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Thread: Check my work - 8 sided pyramid - finding miter cutting angle

  1. #1
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    Check my work - 8 sided pyramid - finding miter cutting angle

    As a part of a large candle-holder project I am making an 8-sided pyramid. I need to figure out the table saw blade angle for the miter-cuts. If you know how to do this, could you check my work?

    I am using this calculator:
    http://www.pdxtex.com/canoe/compound.htm

    I started with the slope calculation. The pyramid is 9" across at the base, so the Horizontal Run is 4.5". The Vertical Rise is 18.75". The resulting slope is 76.5° (76.504 to be exact).

    It has 8 sides so the included angle shows as 135°. That calculates to an end angle of 5.5° (5.522) and a bevel angle of 22° (21.84).

    Does this seem reasonable, before I try it on lumber?
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    Last edited by Brian Kent; 10-27-2015 at 6:35 PM.
    Veni Vidi Vendi Vente! I came, I saw, I bought a large coffee!

  2. #2
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    If you can figure out how to cut those parts on your tablesaw I would be impressed more than the math that got you there. Looks very tricky.
    Last edited by Andrew Hughes; 10-27-2015 at 10:02 PM.

  3. #3
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    I tried a completely different method. I made a Sketchup model, and measured the angles.
    I'm guessing your 9" and 4.5" numbers are to the middle of the flats of the octagon. That is, from tip to tip of the octagon would be a little larger.

    If I look at one of those facets, I get 11 degrees at the tip, not 5.5 degrees. A factor of exactly 2 seems suspicious. You can probably do a rough check on this angle from your paper model. Other than that, my method agrees with you -- 21.9 degree bevel, but you can't set a table saw bevel down to the tenth of a degree.

  4. #4
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    I make my 8 sided light houses using a 22.5º router bit on the edges.

    100_3283.jpg

  5. #5
    Similar to what Jamie came up with, also in SketchUp


    Laying it out graphically helps to make sure the numbers are right.
    Last edited by Dave Richards; 10-27-2015 at 7:58 PM.

  6. #6
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    pyra1.jpg

    Here is what I got in Sketch-up. 22.5 degrees for the octagon.

    84.9 degrees for the isosceles triangle's large angle and 10.2 for sharp, acute angle.

    I assume 1/2" stock in the diagram, FWIW.
    Wood: a fickle medium....

    Did you know SMC is user supported? Please help.

  7. #7
    Quote Originally Posted by Myk Rian View Post
    I make my 8 sided light houses using a 22.5º router bit on the edges.

    100_3283.jpg
    And that jig you posted in your thread would be perfect for this project ,all it needs is a little tweaking here and there.

  8. #8
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    Quote Originally Posted by Chris Padilla View Post
    Here is what I got in Sketch-up. 22.5 degrees for the octagon.

    84.9 degrees for the isosceles triangle's large angle and 10.2 for sharp, acute angle.

    I assume 1/2" stock in the diagram, FWIW.
    So you went 9" point-to-point on the base octagon. That might explain the differences from my version, which is 9" flat-to-flat on the base octagon.
    Last edited by Chris Padilla; 10-27-2015 at 8:33 PM.

  9. #9
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    Quote Originally Posted by Jamie Buxton View Post
    21.9 degree bevel, but you can't set a table saw bevel down to the tenth of a degree.
    Just use one of those Wixley magnetic digital gages set on the blade, zeroed on the saw top:
    NOW you tell me...

  10. #10
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    This one is a lot less. Maybe as good? I don't know.
    Attached Images Attached Images

  11. #11
    Or the Angle Cube from Eagle America is on sale for $24.99.

  12. #12
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    So I'm curious to hear whose measurement/calculations were the closest, Brian!

    Let us know when you build it.
    Wood: a fickle medium....

    Did you know SMC is user supported? Please help.

  13. #13
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    It seems to me that if you were making an 8 sided barrel and not a cone, then its an easy answer that 360 / 8 / 2 = 22.5 deg miter angle for each side of each stave if you will. However, when the barrel is turned into a cone, that 22.5 deg angle changes, right? The thicker each board, the more of an affect it will have. You would need to look at a cross-section through the board that is perpendicular to the face of the board. Too much math for me right now

  14. #14
    Quote Originally Posted by Pat Barry View Post
    ...that 22.5 deg angle changes, right?... Too much math for me right now
    You're right. The angle is not 22.5° Too much math for me, too. That's why I made the drawing I posted.

  15. #15
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    That might be correct but I don't understand why. If the footprint of this cone/pyramid/whatever-it-is is an octagon, then it is an octagon no matter where you slice it and no mater how far the sides tip in to go from a cylinder/barrel to a cone/pyramid. So that should be 22.5 degrees.

    pyra2.jpg

    The way I made this is Sketch-Up was to start with an octagon, expand up the sides to create a cylinder/barrel, and then tip the sides in. I just don't see where that would change it from 22.5 degrees.
    Wood: a fickle medium....

    Did you know SMC is user supported? Please help.

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