I want to take a 4×4 (3-1/2″ actual) and saw it into an octagon with equal width faces. How wide will the faces be, and how do you calculate that?
Do it right, or do it twice.
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Come in about an one inch from each corner and that will leave you with 8 equal sides of +- 1-7/16. The faces are actually 1.4497" which is between 7/16 and 1/2.
As far as how I got the info I cheated and used Acad.
Last fall there was an article on laying out octagons with a framing square. I showed how to use the octagon tabless on the leg of the square.
The next issue had letters to the editor giving two mathematocal solutions to your problem.
JIm
I remember those articles. But I don't remember where I put those issues. I do seem to remember that more and more I remmeber less and less. Uh, what was the question?
Do it right, or do it twice.
Elcid,
Another way to figure the sides is:
3.5/2 * sqrt(2) - (1.75) * (2) = 1.449747 (Length of all 8 Sides)
3.5/2 = 1.75 * sqrt(2) = 2.47487
2.47487 - 1.75 = .724874
.724874 * 2 = 1.449747
If you want to figure how far to come in from the corners you can use this:
3.5/2 * sqrt(2) - (1.75) * sqrt(2) = 1.02512 or 1-1/32" (Come in from each corner)
1.75 * sqrt(2) = 2.47487
2.47487 - 1.75 = .724874
.724874 * sqrt(2) = 1.02512
If you have a Construction Master Calculator to figure the length of the sides you can do this:
22.5 [Pitch]
1.75 [Inch] [Run]
Press [Rise] Returns - .72487
Press [x] 2 = 1.449747 (Length of all 8 Sides)
Joe Carola
Elcid,
My first post to you to figure out the sides was this,
"For any Octagon wether it's a block in your case or a room all you do is take 1/2 the span and multiply that by the Tan(22.5) *2 = .8284."Your 4x4 block is 3-1/2".
Tan(22.5) * 2 * (3.5/2) = 1.449747
For your 3-1/2" Octagon Block you don't have to take half the span to figure the sides, you can take the Span Multiplied by the Tan(22.5).
Tan(22.5) * (3.5) = 1.449747
Joe Carola
Elcid,
The numbers and dots on the Octagon scale on the framing square represent inches. For your 3-1/2" 4x4 you can take your compass and set the one end on the first line which represents zero and then set the other end in between the 3rd dot and the 4th dot and that represents 3-1/2".
Mark the centers on your 4x4 and then take the compass and start from the center marks and scribe and arc on each side of the center mark. The width of the compass represents half the length of your sides.
Another way to do it without the octagon scale is to draw diagonal lines from corner to corner othe top of your 4x4 and then use a 4x4 drop off piece or cardborad cut out 3-1/2" x 3-1/2" and mark 1-3/4" all the way around and and lay it on top of the 4x4with the 4 corners of the drop off in the middle of the 4x4 and just scribe.
Joe Carola
Elcid,
For any Octagon wether it's a block in your case or a room all you do is take 1/2 the span and multiply that by the Tan(22.5) *2 = .8284.
Your 4x4 block is 3-1/2".
Tan(22.5) * 2 * (3.5/2) = 1.449747
Tan(22.5) * 2 = .8284
(3.5/2) = 1.75
.8284 * 1.75 = 1.449747 or 1-7/16 - 1-1/2" (All 8 Sides)
Joe Carola
how do you calculate that?
Oh, it's in the back of Architectural Graphic Standards, and uses a pair of dividers, and escapes me just now.
I cheated, AutoCAD tells me the flats are 1.4498" and are 1.0251" from the edges (shy of 1 1/32" from edge, with a flat about 1 7/16" wide).
I dont have a way of drawing the octagon. But visualize the cuts you are going to make as a the hypontenuse of a right triangle with each side equal (side x - side x - hypontenuse y). The following formula is x + sqrt(x times x + x times x) + x = 3.5 inches.
Solving for x by trial and error x is 1 1/32 and y is 1 7/16
This is pretty funny, there is another thread regarding octogons.
here is a pretty cool cheater for you.
Just what you need, I think.
Check it out
Here's the easiest and most straightforward formula I've come across:
The length of one side of the octagon is equal to 0.828 times 1/2 the width of the original square. Or more succinctly:
S = 0.828r
Where S is the length of any side of the octagon and
r is the radius of a circle that will fit inside the original square.
You can always turn any square into an octagon simply by drawing it.
The most simple way is to look it up, and find out how to use the octagon scale on your square. Then it can be done on site, with nothing more technical than a compass and your rafter square.
Actually, come to think of it, the most simple way is to ask here, and have somebody tell you. ;^}
There was a thread that asked some questions about a carpenter test from the 60's that gave you the ratio of 2.414. With the question of what is it used for.
3.5 / 2.414 = 1.4498
excuse me I meant factor.
Edited 11/12/2003 9:52:06 PM ET by benny