In my project, Cyclone, a comment from Bearpie with a request to know how to find the size of an angle of any segmented project. Here I am answering his request as a blog to be available for anyone wishs to benefit of it.

IF you are interested in finding it mathematically, here is an algebraical law:

The Required Angle= [(360 devided by sides number) – 180] devided by 2

For example:

The required angle for 12 sided= [(360 devided by12)- 180] devided by 2
= (30 – 180) devided by 2
=150 devided by 2
= 75 degrees (The answer)

IF you dont like that, follow this:

The required angle for 6 sided ring is 60 degrees,
8 sided ring is 67.5 degrees ( common ), 10 sided ring is 72 degrees
12 sided ring is 75 degrees (very common),
18 sided ring is 80 degrees,
24 sided ring is 82.5 degrees ( good for open segmented ),
36 sided ring is 85 degrees ( good for open segmented as well) and
48 sided ring is 86.25 degrees ( good for fine design) and so on….

REMEMBER, the angle alone is not enough for perfect tight ring. It needs another two factors, A- all segments must be precisely the same length. B- Cutting must be precisely vertical or 90 degrees.

So, if you insure precise angle, precise length and precise verticallity, you will do a good job.

TO INSURE precise angle: It is not enough to set your miter on a requered angle. You have to test it with a sacrificial piece of timber (we have many of them), probably 2 or 3 times. Every time, ajust your miter accordingly by move it to left or right.

TO INSURE precise same length of all segments, you have to have a LENGTH STOPER on your miter. This stoper has to be ajustable, because you need to ajust it for each level of your project.

TO INSURE vertical cut, I recommend using good electric miter cross cutter.

NOW, How to find out the segment length of each level, needs some drawings which I am preparing but they are not ready. So, I will come back to you in few days time. Thank you all.

-- Sam Shakouri / CREATING WONDERS WITH WOOD.....Sydney,Australia....

## 20 comments so far

ptweedy

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75 posts in 3028 days

#1 posted 08-25-2011 05:09 PM

Go to the segmentedturning.com web site and all will be made clear or at least some will be made clear. I have been using the software for a couple of years, its great. contact me at ptweedy@yahoo.com if you want to kick it around some. phil

Bearpie

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2601 posts in 2653 days

#2 posted 08-25-2011 05:14 PM

Thank you Sam, This is much appreciated! Have you seen my project post?

-- Erwin, Jacksonville, FL

degoose

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7205 posts in 2989 days

#3 posted 08-25-2011 09:25 PM

Now who is the great teacher, Sam…

-- Drink twice... and don't bother to cut... @ lazylarrywoodworks.com.au For lovers of all things timber...

Joe Lyddon

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9716 posts in 3687 days

#4 posted 08-25-2011 09:59 PM

Sam, you are a true Genius!I never would’ve thought there was so much TO IT! I just thought you just glued the rings together, in it’s special way, so when you ‘turned’ it, it would magically appear!

LOL!I will have to admit… that the first time through the calculations, I got the wrong answer…

Here is another way of writing the Formula… that may be clearer…

The Required Angle=[(360 devided by sides number) – 180] devided by 2For example:The required angle for 12 sides:

360 / 12 = 30

30 – 180 = 150 (ABSolute value… ignore the Sign)

150 / 2 = 75

It’s the angle that you actually

CUTit at that is being calculated…It’s easier to adjust the saw to cut a larger angle than a smaller angle…

It saves you the extra saw manipulations/calculations to get the Angle to set the saw at!

There are TWO angled cuts Per Piece(12 pieces x 30 degrees = 360)... Therefore,15 degrees per CUT.90 – 15 =

75 !! WALLA!(saw is cutting at a 75 degree angle… NOT a 15 degree angle…

because it’s easier & more accurate to do it that way)Thank you very much, Sam!You are just AWESOME!-- Have Fun! Joe Lyddon - Alta Loma, CA USA - Home: http://www.WoodworkStuff.net ... My Small Gallery: http://www.ncwoodworker.net/pp/showgallery.php?ppuser=1389&cat=500"

Tootles

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792 posts in 2136 days

#5 posted 08-26-2011 05:17 AM

Would a picture help? And dare I refresh your memories of some geometry from school in order to explain it differentlyl?

With any N-sided polygon where lines are drawn from the corners of the shape to a point inside, the angles around that point always add up to 360°. With regular polygons (all sides the same length) where the point is at the centre of the polygon, the centre angle of each of the triangles is then 360° divided by N. For N = 12, the centre angle of each triangle = 30°

Then the sum of the internal angles of any triangle equals 180°. So the sum of the base angles = 180° – 30° = 150°. But with a regular polygon where the inside point is at the centre of the polygon, the two base angles are equal, so Base Angle 1 = Base Angle 2 = 150° / 2 = 75°, which is exactly as above of course.

Now, what I have explained is sufficient to make a cylinder, no more. I’m sure Sam has a few more tricks to tell us in order to deal with changing diameters. Great going Sam, I’m looking forward to learning more.

-- I may have lost my marbles, but I still have my love of woodworking

Sam Shakouri

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1200 posts in 2722 days

#6 posted 08-26-2011 06:09 AM

As we used to say in the sixties: ” All the ways take you to Rome.”

Thank you for going around me in closed circle, Tootles and Leo.

-- Sam Shakouri / CREATING WONDERS WITH WOOD.....Sydney,Australia....

Bob Collins

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2430 posts in 3318 days

#7 posted 08-26-2011 07:38 AM

Thanks for the info Sam, be a few weeks before I can use any ot it though.

-- Bob C, Australia. Your best teacher is your last mistake.

Joe Lyddon

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9716 posts in 3687 days

#8 posted 08-26-2011 07:43 AM

Tootles…

You’re forgetting that it takes 15° on each side of center; 30° total as you say…

You’re NOT going to set your saw at 15°… at least I don’t think you will…

You will be cutting 75° cuts…(15° away from 90° = EASY) from the Outside edge… Not the Center.

The length of the outside edge determines what the Diameter will be… and gets smaller for each Ring as you reach Top/Bottom of the circle…

-- Have Fun! Joe Lyddon - Alta Loma, CA USA - Home: http://www.WoodworkStuff.net ... My Small Gallery: http://www.ncwoodworker.net/pp/showgallery.php?ppuser=1389&cat=500"

Tootles

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792 posts in 2136 days

#9 posted 08-26-2011 12:00 PM

Joe,

It’s not that I’m forgetting anything, except perhaps to specifically make the link between the calculated angles and the actual setting of the saw blade since I figured, firstly, that had been done already and, secondly, that it would be clear enough from the diagram (I specifically drew the polygon so that the shaded triangle has a horizontal base line to match the table saw surface).

What I have attempted to do is explain the maths (geometry) behind the calculation of the angles – the how and why the formula works if you like. It looks a little different to the way you have explained it, but it is just another equally valid way to the same answer. Trust me, I’m (nearly) a maths teacher.

So to make the link between the calculations and the saw blade – the angle at which the saw blade will be set is the base angle of the triangle, which is 75° for a 12-sided polygon. It’s that simple. As you say, the blade should not be set to either the centre angle (30°) or to the complement of the base angle (15°). Those two angles are only used as steps in calculating the blade angle by one method or the other.

Does that make sense?

-- I may have lost my marbles, but I still have my love of woodworking

Tootles

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792 posts in 2136 days

#10 posted 08-26-2011 04:34 PM

Ah, a bubble has finally popped! The 15° is more relevant than I had been thinking.

The 75° is the angle of the cut relative to the horizontal, or to the surface of the table if you prefer. But most table saws calibrate their blade tilt angle as degrees from vertical, i.e. 0° blade tilt is when the blade is 90° from the table surface. So to get the angle that you need to set on the saw, relative to its calibrated scale, you need to subtract the 75° from 90°, giving 15°.

Is that the point you were trying to remind me of Joe?

-- I may have lost my marbles, but I still have my love of woodworking

Joe Lyddon

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9716 posts in 3687 days

#11 posted 08-26-2011 05:44 PM

Yes… Exactly…

In my head, straight up Vertical is 90° & it goes from there…

About 61 years ago, when I was in school, I loved geometry and got straight A’s in it…

I have forgotten a lot since then… but still remember the Basics… (I think)... (I hope)... LOL

I’m waiting to see how Sam is going to actually Figure the other formula he’s going to Drop on us. LOL

Thank you…

-- Have Fun! Joe Lyddon - Alta Loma, CA USA - Home: http://www.WoodworkStuff.net ... My Small Gallery: http://www.ncwoodworker.net/pp/showgallery.php?ppuser=1389&cat=500"

Sam Shakouri

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1200 posts in 2722 days

#12 posted 08-26-2011 07:04 PM

I would like to thank all of you for taking your time and commenting on this blog. I wanted to make this subject as simple as possible to benefit as many as possible of lumberjocks, those who still understand math after leaving school so many years ago and those who wanted the result only. Unfortunately and inspite their good will, those comments appeared to complicate the case inspite they had the same results.

I think it is very simple and I trust a lumberjock who is looking for any angle to use in his or her project will find the way to cut the timber at that angle. I had added some tips to get even tighter rings. Those tips were forgotten to be discussed and nobody mentioned or added any more tips of their own.

-- Sam Shakouri / CREATING WONDERS WITH WOOD.....Sydney,Australia....

Joe Lyddon

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9716 posts in 3687 days

#13 posted 08-26-2011 07:20 PM

... sorry …

xwingace

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226 posts in 2223 days

#14 posted 08-26-2011 07:30 PM

We need to keep in mind these angles only apply in Euclidean geometric space. If you are in an intense gravity well (such as orbiting a black hole), or if you are traveling at or near the speed of light, you will need to adjust your angles accordingly to account for the increased space-time curvature.

-- I'm not as good as I once was, but I'm as good once as I ever was.

Grumpy

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22208 posts in 3486 days

#15 posted 08-26-2011 10:54 PM

A great subject Sam. Thanks for sharing.

-- Grumpy - "Always look on the bright side of life"- Monty Python

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