I am about to start framing a number of arched ceilings and have a math question.
The arched ceilings are everywhere, they turn 90, 45, and 22.5 degree corners. I’m curious if any one out there knows the math to figure out the valley, or point of intersection. I’m cutting the 4′ radius out of 3/4 ply, so I would love to know how to layout the valley thats 45 degrees to the commons. Hope that makes sense. Thanks for any input.
jeremy
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practice with half splits of paper towel tubes, and an exacto knife..it all will be clear then.
Spheramid Enterprises Architectural Woodworks
Repairs, Remodeling, Restorations.
I seem to have lost Joe Fusco's website addy but somebody here should be able to provide it if he doesn't show up soon as screen name "Resurrected"
He is the grand master at this sort of thing.
Well, almost grand. He does make a mistake once evey year or so.
;)
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The "valleys" and "hips" are elliptical. If you have a quarter circle, then you need a quarter ellipse.
If you imagine it as a roof, it might simplify things. It does for me. Sounds like you already are.
If your "commons" are arches with a 4' radius, then your ellipse would have the same height, 4'. The run or semimajor axis would change though. If your corner is 90°, then figure your semi-major axis as the diagonal of a 4' x 4' box. It would be 5' 7-7/8"
Draw the ellipse with a 11' 3-3/4" semi-major axis. At the center draw a 4' line perpendicular to the semi-major axis.
If you have an intersection other than 90°, then you figure the diagonal similar to the way you would if it's an irregular roof, ie octagon hip (22.5°) has a run of ~13"
This is just an abbreviated post. You can get more info at http://www.josephfusco.org
I'm attaching a link to some pics of a cove ceiling that I framed a couple of weeks ago and a drawing of the ellipse. You can also go to Gary Katz's Carpenter's Gallery and see Ken Drake's work with groin vaults and other really cool framing details. Him and Joe, know way more than I do. Hope you enjoy yourself and please post pics when you can.
http://forums.taunton.com/n/mb/message.asp?webtag=tp-breaktime&msg=40266.1