# How to calculate pieces to build a segmented arch?



## newTim (Jul 11, 2008)

Does anyone know how to calculate the dimensions and glue (joining) angle for straight pieces from which to cut a segmented arch? Here's a picture from a Sketchup model. I think (hope) all the required information is here.

I guess what I'm looking for is a way to use the dimensions of the segmented arch to derive the size and number of pieces that need to be joined in order to have enough area from which I can cut the arch.

I'm thinking there is a formula somewhere that is easier than just drawing lines until it looks right. This would also be helpful for calculating the size, number, and dimension required for segments to make circles.

As you can see (read), I don't even know the correct words to use to ask the question. I need to join two or more pieces to form one part from which I can cut an arch. Given the dimensions of the arch is there a way to calculate the dimensions of the required pieces? I know I've come to the right place. Many thanks.


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## GaryK (Jun 25, 2007)

No SIMPLE way that I know of.

I would just cut up pieces of cardboard and overlap them on a table. Then just adjust them to fit.

But, I'm not sure if this is what you are actually asking. It's just what I got from your post.


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## newTim (Jul 11, 2008)

That's how I do it now. Actually, now that I'm in Sketchup I can use that. The wider the boards you use the easier it is to fit, so I guess what I'm looking for is the narrowest board that can be used to form the arch.


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## Catspaw (Dec 15, 2007)

One thing I learned in all my experience was that imperial measurement is usually the best.

Using Sketchup, figure out a nominal length of board….something you'd use for one segment. Looks like you might use a 7" to 8" segment.

Let's use 8" inches 'cause it's easier. Draw a vertical line 4" to the left and 4" to the right of the vertical centerline. Connect the intersection of the left vertical line and the lower radius with the intersection of the right vertical line and the lower radius, using a horizontal line. Measure from the apex of the upper radius down to the horizontal line. Add some for waste.

General idea works for longer segments.

Most people would just glue two straight boards together to make a 12" or so wide board and wack it out. But, If you really want to see the segments then I guess that wouldn't work.

BTW, the narrowest board you could use is just what you placed in the drawing…..7 1/2". You'll have to make a whole lotta segments….but, that's the narrowest width.


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## RedShirt013 (May 17, 2008)

I did a quick sketch and assuming that is 11 7/16" on the right there, the inner radius would have to be ~13-1/16" for this to look like your picture. Correct me if Im wrong
I don't know of an easy way either, but it seems more practical if you determine the board size you are using first then figure out the # of pieces and angle, or the # of pieces then figure out the min width and angle. If you don't care about the grain you can make it out of as narrow strips as you want, but the difficulty of the angle cuts and the waste would offset any saving from optimizing in material width.


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