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Forum topic by Mike  posted 10012014 02:55 AM  1541 views  2 times favorited  23 replies 
10012014 02:55 AM 
Hi woodworkers. I’m looking for a little help calculating an angle. I know that if I wanted to end join wood pieces to make a circle I would count the number of edges ( the number of boards X 2) and divide 360 degrees by that number. I would then cut all the edges at that angle then when assembled they would make a circle. Now the part that I don’t know how to calculate. The inserted picture is a table that I like and would like to use this style to make several pieces. This is an arch not 360 degree circle. So how does one calculate the angle that I need to put on the edge of each board to make this arch. 
23 replies so far
#1 posted 10012014 03:02 AM 
Maybe this will help. You should be able to use this to figure out how many pieces of a certain size it would take to make a full circle. Once you know the total for a full circle you can calculate the angle using your previously mentioned method.  Bill M. "People change, walnut doesn't" by Gene. 
#2 posted 10012014 03:11 AM 
Since this arc is about at 25 degrees. All you need to do I divided the number of segments you want like described above. In the table above the legs were cut anywhere from 1.7 and 1.8 degrees each joint being around 3.4 to 3.6 Degrees, just figure how many pieces then divide. So 15 Pieces cut at 1.7 degrees would equal to 25.5 
#3 posted 10012014 03:20 AM 
Draw the profile you want to use to scale, then draw in the pieces you want to use, If its not a perfect circle, or portion of one, then no formula is going to work. (that I know anyway)  Because I'm gone, that's why! 
#4 posted 10012014 04:04 AM 
What dimensions do you know ? Do you know the radius ? If not, you can calculate the radius if you know the length of the chord (the distance between the top and bottom edges of the leg) and the height of the segment (the greatest distance from the chord to the arc). Once you know the radius of the circle, do you know the number of sections (the number of wood pieces) or do you want to calcualte the number of sections by knowing the approximate length of each section ? If you know the number of sections, you can calculate the total angle by knowing the radius and the chord length, then divide the total angle by the number of sections and, as you know, each individual angle on each edge would be half that. If, instead, you have an idea in mind for the approximate length of each section, you can calculate the length of the arc (which can be done now that you know the length of the chord and the radius and divide by the number of sections, then adjust the length to make it even. ..And now that you know the number of sections refer to the above paragraph for the angle of each section. So … what dimensions do you know and how do you want to figure the number of sections ? 
#5 posted 10012014 09:31 AM 
If you start by cutting your boards with the saw blade set at an angle of “a” degrees, you are cutting both edges of the board and you have “n” boards above the horizontal “shelf” piece that joins the two legs together. Then the angle to set your saw blade to cut the top board would be (2 x n – 1) x a. So, for instance, if you start by cutting your pieces with an angle of 3° on your blade and you have four pieces above the “shelf” piece, the blade would be set to (2×4 – 1) x 3° = 7×3° = 21°.  I may have lost my marbles, but I still have my love of woodworking 
#6 posted 10012014 12:47 PM 
This seems like a perfect time to learn sketchup if you don’t already know it. Otherwise, math it out like Yonak said. The problem with just cutting everything to the same angle is that some pieces are wider than others. If you cut them all to the same angle, you’re not going to get a nice smooth curve. The shorter pieces would translate to a smaller radius than the long pieces would.   The mightiest oak in the forest is just a little nut that held its ground. 
#7 posted 10012014 12:50 PM 
I’d do what Yonak suggested as well. If you get the dimensions he cited, you can even a use a website like this to do the math.  Our village hasn't lost it's idiot, he was elected to congress. 
#8 posted 10012014 02:34 PM 
Mike once you’ve got the angles mastered, for a bit of fun and adventure, you may consider manipulating the design something like this to add a little strength and maybe some interesting wood contrast design : I hope you can make it out .. just a quick sketch in CAD. The curved panel is glued up and then sliced into three sections and the middle section is rotated a bit. ..Just an idea . . . 
#9 posted 10012014 02:38 PM 
Sorry – I misread the original question. In the image shown, Angle = 180 – 2 x arctan(Height/(2 x Depth)) Now decide how many boards you want to use to make the arc (well, half the complete arc since the angle is from the horizontal line upwards), then divide Angle by the number of boards x 2 – just the same as you would for a full circle. But beware, this works for boards that are the same width. In the picture that you posted, the light and dark strips are different widths. Do you wish to have different width boards? If so, I will need to think about it a little more – but tomorrow as it is midnight for me right now and I must be off.  I may have lost my marbles, but I still have my love of woodworking 
#10 posted 10012014 03:21 PM 
For the sake of simplicity and a smoother curve, you may want to make all of the strips the same size, and if you want thicker bands of a certain color, just double up the strips of that color. You could be picky and mark the strips in order as they’re cut so you can have a closer grain match when you put them consecutively. P.S. Tommy Mac did a glueup like this when he built the coopered leg table. You might try his approach. He just made a form out of plywood, and then did trial and error on scrap until it sat right in the form. Worth a look, it takes all of the math out of the equation.   The mightiest oak in the forest is just a little nut that held its ground. 
#11 posted 10012014 03:33 PM 
Here is another method for you if you draw it out.  Because I'm gone, that's why! 
#12 posted 10012014 05:24 PM 
Wow, This is the first time I posted a question and I’m very impressed with the great advise. Thanks to everyone who posted solutions. I have a bunch of scrap wood and was getting tired of just making cutting boards and the picture I saw of a table and chairs got my mind working overtime. I think that I will start with a piece that has boards of equal widths so my first attempt at the math will be a bit easier. The input and direction you guys have given my should help me move from building on one plain to creating on the arch. THANKS AGAIN. 
#13 posted 10012014 05:54 PM 
How do you plan on doing the glueup?   The mightiest oak in the forest is just a little nut that held its ground. 
#14 posted 10022014 04:54 AM 
Good idea Ed.
Now you’re just being difficult ;). Okay, not really – it’s is a very good question that Ed has asked Mike. It is well worth thinking that through right up front.  I may have lost my marbles, but I still have my love of woodworking 
#15 posted 10022014 12:40 PM 
I’m not in any way affiliated with TMac in any way except that I enjoy the show…but it’s worth googling the coopered leg table. He does a glue up just like yours, just about 5x bigger. I uses a for and gets all the pieces wedged in.
Maybe :) But probably not as difficult as not having a glueup plan! That’d be moronic. Probably something I would do.   The mightiest oak in the forest is just a little nut that held its ground. 
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