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I was just reading about all the different ways carpenters find and make the radius of an arch in some old question dated Jan. 1. I laughed, but was also worried that so many people were using such complicated techniques to do something so simple. I think my method(i did not invent it),is so easy, everyone will put down their chaulk lines and construction masters… Here goes: Measure width of arch(chord), measure max height perpendicular to chord. Layout on plywood with three nails marking width and max height, they make a triangle. Take two straight boards, align one with two nails, Screw second board to the first at the top, perpendicular to chord(think about it). Stick pencil in corner where boards are connected, also location of nail marking height of radius. Move rigidly connected boards along nails, never leaving contact with two. You must do this in either direction. Cut it out, trace it, framing it, install it. This yields arch with no big swings or centering or advanced mathmatic maneouvers… Good luck…
Zap
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here's the summary of what i contributed:
"... r = d(squared)/2H
where
H=height of ellipse
d=length of diagonal from top of ellipse to end of chord
this equation gives the right result in as simple terms as possible...
practical example...
for an ellipse window above a door, make a point above the door representing the desired height of the ellipse window, then measure to a point of your chosing for the lower corner of the ellipse window (practically speaking, this would be in-line with the outside edge of the door). this is "d".
make a level line above the door off your window lower corner mark. with a square, measure from your height point down to the level line. this is "h".
square the diagonal measure and divide this by double the height measure.
this is your radius.
and here's a way to remember it...
square one,
square off the other,
double and divide. "
how complicated is that?
isaac. can you provide a picture or drawing? i'm having difficulty visualizing. sorry.
let me ask you something. using the approach i've described, one can simply determine what size glass to order to fill inside an elliptical frame, because a new radius for the glass can be simply determined without layouts.
i honestly tried to distill everything that i read in the thread to offer the simplest solution. still think it is...
brian
*Brian:I use your method all the time....one correction though....it is not the height of an ellipse, it is a segment. An ellipse has a constantly changing curve with a semi-minor and a semi-major axis. A segment is the part of a circle cut off by a chord. That formulae given will not work for an ellipse.Not trying to be picky, ok?Back when I would make curved trim, I would go out and measure for an elliptical window.... and then find what they meant to tell me was that they had a circle top window instead. :)
*you're right, of course. i meant arch...brian
*Brian: I knew what you meant. I used to keep calling the axis lengths of an ellipse the major and minor axis....until Joe Fusco corrected me into calling them semi-major and semi-minor axis.