Mathematical analysis of dome geometry

[texassourdough]

Re: Mathematical analysis of dome geometry

Thanks, mklingles!

Would be interesting to do a conical oven also - easy shape to specify. I think you will find all of the options are very similar for the no fire case.

I believe the biggest advantage of the lower oven for pizza lies in the flame being closer to the pie - and wrapping more over the top of the pie. If we assume the flames are say 16 inches "tall" they will reach an inch or two further across a "low" dome compared to a taller one and will be several inches closer. We are all familiar with the fact that the side of a pizza cooks faster than the "dark" side (which is receives less flame radiation and more black body refractory radiation from a cooler source than the flame). As a note, for small flames there would be little difference.

Thanks for bringing up the topic and for your calculations!
Jay

[Neil2]

Re: Mathematical analysis of dome geometry

To sum it up then, for pizza cooking:

For smaller ovens a hemispherical shape will do fine and provide the opportunity for a somewhat higher door (maintaining the 63% door/dome ratio).

For a larger oven, say 40 inches or more, an elliptical or low dome shape might be more efficient for cooking pizza.

[mklingles]

Re: Mathematical analysis of dome geometry

Mathmatically:

- A parabola will focus radiant heat at a single point somewhere above the floor.
- A hemisphere will focus at a single point on the floor (center)
- An ellipse will focus on two points on the floor (or in three dimensions, a ring).

What Neil2 is describing here is the behavior of photons that are reflected off of the surface. For that fraction of the inferred radiation that is not absorbed and re-admitted the reflective properties would apply. This article at wikipedia has a good description of specular reflection from curved mirrors. Wikipedia - Curved Mirrors

I have not been able to find a reliable source of data on the amount of energy absorbed by fire brick vs the amount reflected. I believe from the numbers I have found that ~80% of the energy is absorbed and only 20% reflected.

Also the roughness of the firebrick will greatly distort any reflected "image

[Lburou]

Re: Mathematical analysis of dome geometry

I thought we had a good beginning for this discussion....Are we done? Ready to read more

[mklingles]

Re: Mathematical analysis of dome geometry

I'm working on adding the door opening to the calculation. Maybe a week or so, I'll get the next round of math done.

[benguilford]

Re: Mathematical analysis of dome geometry

mkingles, as an engineer I salute you sir! I liked your quote from a while back 'The maths keeps me out of trouble'

Surely there must be an engineer on this Forum with access to some professional thermal modelling software, three dimensional modelling of radiated heat is fairly complicated, and it doesn't take the effect of convection into account - even in a sealed dome there will be a surface temperature differential between the floor and the walls, which would set up a circulating air flow within the oven. Would this be considered negligible in this situation?

[mklingles]

Re: Mathematical analysis of dome geometry

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).

[Neil2]

Re: Mathematical analysis of dome geometry

It is not too complicated.

An elliptical oven has a lower dome than a hemisphere of the same diameter. The heat from the ceiling bricks is closer to the top of the pizza.

[david s]

Re: Mathematical analysis of dome geometry

This also applies to small ovens. The dome and flame from the active fire are much closer to the pizza. My own oven has the interior height at only 10 and a half inches. It still cooks much the same 90 sec to 2min pizzas. The larger the oven, the larger the fire so I guess it all evens out.

[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...,

[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?

[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

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!

[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!!

[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.