Geodesic dome measurements

[Brennan Oleary]

Hello all,

I am new to this group and new to geodesic domes. I am hoping to build one this spring. Thank you for all your help in keeping the domerama site up and helping to make the calculators. 

Can anyone tell me why the calculator says a 14' diameter 3V 5/8 dome has a floor area of 136.524 sq feet and not 153.94 sq ft according to the formula for the area of a circle?

Brennan

[Blair Wolfram]

Brennan,

There may be a couple reasons for a discrepancy in the area calculations of a 14' diameter dome. 

14' may be the spherical diameter of the sphere, which is measured at the hemisphere, not at the ground level diameter. If 14' is the spherical diameter of the sphere, the 5/8 level or the level similar to the Tropic of Capricorn on the globe will be less than 14'.

Or, an adjustment may have been made from using chords around the perimeter instead of a continuous arc in a circle. The chords being straight sections will shave off some of the floor area measurement.

Blair

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[Levente Likhanecz]

hello brennan,

the 3V dome does not cut at the equator. (the nominal diameter of your sphere 14')

below the blue line represent the equator.

so this might be the difference, not a great circle of 14', but a lesser circle above, or below. (don't know, should calculate)

cheers, lev 

[Levente Likhanecz]

[Levente Likhanecz]

[Paul Kranz]

Brennan: The calc for the floor area is based on the formula for a polygon, not a circle.

Welcome to the group.

Paul sends...

[Brennan Oleary]

Thanks for welcoming me to your group. 

Yes, I am aware that the measurement is not at the hemisphere, but I wanted to be certain that this was the issue since the calculator at ziptie domes provides the hemisphere value. 

Thank you Blair and Paul for revealing that the formula is for a polygon and not a circle. If I may suggest, it might be helpful to state this on the domerama site.

Thank you Levente for bringing the graphic to my attention, I probably didn't notice it since it resembles an ad, and I suspect we all tend to mind−block them lol.

Brennan

[Eric Marceau]

Hi Brennan,

Don't want to impose by stating the obvious ... but by using the floor positioned below the hemisphere (as shown in Levente's more recent cross-section image), you have more usable space at the "bulging circumference", which would not be available to you by using the floor positioned above the hemisphere, for a same investment in foundation/anchor construction costs.

The added benefit of that second geometry is that it facilitates the adaptation for a second floor, if that is of any interest.  

On the other hand, if your intent is for single floor, the earlier profile is likely the better-suited for your needs.

Eric

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[Brennan Oleary]

Hi Eric,

No imposition, thanks for the information. Besides the extra height, is there any other reason it facilitates a second floor?

Brennan

[Eric Marceau]

No.  The extra height is the only factor that facilitates the second floor, if the foundation size is restricted within property borders.

[Gerry in Quebec]

Hi Brennan,
Sorry to have missed your query about the floor area of a 3v "5/8" dome as presented on Domerama. I normally read the group's daily digest but was out of the country at the time.

A few points:
 - There are several errors of presentation and math on the Domerama website. This is a "ghost" website. I believe the current owner, the site creator's father, is unable to edit/correct/update content. If anyone has info to the contrary, please let me know.
 - Blair's explanation for the floor area discrepancy is correct, but there is one further factor to consider: When you use the calculator for the "3V 5/8 geodesic dome", the floor area calculation is for a dome whose base or footprint has 10 sides, not 15.
 - To the right of the calculated dome dimensions, there is a drawing (copied in this thread by Lev), saying: "This calculator uses the spherical radius to output the floor area." This is incorrect, and is an edited version of a drawing I gave the original website owner over a decade ago.
 - The so-called 3v icosa, class I, method 1 dome does not sit flat at either of the two truncations just above and below the equator. So you can't calculate a usable floor area because it isn't a planar surface. By going to a 10-edge footprint, you solve the problem. Several companies have used this configuration and take advantage of the dome's five trapezoidal openings to include extensions to the building. See the appended drawings. Many other companies, such as Blair's, Dome Inc., use a different geometry, typically referred to as the Kruschke subdivision method. In that case the 15-sided version of the dome sits flat at both truncations, just above and below the "equator" of the geodesic sphere. It is a more elegant and practical geometry, in my view, but comes at the price of having three instead of two triangle types and four instead of three strut lengths.
- The floor area of a 10-sided, 3v icosa geodesic dome using so-called "method 1" geometry is 132.564 sq. ft when the spherical radius is 7 ft, as given in the Domerama calculator. For a 15-sided, 3v icosa Kruschke dome, the area will be 144.187 sq. ft.

I hope this helps. Good luck with your project.
- Gerry in Québec

[Gerry in Quebec]

Oops.... In replying to Brennan, in the last point, I should have typed 136.524 sq. ft, not 132.564.
- Gerry in Québec

[Brennan Oleary]

Thank you for that explanation Gerry. 

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[Dx G]

You might want to review Hugh Kenner's book, Geodesic Math. There is an entire chapter on truncations.  In one example he explains a method of replacing some struts at the ground level to eliminate the uneven bottom.  The rest of the dome uses routine struts, which reduces the number of odd sized struts.   He also explains some additional options that are often overlooked, such as using an edge-up configuration instead of the more common vertex-up orientation, since it can provide a true flat base from a great circle. 

Dx G

 

[Levente Likhanecz]

there is a new tv show "murderbot" on appletv+. the very first episode has these living quarters in it.

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[Brennan Oleary]

I saw that Levente, looks like a good show too! Though I do not even know how tv's work anymore lol

[Levente Likhanecz]

i guess still called tv show regardless if streamed over internet.　

the funny part, i'm using smart tv as pc monitor.

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