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Octagon Question

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Blog entry by GaryCN posted 2203 days ago 5010 reads 1 time favorited 16 comments Add to Favorites Watch

For a landscape project I’ll be cutting an Octagon from 4” X 6” X 12” timber.
To get one octagon from 12’ how do I calculate the length of one side to minimze waste?
By flipping the board how much longer than 18” can I go?

-- Quando Omni Flunkus Moritati



16 comments so far

View lew's profile

lew

9954 posts in 2359 days


#1 posted 2203 days ago

View Russel's profile

Russel

2199 posts in 2542 days


#2 posted 2203 days ago

Hey!!! I thought this was a woodworking site. What’s with the math problem? And a story problem no less.

Actually, I’m glad you asked and Lew posted the links because I’ve been looking for a reference to keep handy.

-- Working at Woodworking http://www.VillageLaneFurniture.com

View OutPutter's profile

OutPutter

1194 posts in 2594 days


#3 posted 2203 days ago

That sounds like a trick question but it’s actually quiet simple. The outside perimeter is the longest distance your octagon can occupy. So, divide 12/8 and you will get the longest “equal length” sides. That length is 18”.

The amount of wood that has to be removed to get the board to “wrap” around into an octagonal circle depends on which thickness you use – either 4” or 6”. Ultimately the waste depends on your definition of waste. If you want to minimize the amount of wood removed from the timber, you will have to do some math, if you just want the longest outside perimeter, it doesn’t matter which thickness you use. For stability of whatever you put on top of the perimeter, use the 6” thickness.

-- Jim

View FlWoodRat's profile

FlWoodRat

732 posts in 2512 days


#4 posted 2203 days ago

OutPutter’s explaination is great. The length of your piece of wood is the only limit you have. Given you want 8 sides of equal lenth, then divide the board lenght by 8. Cut your angles at 22.5 degrees (lefts and rights) at your calculated length. If you managed to get 17.75” inch sections, then your OUTSIDE perimeter will be 142 inches. The INSIDE perimeter wll be based upon the thickness of the timber. The thicker your timbers, the smaller the inside perimeter of your octagon.

-- I love the smell of sawdust in the morning....

View davidtheboxmaker's profile

davidtheboxmaker

373 posts in 2409 days


#5 posted 2202 days ago

If you resaw the boards you can get up to 36” sides, but will they be thick enough for the load they may have to bear?

View Ben Griffith's profile

Ben Griffith

50 posts in 2283 days


#6 posted 2202 days ago

No, not that simple… as Gary noted you can go longer than 18” by flipping over the board with every cut, so the only waste is a triangular piece at each end, instead of a triangle between each piece.

If the sides are 4” thick, they’ll be about 19 3/4” long on the outside and 15 1/4” on the inside. If the sides are 6” thick they’ll be about 20 3/4” long on the outside and 14” on the inside.

Quick explanation is I used trig to figure out what the difference between the inside of a side and the outside of a side would be, then called the short side X and the long side X+difference, and figuring there are four of each along the 12 feet (minus a scrap at the end which happens to be half of the difference long) solved for X. I’d upload a drawing, but I can’t from inside the corporate firewall.

However, it would make a whole lot more sense to use a rafter square and a tape measure instead of trig and algebra. The ends of each board will be cut at 22.5 degrees. Use a rafter square to mark a 22.5 degree line on one end of the timber, so you’re cutting off a triangle. If you cut that triangle off (and you don’t have to yet, it’s just easier to explain this way), one side of the timber will be shorter than the other, right… so measure that “short” side. Divide that number by 8 and call it X. Now shift your tape measure over to the “long” side and make a mark every X, starting at the end where you cut off the triangle. Now, on the 2nd, 4th, 6th, 8th marks, use the rafter square to make a 22.5 degree line, slanting the same way as the first one you made. Then use the square to extend the other four marks to the “short” side, and on each of those make a 22.5 degree line slanting the other way from the others. Now just cut on the lines, and center the kerf on the lines.

Double check it before you cut the first time… I’ve only just done this on paper and wouldn’t want to be the cause of a wasted landscaping timber!

-Ben

View BroDave's profile

BroDave

107 posts in 2417 days


#7 posted 2202 days ago

To answer the question;

By flipping the board how much longer than 18” can I go?

You will not be able to get 8 – 18” cuts from a 12’ board/timber.
You can get 8 equal lengths from the board.

To know the length of each section you simply need to take the total length of your board minus the thickness of your saw blade multiplied by 8. This will give you the length of each of the eight sides.
1/8” kerf X 8 = 1”
A board that is 12’ long = 144”
144 – 1 kerf = 143
143 divided by 8 = 17.875
So, each side will be 17.875”

For example;

If it were me, and it ain’t, I would cut 8 – 17” pieces and then cut them on a 22.5 degree angle from the long side, just to simplify things.
This should give you an octagon that is 3’ 5 1/16”

You can check the numbers at the first link in lew’s post to make your finish calculations.
http://www.pagetutor.com/octagonlayout/index.html

The saw kerf makes a little difference in a 12’ octagon, it makes a lot of difference in a 12” octagon.

-- .

View GaryCN's profile

GaryCN

277 posts in 2538 days


#8 posted 2202 days ago

Thank’s to all for the tips, I’m cutting this with the 6” width at the height BroDave your tip
seems to be the easiest 17” or 17.5” That will make handling this easier, But when I input
1’ 3” into (B) in the Octagon Calculator it twlls me (A) will be 3’ 1” thus making me come up
4” short. But all the info has helped. I’ll lay it out today and see how it goes.

-- Quando Omni Flunkus Moritati

View BroDave's profile

BroDave

107 posts in 2417 days


#9 posted 2202 days ago

Gary, the number to use in “B” is 1’ 5”

1’ 3” is only 15” total.

-- .

View Ben Griffith's profile

Ben Griffith

50 posts in 2283 days


#10 posted 2202 days ago

I know my solution sounded the most complicated, but if you cut it this way you really can have each side be up to 19 3/4” long on the outside (this is with the structure being 6” tall):

Timber

Ok, so it doesn’t quite fit in the window, but you get the idea.
19 3/4 + 15 1/4 + 19 3/4 + 15 1/4 + 19 3/4 + 15 1/4 + 19 3/4 + 15 1/4 = 140
The little scraps at the end will be 2 1/4” so you have 1 3/4” left for kerfs.

Now, notice that the difference between the short side of a piece and the long side of a piece is 4 1/2”. It’s actually supposed to be 4.46”, which means you’d be off by almost 1/4” by the time you get to the end of the timber if you lay it out exactly like the picture.
To avoid that, you just go by the 19 3/4” side. Mark the first 22.5 degree line at the end, then measure 19 3/4”, make the second line slanting the other way, then measure 19 3/4 from the other side of that line, and so on.

When you figure in the kerfs, this will get it really close to using the whole timber. In fact, if your kerf is more than 1/8” or the timber is a hair less than 12’ you might want to go 1/4” or 1/2” shorter.

This description is tailored for a 12’ timber. My earlier one will work for any length.

-Ben

View GaryCN's profile

GaryCN

277 posts in 2538 days


#11 posted 2199 days ago

Photo of Octagon. I cut a 6’ story stick first to plan my layout to avoid a few knots at the miters.
measured the outside length to 18 1/4 ” and ended up with an octagon O.D.44” scrap was 2 pcs
total length 9” on long side 7.5” on short side overall one hade a few knots in the last 3”
Measures 44” top to bottom and left to right at the outside
Landscape-octagon

-- Quando Omni Flunkus Moritati

View GaryCN's profile

GaryCN

277 posts in 2538 days


#12 posted 2199 days ago

actual timber is 3.5” X 5.5” X 144”

-- Quando Omni Flunkus Moritati

View OutPutter's profile

OutPutter

1194 posts in 2594 days


#13 posted 2199 days ago

I applaude Ben for hauling out the trig, lew for posting all the links, BroDave for throwing in the kerf, Ben for reminding us that a carpenter can probably lay out an octagon in about the time it takes to make one cut, and Gary on the extra 1/4” x 8 = 2” he saved. Don’t I look silly. Simple? No way. Not when we can make it hard. LOL

-- Jim

View Ben Griffith's profile

Ben Griffith

50 posts in 2283 days


#14 posted 2198 days ago

I just went back to look at this and realized that my calculator was set to use radians instead of degrees. Don’t I look silly! So the difference between the short edge and long edge is an inch or so less than what I said. But as I mentioned it’s a good idea to only use one edge length to lay it out anyway. The method I described in my first post isn’t affected by my goof, only the numbers are, a little bit.

Gary, it looks like you got the biggest octagon that board had to offer! So what’s it for? Sandbox? Flower bed? Giant stop sign?

View GaryCN's profile

GaryCN

277 posts in 2538 days


#15 posted 2198 days ago

I was going to use it as a tree ring but my wife is not sold on that idea, As the the other tree on our lawn has a large rock edge but it’s much bigger. I have a 2 acre lot so it will go somewhere but not quite where I intended to put it. I’ll still be bumping my head on tree branches as I attempt to mow around the trunk of a Magnolia tree for now. It may well end up as a sandbox. Stay tuned for details.
It was a good learning experience, and the octogon layout calucalator may benefit others.

-- Quando Omni Flunkus Moritati

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