8.5" door-height like the Panyol 66 would certainly come with its own set of challenges.

[di11on]

Re: Mathematical analysis of dome geometry

Think I'll just copy the dimensions of the Panyol 66 :-)

https://mainewoodheat.com/wood-fired...nyol-model-66/

[stonecutter]

Re: Mathematical analysis of dome geometry

So what is the conclusion?

- A parabolic dome will focus reflected energy onto a point
-An elliptical dome will focus the energy onto a ring

The latter sounds ideal for pizza cooking... if I calculate the elliptical shape I need to maintain the 64% height rule and so the ring is somewhere in the centre of my pizza, I'll see what shape I get!!

It is...but you need not look further than ovens built centuries ago.

[di11on]

Re: Mathematical analysis of dome geometry

Interesting thread...

The discussion only seems to focus on the impact of the dome curvature on the distribution of heat... but isn't the whole 63% ratio of dome height to door height thing about the flow of air and the heat generation capacity of the oven... surely this is an important factor. You might build a dome that is optimal for distributing the heat for a particular purpose, but if it doesn't work from an airflow heat generation point of view, you might not get the heat to distribute in the first place???

So what is the conclusion?

- A parabolic dome will focus reflected energy onto a point
-An elliptical dome will focus the energy onto a ring

The latter sounds ideal for pizza cooking... if I calculate the elliptical shape I need to maintain the 64% height rule and so the ring is somewhere in the centre of my pizza, I'll see what shape I get!!

[Coastman]

Re: Mathematical analysis of dome geometry

I think this problem has so many variables it would be very difficult to calculate without a very large number of variables as input. Here is just a limited number of the variables.

Density of the firebrick dome and floor separately.
Thickness of dome if uniform then easier if it varies then more difficult.
Number of thermal breaks and then calculated heat transfer for each break
Thickness of floor.
Floor insulation and type and how much of each type.
Dome insulation, and type and how much of each type.
Flue arch, and all of the variables associated with dome or floor.
Ambient temperature of surroundings.
Barometric pressure
Humidity
Wind velocity and direction.
Altitude
Turbulence related to flue arch geometry there are many variables here such as floor at same level as oven, tapered entry vs straight, how much reveal at inner arch, arch to flue funnel size and shape etc...

Then there are all of the variables related to the pizza, dough hydration, number, type, mass, and hydration levels of each ingredient.
Placement of pizza relative to fire, last pizza location, number of pizzas in the oven,

Some calculation as to the amount of fire that is currently in the oven and values to account for ash insulation.

And this does not even begin to cover the types of tools being used, their materials, and how long they are in the oven and or how much heat they remove from the oven based on these variables.

So what is the bottom line for me....

If the oven is cooking well I throw another pizza in, if it is to cold I throw in more wood and wait a couple of minutes, if it is to hot I might lightly mop the floor or toss in a quick thin cheesy bread pizza to cool the floor a little.

Reminds me of my aero engineering days! Despite the various disciplines of fluid dynamics, finite stress analysis, the more human side of ergonomics, a general rule of thumb was "if it looks good it might be, if it looks bad it might be". Looking at all the different traditional designs around the world, let alone the different ratios and dimensions fom current manufacturers, it seems that within certain bandwidths there are quite a lot of differences too. Yet various users of each type sing their praises. Thanks for reply!

I'm going to take a suck it and see approach: use loads of insulation, start with a door on the large size and reduce it if necessary.extend the chimney if necessary, use 2 to 3 inches of heat screed. It'll be fun!

[mrchipster]

Re: Mathematical analysis of dome geometry

I think this problem has so many variables it would be very difficult to calculate without a very large number of variables as input. Here is just a limited number of the variables.

Density of the firebrick dome and floor separately.
Thickness of dome if uniform then easier if it varies then more difficult.
Number of thermal breaks and then calculated heat transfer for each break
Thickness of floor.
Floor insulation and type and how much of each type.
Dome insulation, and type and how much of each type.
Flue arch, and all of the variables associated with dome or floor.
Ambient temperature of surroundings.
Barometric pressure
Humidity
Wind velocity and direction.
Altitude
Turbulence related to flue arch geometry there are many variables here such as floor at same level as oven, tapered entry vs straight, how much reveal at inner arch, arch to flue funnel size and shape etc...

Then there are all of the variables related to the pizza, dough hydration, number, type, mass, and hydration levels of each ingredient.
Placement of pizza relative to fire, last pizza location, number of pizzas in the oven,

Some calculation as to the amount of fire that is currently in the oven and values to account for ash insulation.

And this does not even begin to cover the types of tools being used, their materials, and how long they are in the oven and or how much heat they remove from the oven based on these variables.

So what is the bottom line for me....

If the oven is cooking well I throw another pizza in, if it is to cold I throw in more wood and wait a couple of minutes, if it is to hot I might lightly mop the floor or toss in a quick thin cheesy bread pizza to cool the floor a little.

[Coastman]

Re: Mathematical analysis of dome geometry

Works for me! Can we get hold of your model and try to plug in our own designs please?

[Wild-Yeast]

Re: Mathematical analysis of dome geometry

A late first entry to this thread.

In the first post on this thread mklingles said:

Quote: "If anyone knows the absorption / reflection coefficients for fire brick at ~800degF please post."

No one answered...,

On the last page of posts mklingles posted:

Quote: "For sure the Convection is a dominant factor in heating the oven and distributing the heat within the oven. For cooking, I think the radiation factor dominates. However, I don't know that to be the case.

I did talk to one physics professor about handing this off to have a student do some more work on it, but haven't even followed up on that. (To busy cooking pizzas, building wood shed, etc)."

The post runs out at that point.

mklingle (I think) is on the right path as regards the investigation of how items are baked within a wood fired oven. Little, if any, quantitative study has been done on why this combination is able to produce such amazing gastronomic results.

The most likely candidate is the effect of radiant energy on water molecules - especially the distribution of radiant energy excitation on those water molecules...,

Has anyone added to this discourse anywhere else on the site?

Wild-Yeast

P.S. I have ulterior motives on this subject - that's for later...,