I am lloking for a formula to figure out the ellipse formed by a barrel vault dormer as it cuts into the plain of a roof. The dormer is in a cathedral ceiling and I want the transition to be flawless. If you have any input, I will explain the details further if needed.
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Replies
Can you give me some more details? What's the slope of the roof plane? What is the shape of the thing that's cutting through it?
scott
I have wanted to do one of these for a long time. Take some pics, I'd love to see how you frame the transition.
What I would do to trace the ellipse is to take your width and then the height above the plates at the point where the roofs intersect and the with those two numbers you can layout the ellipse.
Do you know how to layout an ellipse?
An ellipse is a plane intersecting a cylinder at other than perpendicular. What's the radius of the barrel vault (you'll have to pick inner or outer radius) and what angle does the peak of the barrel vault form with the roofline?
Jes,
If you start the vault with a semicircle from the plate line the minor axis will always equal the radius of the barrel vault x 2. The major axis will equal the radius of the vault / Sin of the roof pitch angle x 2.
Minor Axis = R * 2
Major Axis = (R / SIN (roof pitch angle)) * 2
If you have a 5ft barrel vault and an 8/12 pitch roof you wind up with a minor axis of 10 and a major axis of ~18’
Edited 5/19/2003 11:14:48 PM ET by Joe Fusco
The handy ellipse facts that I remember:
1. There are two points on the major axis called Foci, and if you pin the ends of a string to the foci in such a way that it can be stretched tight to any point on the ellipse, then stretching it tight will reach every point on the ellipse.
2. If you draw a circle whose diameter is equal to the major axis, and whose center is at one end of the minor axis, it'll intersect the major axis at the foci.
So, to do this using plywood and string, draw the major and minor axes, or as much of them as you need. Put a small nail in one end of the minor axis, tie a string to it, and stretch the string out and hold a pencil at a distance equal to half the major axis. Use this to draw two arcs that intersect the major axis at the foci. Leave the first nail in, and put nails in the foci. Re-tie the string at one focus, stretch it over the first nail, and tie it off tight at the other focus. Pull the first nail, substitute a pencil, and run it around with the string stretched tight to draw one half of the ellipse. If you need the other half, stretch the string to the other side of the major axis and keep drawing.
-- J.S.
View Image
AWSOME !!!!!
How did you do that?
Yes, exactly. One picture is worth a thousand words. And a moving picture is even better than that. Can you add to the animation to show the pencil and string tied to the foci for drawing the actual locus of points that forms the ellipse? That would be even better.
-- J.S.
Er...ah....thats what I was gonna say. Seriously....you're my hero!
SHOW-OFF! Very cool, you rock, dude.
if you're looking for a very low tech way to figure this out-
determine the slope of the roof relative to the intersecting barrel vault, in other words, the angle at which they meet. then go to a art/architecture/drafting supply store and find the green vinyl ellipse template closest to that projection angle, if it's between two standard degree projections, buy both and split the difference in the next step- trace it out as big as you can on a piece of graph paper, have them blow it up if you need to (note- do not do this on a plain office copier- they distort images!) then lay out the appropriate sized matching grid on your roof and connect the dots just like they taught you to transfer/enlarge a drawing in woodshop back in junior high. (another possibility- some cad programs can probably draw an ellipse of a specific projection angle to match your roof angle exactly)
this is an oversimplification of the process but if you're smarter enough to actually build a barrel vault dormer, you should have no difficulty figuring out the details.
m