Interior Dome. I need ideas and photos

[Dragon]

I have a customer that is planning on putting up a plaster dome in a foyer. I am trying to talk him into letting me build one for him out of oak, but I need some photos for reference. So far my googling is not returning the results I'm seeking.

So, anyone know where I can find some pics?

:D

[Rich]

I wish ours was done :)
Will you be veneering a dome structure?

[Dragon]

Basically, or bending bending bending.

Its about 6' in diameter.

I can't find a single photo on the net anywhere.

[Joe Bartok]

I can't find anything either!
I've found geodesic domes, mosques and minarets, igloos (those are definitely out of the question), and photos of the exteriors of domes in G :? :? gle images. But no photos of interiors in a more "modern" style.
And I thought it was possible to find ANYTHING on the Internet. :?

[Joe Bartok]

Dragon, what kind of a dome are you looking for? From your question ("dome in a foyer"), it sounds like two arches meeting along a ridge. Or is it a dome with a rectangular base, or a circular base, with the arches meeting at one point?
As far as a working description of a layout goes, I haven't had any luck yet. The information I've found so far is either common knowledge (domes are spherical, elliptical, etc), or on the other extreme, the descriptions are so technical they're no help at all.

[Rich]

The problem with veneering it is that's it's fairly difficult to get it to bend in 2 directions without an excessive amount of fitting. Ever seen a globe cut so it'll lay flat? That's about the same way the veneering would need to be done. The one we're doing is about 8' in diameter and is going to be done like the globe (if the owner doesn't cut it from the project) - the biggest issue here is cost. Compare a wood dome to a plaster dome - I would imagine a wood dome is 10 times the cost if not more :)
I couldn't find any actual pictures of a dome either - except for the geodesic stuff Joe mentioned.

[Joe Bartok]

Yes, the same problem map makers have! Kind of like the proverbial square peg in a round hole problem, except this is in 3D. Bending transverse pieces and arches doesn't sound too difficult, but veneer curving in more than one direction is a different proposition.
There's got to be a way, though ... I'm off to check out some websites on how to build wooden boats and canoes ...

[Tom R]

I'm thinkin' off the top of my head that it would want to be done in at least 4 'cone-shaped' pieces with convex sides and bottoms.

[Dragon]

Something like this.

http://www.imperialdesign.on.ca/ELEMENTS/DOMES/dome-grgcoff/domegrgcof.htm

So far that is the only one I have been able to find.

6' diameter circle

[Joe Bartok]

Dragon: Too bad I don’t have a digital camera, or you would have your photo of a dome. Not as grand as the images of the architecture on the Internet, which I didn’t have access to yesterday, so I surfed the “innernet” instead. My dome is a mere bristol board model, but it demonstrates the principle in fact as well as theory. I’ve attached a Word file (pdf tomorrow) of how it was done, and you can see for yourself that the numbers make sense. It’s not difficult, and obviously this has been known for centuries, all I’ve done is re-invented the wheel. The curves were hand drawn, and the remaining five templates traced from the original, so there were minor cumulative errors in the model. (The sections were developed to three times the scale in the table in centimeters, so even a half a millimeter of inaccuracy had an effect.) Still, the results were satisfactory.
As you may expect, the larger the section, the easier it flexed. Bending was easier near the narrow peak, a little more difficult at the base because the length was relatively short. If it’s necessary to bend the sheets in advance, it isn’t too difficult to make an inexpensive jig, but the effect that steaming will have on the veneer finish, glues, etc, well, I haven’t got a clue. A slight ridge also formed at the seams between the sections, but it’s not objectionable, and I assume there’s going to be trim hiding the joints anyhow.
A couple of other things: The curve is a sinusoid; entering the formula I’ve used in a graphing calculator and invoking the “trace” function is another way to plot points (I didn’t actually try this, the calcs were done on a basic scientific calculator). The “stretch” for the height is easy to calculate, and for those who don’t like trig, it’s possible to determine the widths for the development graphically. This isn’t shown on the diagram, but if anyone’s interested, just say so, and I’ll explain how when I get back tomorrow. Final thought; the horizontal and vertical sections need not be equal or circular. The dome can be a circle in the horizontal section, and parabolic on the plumb view, and it’s just as easy to calculate and develop. (I have programs that will crunch the numbers for elliptic and parabolic arc lengths).
Sorry, I didn’t intend to turn this into an “essay”, but hopefully this information helps.

[Dragon]

No apology necessary Joe. I enjoy your posts, namely because you usually 'say' what I 'see' in them.

I am what is known as a visual mathmetician. I can 'see' it all in my head. I have trouble explaining it to others though.

Its nice to meet a peer.

[Joe Bartok]

Well, it’s good to know someone’s enjoying my “essays”. :) And a good thing the math for construction is visual (whereas the same math applied to electronics is very theoretical), it sure makes communication of ideas easier. We could use a visual medium now, and I really wish I could post a photo of my model, since it would have spared typing out the following description.
The last post was typed in haste, and I intended to mention that in addition to the slight ridges at the joints, the peak of my cardboard model tends to come to a point. Not as pronounced as seen in Muslim or some Russian buildings, where it was done on purpose, but it’s there in my model nonetheless. Meanwhile, on the circular base where the center of each section is attached, the material is slightly dragged upwards, creating a bit of “waviness” around the perimeter. My “intuition” says it’s natural tension, since the pieces want to return to their natural flat configurations. This isn’t a big deal, in the real world these minor incosistencies would be covered by trim. And if it is tension, it would be working in our favour anyway. The veneer would be flexing the roof upward, adding it’s two cents worth toward doing what a dome is designed to do.
Or, does the math need a bit of tweaking? When I first looked at the geometry for the sphere, I reasoned that the distance from the “pole” to “equator” was always equal. But the same is true for a cone. So, if anyone’s interested, take a look at the Development of a Cone pdf in the Math Questions forum, on the last (fourth) page. There’s certainly a radius involved in the development in this case, yet the distance from “pole” to “equator” (vertex to base) is consistent for a cone as well as a sphere. So, should the reference line, and all lines parallel to it shown in the diagram for the Development of a Sphere have a slight radius rather than being flat as currently drawn? I think so! It would have to be, to keep the distance from the peak of the dome consistent to the circumference. And is it that simple? Since we’re dealing with curvature on more than one axis, the edges turned out to be sinusoids. Perhaps the same is true for the bottom edge as well? But whether this curve turns out to be a radius or a sine wave, in either event the sections are effectively lengthened, contributing to more of a “peak” at the ceiling. Or so it seems, perhaps the greater length will permit the sections to bow to more, creating a smoother circular arc at the dome.
For the mathematicians among you, something to consider. And as sometimes happens, this wasn’t as easy as I thought, and it seems I’ve been caught with my pants down! But then, that’s why it’s generally a good idea to make a scale model to test the theory. Looks like it’s time to make another one.

[Dragon]

Enjoy.

The customer likes my idea and I will be fabricating a coffered dome like the one in the link I posted above. It will have a 6' diameter and a 2' rise, creating something of a bowl shape.

I'll post pics of the finished project. I'm looking forward to this one. I get to do something different for a change.

[Rich]

Right on.. the challenge of construction is what keeps me going. Anxiously awaiting the images :)

[Joe Bartok]

Looking forward to your images as well.
To make a long story short, I tried out my "new" model of a spherical dome, and found more flaws. There doesn't seem to be a quick-and-dirty way to do this, and now have some appreciation for what cartographers have gone through for centuries to create their maps. And why there are so many projections, none of them "perfect".
Perhaps the best way is to cut the section out of a hollow rubber ball, flatten it out, and trace it. Draw a grid over it, and transfer the drawing to a larger scaled grid on the work. Well, it was fun trying!

[Dragon]

Since I'm going coffered I don't have to. Build the rectangles, fill in the rectangles.


And the really fun part is that I'm going to get to teach people how to bend wood on two planes!

:D

I've got to go buy more clamps.

[Sweep]

A true dome is technically a structure on the exterior of a building and the false-work or ceiling inside is a vault. The architectural term for what you want to do is a "ceiling vault" or a "vaulted ceiling" more specifically a "domical vault" or a "cylindrical vault" depending on whether it starts on a square of round base. Perhaps this will help with your internet search.

Of course, it will probably get you a lot of historic examples.
http://www.archives.gov/exhibit_hall/designs_for_democracy/symbols_and_substance/articles/hall_of_representatives_improvements.html
http://www.generativeart.com/salgado/salgado.htm
http://www.generativeart.com/salgado/anamorphic.htm

Armstrong makes a vaulting system:
http://www.armstrong.com/commceilingsna/article17392.html

Flex-C Trac makes a flexible metal stud track
http://www.proplaster.com.au/FlexCTracProdCatal.htm

And some people just can't enough of curves (Flex-C Trac)
http://www.domeofahome.com/gallery/picture_details.asp?ID=1319

[Joe Bartok]

Dragon: The question of framing a groin vault came up in another forum. I thought this might interest you as it’s related to your query:
Geometric Method of Framing a Vault (http://ca.geocities.com/web_sketches/cross_vault/Vault_Purlin_Development.html).
Everything can be achieved with nothing more than compass and a straightedge. String, nails and a framing square are optional. The Pitch Angle at each point is easily determined as per the sketch of the ellipse. The developments are simply a section of a typical Hip roof laid out flat. This is likely how timber framers of centuries ago determined miter angles for vaulted ceilings. For folks who prefer to calculate the angles there’s a link in this weblog to a somewhat overthought trigonometric resolution (actually, that my first solution).
More information and drawings will be added in future detailing the math involved in Developing Curves on the Faces (http://ca.geocities.com/web_sketches/cross_vault/Vault_Surface_Developments.html) of the finish material; for example, two intercepting circular sections produce an arrcosine curve. The numbers will pretty much remain in the realm of theory. In practical terms it looks like the best way to develop the curves is by transferring measurements and projection.

EDIT and CORRECTION: I goofed! I went over the math again, and that curve developed on the face of the finish material is an arcsine curve. Sketches have been added to the Developing Curves on the Faces web page to complement the information in the table.