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Old 12-22-2009, 09:45 AM   #1
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Matching an arch


I'm going to build a built-in bookcase and I need the top to match the arch of the opening in the picture. What is the best way to match the arch? I know that there is math involved, but I really have no idea of how to begin.

I swear that I saw Tom Silva match an arch on This Old House a few weeks ago with two right angle squares clamped to a board, but I didn't record the episode.
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Old 12-22-2009, 09:47 AM   #2
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Matching an arch


Cardboard template would work
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Old 12-22-2009, 09:50 AM   #3
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Matching an arch


Yeh, cardboard or maybe a piece of luan (thin) plywood. I'd love to see how anyone can match an arch with a board and two squares. Thanks, David
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Old 12-22-2009, 09:52 AM   #4
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Matching an arch


I'm with dave and thurman. cardboard or thin luan butted to ceiling
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Old 12-22-2009, 10:29 AM   #5
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Matching an arch


Just to clarify, I want the top of the bookcase to match the arc of the arch of the existing opening. I can't use the existing arch as a template because it is seven feet wide, and the bookcase will only be two feet wide.
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Old 12-22-2009, 10:37 AM   #6
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Matching an arch


This should help
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Old 12-22-2009, 10:50 AM   #7
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Matching an arch


I think that I found it.

http://tomkile.yourkwagent.com/atj/u...o?pageId=89811
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Old 12-22-2009, 11:15 AM   #8
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Matching an arch


Since the width of the bookcase is different than the width of the opening, I assume by matching the arch you mean you would like the radius of the top of the bookcase to match the radius of the arch. The arcs would be different, because the subtended angle would be larger for the opening than for the bookcase.

To calculate the radius of the arch, you need to measure the width of the opening W, and the height of the opening H. H is measured from the top of the door frame to the top of the arch, in your case it looks like about 8 inches or .67 feet. Make sure your units are consistent, i.e. either measure entirely in feet or entirely in inches. The radius R of the arch can be calculated by using the formula

R = H/2 + W^2/8H

where the ^ means raised to the power, so this means W squared.

Example:

Your width is 7 feet, your height H is 9 inches (.75 feet), the radius of the arch is .75/2 + 7^2/8*.75 = 8.54 feet. You can then lay out the radius of the arc for the bookcase.
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Old 12-22-2009, 11:19 AM   #9
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Matching an arch


I assume you mean the distant arc in the photo.

The radius calc. assumes the existing arc is part of a circle. How do you know it is not part of an ellipse?

I'd make a template just to use to determine what sort of curve you have.

Also, whatever curve it is may not scale; that is, the visual effect may not be the same in smaller sizes.

Last edited by Yoyizit; 12-22-2009 at 11:22 AM.
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Old 12-22-2009, 12:04 PM   #10
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Matching an arch


why can you not use the top of the elipse that works between your dimensions if you are trying to duplicate that exat radius, otherwise it will have to be different
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Old 12-22-2009, 12:24 PM   #11
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Matching an arch


Measure the bottom of the distance across the opening. 1/2 that distance should be the arc. Use a pencil and string tied to it, the string the length of the arc. Lay this out on a piece of cardboard if you wish to verify, but this will duplicate the arc of the doorway. Use the pencil and string to put the marked arc on the wood for the bookcase; works every-time!

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Old 12-22-2009, 01:03 PM   #12
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Matching an arch


tedmc, the method you used will give you half the chord, not the radius of the arc. See my previous post to determine the radius.

If the curve is an ellipse, it is much more difficult to do the mathematics to duplicate the curve, previous techniques using a cardboard template would then be easier. One of the posts noted, quite accurately, that extracting a piece of an arc or part of an ellipse, as you are intending to do, may not look right visually. Simply matching the radius can produce odd effects based on perspective, however it is a relatively simple method for matching a curved surface.

Also note that even if the curve is an ellipse, computing the radius using the circle formula and cutting an arc will not make more than a very small difference versus trying to duplicate a piece of an ellipse, and I doubt you will be able to tell the difference between a two foot wide arc of a circle and a two foot wide piece of an ellipse.
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Old 12-22-2009, 03:26 PM   #13
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Matching an arch


I worked in a custom millwork shop for a year and I would guess thats an elipse he is trying to duplicate vs a half circle radius like the arch in the doorway he took the pic from. still think the template easiest for duplicating that shape. I agree with daniel at 2' unless they are right next to each other will be hard to see the diff
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Old 12-22-2009, 05:26 PM   #14
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Matching an arch


I think the answer to all of this is nothing more than a simple calculation. Take accurate measurements on your opening that you are duplicating. You'll need width(a) and rise(b). You'll also need to determine the actual width that you are going to make the bookcase(c). Then make a formula to actually find the height of the geometric shape which we'll call d. So you should have a/c=b/d. Work out the math and you should have a exactly proportionate geometric shape. I remember seeing This Old House do a short blip on an ellipse but all the dimensions were already known. There are also methods for doing arcs that you can find on the internet. I think once you have your dimensions you should be able to do the rest.
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Old 12-22-2009, 05:38 PM   #15
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Matching an arch


Personaly, I would take a 2 foot wide piece of cardboard, center it in the opening, and trace the arch. Then transfer it to your project.
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