I know this is probably sounds like a Breaktime question but Hopefully somebody has an idea here or even better the formula I seek.
What I want to do is create a dome in my tower.. Like Jeffersons’ Monticello my tower serves as a distribution room. Thus I thought i would pay homage to Jeffersons’ monticello and dome the inside of my tower..
I have a center light as does Monticello so the pssible similarity could be a real statement.
I intend to use hard maple and steam bend it into shape however I know that the pie shaped pieces won’t be a straight line if a want a true dome.. that curve should have some clever sort of formula behind it..
Does anybody know the formula or will I have to do my usual, which is climb up 18 feet, bend and bow pieces untill I figure out what needs to be done?
I can easily imagine how to do the blocking for backing needed, so all I reaaly need is that magic formula..
Replies
I would make a template frenchy with whatever dimensions I already know; you'll have to make one eventually for a proper fit no matter what the mathematicians say.
You only need 2 dimensions; the diameter of the dome and the radius of the rise; make 23 identical wedges at say 15 degrees and the closing piece would be a field fit.
Just a thought, you could probably make this dome entirely on the ground, attach a cable to the top and hoist the finished piece into position and anchor it.
Edited 6/14/2006 2:02 pm by skidkid
Skid Kid,
It would help if I had a starting point. If I make carboard templates they will flop around and be a real handfull. If I make templates out of something a little more substanual say 1/4 plywood they will be easier to work with but still a real wrestling match as I bend them into place to check fit 18 feet in the air.
Why not do it to scale on paper and then make a scale model 1/10 should be accurate enough to be able to get the full-sized dimensions right. OK, who are the analytical geometry and calculus experts here?
"I cut this piece four times and it's still too short."
An auto cad progam would be your best resource. Sketch-up is a free cad program available for Windows. You might try startng backwards with a large rubber ball and draw the lines radiating from the top down and razor the strips and peel it back to get a quick visual. A good geometry text book would be well worth your look and if anything would have this magic formula it would be there.
Steam bending maple is the hard way to go. There's bending plywood such as wacky board and bending poplar. You could veneer it later with maple. Definitleey check out the breaktime guys. Pretty advanced project you picked out for yourself.
RickL,
Cad program?
I can't even post pictures here and you want me top work with Cad?
No way will I buy bending board etc. Those are real black walnut timbers on the exterior, real white oak timbers on the inside.. real mortice and tenions real real real!!!
(besides I actually dreamt up this wacky idea as a way to get rid of some of my surplus maple)
I'm so cheap I squeak and the idea of me actaully paying market price for something like bending board makes my wallet quake <G>
You could cooper the pieces and make a sled for your planer that would hold the pieces at the proper angle (miter). You will need to know how many sections.
I would think of laminating the pieces in order to get some sort of regularity to the shape.
Michael Cullen wrote an article about coopering curves for such a project in Woodwork Magazine. If you want I could scan it and e-mail it to you if you like.
J.P.
JP,
There was a similar article in Fine wood working so I'm familar with the process, just lack the math skills to figure out how to do it..
I don''t think I'll want to laminate the maple. I was forced to on the curved roof on both my tower and the dormers..
My eves are curved rather than square the way a normal eve is. If you add the compound curve of the round tower with a curved eve the only solution is to laminate the black walnut strips. UGH!
it weren't fun a bit!
Shoot, Frenchy,
All that lumber you got piled around out there, why don't you just glue that thing up solid, and carve your dome inside and out, with a chainsaw--don't need no stinkin' geometry fer that. Better yet, spin it like a bowl, on a BIG lathe... use a scoop shovel for a gouge...no, a front-end loader bucket... big problems need big solutions.
Good luck,
Ray Pine
joinerswork,
Trust me, I actually considered that! Giant bowl!
As others mentioned this is too complicated to risk experimenting with wood. Make a template from heavy cardboard or hardboard. Then you can work out all the issues.
Mike
Pardon my spelling,
Mike
Make sure that your next project is beyond your skill and requires tools you don't have. You won't regret it.
I'll try to explain this in words Pictures are better. Best is to show you in person, but that isn't very likely. Do all this drawing to scale, rather large but it needn't be full size. You can scale it up.
Draw a profile of your dome.
Draw a vertical line from the tippy-top to the base line.
Divide that vertical into a bunch of increments.
Draw horizontal lines at each of these vertical divisions.
Measure the lengths of those horizontal lines from dome edge to dome edge. Now, these dimensions are diameters of the dome at the incremental elevations.Multiply these diameters by pi to get the circumferences. Decide on how many segments you're going to use.... divide this number into each circumference. Call these dimensions: w.
Looking at the dome elevation drawing, measure along the outer edge (your going along a curve) to each of the points where the horizontal lines you drew intersect the dome edge. The last one you measure will be at the tippy-top. To put this another way: you are measuring along longitude lines from the equator towards the north (or south) pole. You measure from the equator to each latitude line. Got it?
Get another piece of paper.
Draw a base line and a line perpendicular to it.
From the base line lay off all those measurements I just had you get.... you know... the longitude lengths.
At each point just marked, draw a horizontal line. That's parallel to the base line. These lines are centered at that vertical line and are as long as each dimension you calculated earlier: w.
Connect the dots. You will draw two curves that will form a curved sided triangle. This is your template.
Got questions? I'll look in again tomorrow (Friday).
F,
It can be worked out mathematically, but I'm not sure from your description what you're bending. Are you talking about bending vertical members of your framing, or horizontal members, or both? What is the actual profile of the dome, i.e., is it a hemisphere, or is it ellipsoid in shape? I might be able to work something out for you -- if I can clear the cobwebs out of my brain & find a few old text books, but would need to know more about the basic geometry.
After thinking about it (ouch! that hurt!) for a few minutes, the ellipse/ellipsoidal shape would be the more general case and the circular or spherical based dome would be a subset of that. Will see what I can come up with.
Edited 6/16/2006 8:33 pm ET by bd
bd,
thank you bd.. the ideas are that I will take a 12 foot circumference (6 foot radius) and put a hemisphere at the top of the cylinder..
To add to the problem there is a 2 foot octagon in the center to admit light from the copula however to make things simpler I will convert the octagon into a 2 foot circumference.
I'm math challenged. If I add two plus two the answer is variable. What I had planned on doing was climbing up there and figure the radius needed, come down and carve out the required # of ribs on a bandsaw (probably 76). I would then climb back up there and install them. Once installed I' plan on taking a stiff piece of cardboard and hold it into place while I trace whatever that curve winds up to be..
I know it should be some radius and my gut tells me it's really big one but lacking the math skills my crude and rude methods seems to be my only solution.
Opps! I forgot to mention that I'm putting up hard maple boards from sawmill thins (thins are boards of less than 1 inch thickness that mother nature was foolish enough to grow.
I don't yet know exactly how thick I'll use, it's a bit up in the air depending on a variety of things.. For example if I use 3/4 inch finished thickness will it steam bend flexibly enough to do the required compund curve, if I use say 1/4 inch while that may flex into position easier after steaming, maybe it will be too flexible and not produce a smooth curve..
Most of the boards will be around 6 inches wide so I'll start out with that as a standard. I have several hundred boards to choose from so I can waste a few trying.
I think it was last year I gave away about a thousand thins to people both cherry and maple.. when I finish this year I'll do the same..
Edited 6/17/2006 11:44 am ET by frenchy
20 something years ago we built a dome that sounds very similar in design to what you describe. About 20" octagon center, 8 curved trusses that framed into the octagon.We built it on the ground,hoisted it with a large chainfall that is still there.
The trusses were site built from plywood and covered with a sawn white oak 3/4"x10" planks. The underside was 3/8" x 6" white oak.2x4's were band sawed to a radius to get a fair curve between the trusses.These were installed on top of the trusses on 12" centers. 1/4" luan glued and stapled to the 2x4's. Then the pie shaped 1/4" maple plywood glued and brad nailed to the luan base.Everything was finished on the ground, the white oak and the maple ply were finished with shellac,orange shellac for the maple,blonde for the white oak.
The trusses were made by making a template of the arc using 1/2" thick mdf. The template was tacked to the plywood and cut in four passes with a router and top bearing bit. It took a couple of days just to cut the pieces as there were 96 pieces .The trusses were 6" thick,needed 12 pcs for each truss.We used a boat builders glue,CA glue I believe it was called. The trusses were also nailed and thru bolts that were counter bored.The connections from truss to octagon were special made steel connectors from 1/4" thick steel.
A chandelier hung from the octagon, the chandelier can be lowered and raised with a switch someplace in the room.Curved walls provided a resting place for the dome, the walls were framed but quite a bit of tube steel was added to support the weight .
If I recall the entire job took 5 weeks with myself and two other carpenters.This was built to be a home museum of some sort.
mike
frenchyThe pie shaped pieces you mention in your initial post are called gores. Probably the best example of these shapes is on a geographic globe, where the printing is done on the flat, then cut into gores and wrapped onto a basic sphere. There are other applications besides geographic globes that use gore shapes, and fortunately someone involved with concrete dome homes has been kind enough to generate a spreadsheet that calculates plot points for gores. If you go to http://www.axwoodfarm.com/house/DomePaper/index.php?inc=1and click on the “Spreadsheet” link, you can download an Excel spreadsheet that has calc sheets for oblate and prolate domes, and plots of the associated gores. Examples of oblate and prolate shapes are shown on the “Rotated-ellipse shapes” page of the site. As bd noted in his 30389.12 to you, a spherical dome is a subset of the ellipsoid. So if you have a 6 foot radius for your dome, I believe what you would do is use the first (oblate dome) sheet and plug in 6 for the lengths of BOTH half-axes and 76 for the number of gores. Note that for those inputs, the outputs "Cum L" and "gore width" are in decimal feet. You’ll need to convert that to whatever system of measurements you’re using. If you can do your measuring in metric, you could plug in 1.8288 instead of 6 and the output would be directly in meters, no further conversion required. I should probably note that I haven’t done anything with this myself, I just found the site interesting. So I can’t really guarantee anything, but it looks OK and maybe it will help.Dan
Edited 6/18/2006 5:13 pm ET by DanG
Not sure what the Prospero elves were doing. They deleted every return in the message and rendered it unreadable. All I did was hit Edit and Apply, and they put them back. Maybe they just borrowed them for a while. Or maybe they don't like Macs and Firefox. Anyway, sorry about the confusion.Dan
I'm pretty sure all the formulas you'd need would be in this book.
http://www.woodcraft.com/family.aspx?familyid=3417
I borrowed it from a neighbor (since moved) several years ago and it's stuffed with lots of diagrams, formulas, etc. for all sort of arched and curved work. If you've got a Woodcraft near you, it would be worth a look to see if answers your questions.
If you build it he will come.
Sounds like a neat project. What is the inside finish going to be? If you are planning plaster board and paint then I think the simplest way is cut as many ribs as needed to support the weight, and do some version of plaster and lath on the inside. Plaster will let you make as nice a curve as you wish to have and be one monolithic piece.
If you are planning wood strips and stain then that is a whole different set of trouble.
Jefferson was quite the architect and there must be books on Monticello and its' restoration/upkeep that would show how he did it.
Andy
"It seemed like a good idea at the time"
AndyE
It will be hard maple with a faux rail and style system done on top of it. (that is there will actually be wood rails and styles but they will be surface applied rather than used as a true panel construction)
I've got several books on the subject of Jeffersons Monticello, I realize it's pretty shameless of me to blatently steal ideas and then not even do them properly but maybe I serve a little less time in hell because I attribute it? <G>
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