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Geometric Shapes #1: Geodesic Domes

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Blog entry by rance posted 08-13-2011 06:55 PM 7472 reads 1 time favorited 24 comments Add to Favorites Watch
no previous part Part 1 of Geometric Shapes series Part 2: Truncated Icosahedron (without the math) »

In some discussions both online and back channel(PM), Moment brought up the question of the angles used in building a Geodesic dome from watching this video. With a little research I found that someone had published the lengths and angles for pipes, if you were building a structure you might cover with a parachute. What Moment asked about was as if you were building it from solid wood(or framed) panels. Specifically, the angles between the panels.

Background: From his post and some research, I learned of the different levels(or frequencies) of the domes. Namely, 2v, 3v, 4v… I won’t go into detail here since it is easilly found on the internet by googling Dome calculations. Just to say we are looking at a 3v model:
 

Panels: Another thing I found out is that even if you use all triangle panels, not all triangles are the same size. This too can be found from searching the internet. Maybe the guy in the video ignored this rule. I don’t know because I couldn’t hear all of the audio. I could be wrong in my deduction here.

Size: From looking at the models and with more research, I have also deduced that the overall size of a dome(or sphere) does not in any way affect the angle relationship between the panels as long as you stay within the same Level(3v in our case). It only affects the size of the panels.

Angles: I do like math, and I’m sure there is a simple equation to figure this out, but I’m not familiar with the formulas needed to calculate such angles. And having failed at being able to find this answer on the internet, I resort to the brute force method. I do, however, have SketchUp at my beck and call as an aid. I will post my progress as it happens. And I’m not promising this at any lightening speed either. At first I thought this might be easy. I have failed twice in my attempts to figure this out using SU alone.

Guessing & “I think”: On this page , about 2/3 of the way down, Jacques asks this same question with guessing answers. If someone says “I think…”, then to me, that is not an answer in the case of building a G. Dome. I prefer to have more accurate answers. Oh, and let me do the rounding myself. :)

I welcome anyone to interrupt the previously scheduled program to save me some grief, set me straight, or to help me along. The 3v model may be exactly the same as a Soccer Ball, which Sam Shakouri has built many times. Sam, feel free to shut me up and put me out of my misery. :D

Thanks in advance for any and all input to this puzzling question.

-- Backer boards, stop blocks, build oversized, and never buy a hand plane--



24 comments so far

View ptweedy's profile

ptweedy

75 posts in 2045 days


#1 posted 08-13-2011 07:21 PM

try goggling buckminister fuller for domes and calculations. he invented the thing

View rance's profile

rance

4132 posts in 1812 days


#2 posted 08-13-2011 07:50 PM

Yeah, I should have done that first. I did find This site ‘claims’ to have the Dome Math(4.2 about 1/4 down the page). However, I can’t get past the physiwidgamafloogle to understand what they are telling me. They even have an alternate creator of the thing.

“Spherical Trigonometry”, “Chord Factors”, “How to tesselate a sphere”? I didn’t even know these domes had testicles. I’m not sure I want to even build one now. I can see it now. For its annual checkup, the doctor comes out, he says “OK, now make it cough”, and I tap on the roof of the dome real hard.

-- Backer boards, stop blocks, build oversized, and never buy a hand plane--

View Joe Lyddon's profile

Joe Lyddon

7710 posts in 2703 days


#3 posted 08-13-2011 08:17 PM

Rand, you’re SO FUNNY!!

It’s been a LONG time since I’ve had to turn my head and cough! LOL

I don’t know much about them domes either…

At first glance, I thought “Oh, just a bunch of equilateral triangles… aka 60,60,60.
You know what a 45,45,90 and a 30,60,90 are YES?
It looks like these start out at 60,60,60 and are merely put together!
But, without making slight changes (as it appears) you could not get it to go in curve for a circle…
Their edges would have to be cut a certain angles to make them fit nice and flush with each other.
The more I think about it, just trying to follow a set of plans would be a nightmare… having to Number every triangle and sides too!

The more I think about it, it boggles my mind… I guess I’m too old for that kind of stuff now…
I think I could’ve handled OK when I was younger.

Good luck, Rand…

Now, turn head, cough, laugh, and do something you can easily handle! LOL

-- Have Fun! Joe Lyddon - Alta Loma, CA USA - Home: http://www.WoodworkStuff.net ... My Small Gallery: http://www.ncwoodworker.net/pp/showgallery.php?ppuser=1389&cat=500"

View rance's profile

rance

4132 posts in 1812 days


#4 posted 08-13-2011 10:39 PM

More simple than mere math. Just go to Google 3D Warehouse. They have the models. EVERYTHING is on the INTERNET. It is simply a matter of measuring the angles between the faces on that completed SU model. Arrrrrgh.

From one of the links above:
>“On the red edges the bevel is 7.2, on the green edges it’s 6.8, on the blue edge of the red-red-blue triangles it’s 4.1 and on the blue edge of the green-green-blue triangles it’s 7.2 – I think, perhaps someone else will confirm.”

Well, when I measured the first one, I got 7.2°. The same as what was posted. I’m gonna assume(I know) the rest are correct. Of course I need to figure out the relationship of Red/Green/Blue edges to A/B/C on the drawing, but I think I can handle that.

I still want to figure out how to do it in SU. It’ll be an interesting exercise to compare the two. My contention is that it can be done with a means that does NOT require an inborn knowledge of physiwidgamafloogle mathematics.

Thank you, all 104 of you for bearing with me through this exercise. No eta on my SU solution.

-- Backer boards, stop blocks, build oversized, and never buy a hand plane--

View Joe Lyddon's profile

Joe Lyddon

7710 posts in 2703 days


#5 posted 08-13-2011 10:56 PM

Rance… sorry, I called you Rand by mistake…

OK, are you going to make one to live in?
... Doll house?

What?

-- Have Fun! Joe Lyddon - Alta Loma, CA USA - Home: http://www.WoodworkStuff.net ... My Small Gallery: http://www.ncwoodworker.net/pp/showgallery.php?ppuser=1389&cat=500"

View rance's profile

rance

4132 posts in 1812 days


#6 posted 08-13-2011 11:22 PM

No problem Joe. :) I knew what you meant. There’s really only 3 kinds of triangles made up from 4 different edge bevels. Kinda interesting actually. Now when it comes to assembling them, that might complicate things.

I think I want to eventually take this to the table saw. Maybe a box of some kind.

-- Backer boards, stop blocks, build oversized, and never buy a hand plane--

View Joe Lyddon's profile

Joe Lyddon

7710 posts in 2703 days


#7 posted 08-14-2011 12:40 AM

I see a lot of hole drilling for Nuts & Bolts… One DP setup… 1,000’s of holes!

I can’t see nailing them together… Nuts & Bolts would be easier… a ton of expense!! Weight too!

So, you just make so many of three dif. triangles… I picture a half-lap joint at each angled point… Glue & pin-nail the individual triangle points.

One heck of a lot of angle cutting…

... then, bolt them together?

I picture triangles using about 36” long pieces…

2×4x10 ??

Sounds like a lot of work! ...but it might be a little FUN to do…

Maybe a small Greenhouse for starters… to get the procedure & jigs squared away… LOL

I just thought of the foundation! That would be a paid to layout… Cut a few 2×4’s with the proper angle on them and start laying them on the ground (flat level ground), pound stakes, start digging the trench… or just make it as part of a slab… different ways to do that I guess…

I also see Brace pieces to be used as you go from level to level up the curve… either that or using LONG ladders… or a combination…

So, what you gonna do? LOL

-- Have Fun! Joe Lyddon - Alta Loma, CA USA - Home: http://www.WoodworkStuff.net ... My Small Gallery: http://www.ncwoodworker.net/pp/showgallery.php?ppuser=1389&cat=500"

View moment's profile

moment

2123 posts in 1332 days


#8 posted 08-14-2011 05:02 AM

Thanks rance , Let me know your progress on the SU , that should be interesting . I guess its time to make a small model and see how that goes . Although obtaining accurate results when comparing the Diff.
of 5 degrees and 7 degress on small pieces is problematical for me . How accurate is your TS ? lol . Proxxon needs to come out with a tilting blade . : )

View rance's profile

rance

4132 posts in 1812 days


#9 posted 08-14-2011 09:15 PM

Moment, You could make a tilting sled to accomplish almost the same thing. ‘Will do’ on the progress.

Joe, I’d use screws, not bolts. Much faster and less labor intensive. No holes to drill.

>“One heck of a lot of angle cutting…”
Have you ever built a house? The G. Dome method seems about par to me.

I like your idea about half lapping the corners. Actually, you gave me another idea. Build ALL the triangles with rectangular lumber, then once built, I could cut the bevels.

Also understand that the bottowm row that rests on the foundation is not naturally a flat line. Provisions have to be made for that.

-- Backer boards, stop blocks, build oversized, and never buy a hand plane--

View Joe Lyddon's profile

Joe Lyddon

7710 posts in 2703 days


#10 posted 08-15-2011 12:54 AM

rance,

”the bottom row that rests on the foundation is not naturally a flat line.”

I do not understand how that can be… each triangle has straight sides… straight sides on a foundation equals one straight side or flat side. (if the the proper angle is cut, of course). LOL

They are at a compound angle… Vertically inward… Horizontally inward… but seems like they should still be in a flat line… NO? By how much? Maybe they have to be Set with mortar like concrete blocks on the bottom edge?

OK, use SPAX screws instead of bolts… They’re good at drilling their own holes… I use’em from McFeeley’s… Love’em…

-- Have Fun! Joe Lyddon - Alta Loma, CA USA - Home: http://www.WoodworkStuff.net ... My Small Gallery: http://www.ncwoodworker.net/pp/showgallery.php?ppuser=1389&cat=500"

View rance's profile

rance

4132 posts in 1812 days


#11 posted 08-15-2011 01:10 AM

Joe, look carefully at the picture above. You can see that there is a slight zig zag. It CAN be flat, but it takes more work on that bottom row.

-- Backer boards, stop blocks, build oversized, and never buy a hand plane--

View Joe Lyddon's profile

Joe Lyddon

7710 posts in 2703 days


#12 posted 08-15-2011 02:04 AM

Yes, it looks like ALL of the lines are zig-zagging all over the place!

Weird…

Also looks like it might be easy to put groups of hexagons together then, arrange them around the bottom row, filling-in with single triangles between them…
Then, go on to the next row with another set of Hexagons & triangles…

Very interesting…

-- Have Fun! Joe Lyddon - Alta Loma, CA USA - Home: http://www.WoodworkStuff.net ... My Small Gallery: http://www.ncwoodworker.net/pp/showgallery.php?ppuser=1389&cat=500"

View rance's profile

rance

4132 posts in 1812 days


#13 posted 08-17-2011 12:34 AM

Joe, there’s a little bit of discussion of this problem at the following page:
http://www.geo-dome.co.uk/article.asp?uname=stressdome
Just past half way down the page. They try to fudge it out by distorting the dome, but I’d rather build special shims for that bottom row. That’s the right way to do it IMO.

-- Backer boards, stop blocks, build oversized, and never buy a hand plane--

View Joe Lyddon's profile

Joe Lyddon

7710 posts in 2703 days


#14 posted 08-17-2011 03:25 AM

Yeah… that’s probably the best way to do it… Seems Mickey Mouse though…

-- Have Fun! Joe Lyddon - Alta Loma, CA USA - Home: http://www.WoodworkStuff.net ... My Small Gallery: http://www.ncwoodworker.net/pp/showgallery.php?ppuser=1389&cat=500"

View Domerama's profile

Domerama

1 post in 948 days


#15 posted 02-11-2012 04:59 PM

Here something I put together as a 3V flat base calculator:

http://www.domerama.com/calculators/3v-geodesic-dome-calculator/3v-38-flat-base-krushke-calculator/

To get a flat base, use the Kruschke method. A regular 3V uses 3 lengths. Kruschke method uses 4 lengths.

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