I had asked Total Tranny about this in the comments here, but as I thought about it, it’s pretty easy to calculate.
NOTE: If you don’t care about how the formula gets arrived at, and want to skip the explanation, here’s the formula for figuring the “lving area” of a dome.
L = 3.1415 x (r^2-w^2)
Where “r” is the radius of the dome (sometimes called dome height) and “w” is the minimum height of the walls in the living area (usually between 7′ and 8′)
Start with a cross section of your favorite dome:
Where r is the inside radius of the dome, w represents the height of an interior wall–in this case we are going to use 7′ to give us a 7′ ceiling, and u represents the usable diameter for the living area of the dome (i.e.: The amount of the dome with a ceiling of 7′ or more.
Pythagoras, an ancient mathemetician who was anything but square, took the time to teach us how to calculate the length of one side of a right triangle when the other two sides are known.
u^2 + w^2 = r^2
Now, if we have a dome where we know the height (radius – r), and we know the height of wall we want to have (w), then we can solve for the usable radius (u) using this formula.
u^2 = r^2 – w^2
We could take the square root of both sides and find u, but that’s not necessary since we are about to square u in order to find the living area square footage.
To calculate the living space you would just find the area of the cirle with the radius of u. The formula for calculating the area of a circular space is:
Area = 3.1415 x the radius of the circle sqaured.
So if we want to find the living area of our dome (let’s call it “L”), it would be:
L = 3.1415 x u^2
Holy Math, Batman! We already know the square of u–it’s r^2-w^2.
That means we can write our fomula this way:
L = 3.1415 x (r^2-w^2)
Let’s distribute the multiplication:
L = 3.1415 x r^2 – 3.1415 x w^2
In fact, just for fun, let’s plug in our 7′ for w:
L = 3.1415 x r^2 – 3.1415 x 7 x 7
L= 3.1415 x r^2 – 153.93
Now if you know the hieght of the dome, you can find the usable living area:
20′ dome:
L = 3.1415 x 20 x 20 – 153.93 = 1,102.70 sq ft
25′ dome:
L = 3.1415 x 25 x 25 – 153.93 = 1,815.70 sq ft
June 5, 2007 at 2:06 am |
Umm, that was all Greek to me. I don’t have a mathematically inclined mind. At least I know my limitation.
June 5, 2007 at 2:07 am |
BTW, the above is good news right? lol.
June 5, 2007 at 2:35 am |
Pretty much. In looking at the pictures of completed models it seems as if they aren’t using a full sphere but instead are using the “crown” of a larger diameter sphere. This is both a plus and minus.
And I just realized in looking at the calculations above–the figures for the first level are correct, those for upper levels are not, meaning the 2nd+ level calculations I have above are much higher than they would be in real life.
Shoot. I’ll have to correct them tomorrow. I’ll pull them until then.
June 5, 2007 at 4:24 pm |
D’oh!
June 5, 2007 at 5:08 pm |
I feel only slightly better…my math genius son can’t figure out the proper way to do it without just drawing it out and measuring either. Maybe that’s why he’s working this summer at Little Caesars’.
June 5, 2007 at 6:11 pm |
Well regardless of your math errors, we are already planning out how we will us the space in our future home. I am thinking of a 25 footer just for my library. My book collection is already 3,000 strong and growing.
I am thinking of two connected (on the site I think you can see the tunnels they offer to connect multiple units)- the main house and my library.
For the main house almost everything would be on the first floor, the only thing on the second floor would be our master bedroom and bath space.
BTW did you look at the examples on their site? It seems like their past buyers have done some interesting things with that space. I would love to walk through one of these homes though. Sadly, there are none in my area.
June 6, 2007 at 2:16 am |
A 25′ high dome has a single story sq ft of 2016, according to the builder here:
http://www.earthshelter.com/50ftmod.html
But that wouldn’t take into account height.
You can add another 1,710 with a second floor, according to the builder. Again, that wouldn’t account for wall height. I really want to figure out how to calculate usable floor space for a 2+ story dome.
There are a couple problems I see with domes or with any circular building when it comes to cost/sq ft: Standard building materials are all straight and square. Some of them can be easily bent into a gentle arc, but most have to be cut on an arc. That means lots of waste materials. That means lots of labor cost in cutting off all that waste material. That means even more labor cost because a building crew, for instance, is used to dealing with right angles, not curves.
So I suspect any savings over a well designed “square” home might be lost in waste costs.
The second thing I wonder is how many people will be willing to:
1. Live in a dome home.
2. Allow a dome home to be built in their neighborhood.
3. Buy a home from its original owners.
A subdivision near here has a dome home. It is surrounded by the regular ranch and split levels. While the home is great by itself, it stands out like a proverbial pain filled digit when viewed as a part of the whole.
June 6, 2007 at 2:31 am |
1. Live in a dome home.
2. Allow a dome home to be built in their neighborhood.
3. Buy a home from its original owners.
Luckily none of these concern me.
1. Me.
2. I plan on living on quite a few acres. My nearest neighbor won’t be able to see me.
3. When I build it I plan on it being the home I die in- unless the Lord has other plans.
June 6, 2007 at 2:57 am |
For a given individual, I agree these may not be issues. But I am actually wanting to explore technologies that will allow people to live in “normal” looking houses to live a low-eco-impact existence.
Earth ships have been around since the late 60’s and have their merits. They have yet to catch on because they aren’t simply an evolution of current technology/fad, they are a depature. Which is cool for the right individuals, but it won’t work on the scale of a populace.
November 4, 2007 at 8:43 pm |
Talking with some friends who owned a dome home for over a decade they could tell ‘ya many a headache came with their home from leaking windows, uneven floors, hard to find contractor’s who know how to construct/repair dome homes….think twice:-))
Di