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  1. 21st May 2010, 04:07 PM #1
    Rod Martin
    Rod Martin is offline New Member
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    Default octagonal pyramidal cylinder

    If I've got a base octagon with a circumradius of 175mm and a top octagon with a circumradius of 80mm separated by a height of 680mm, what is the outer angle of the rise from the base plate?

    NB. Both octagons are centred and are effectively in a cone shape with the pointy bit chopped off.

    Any help would be awesome.

    Ta,
    Rod
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  2. 21st May 2010 04:07 PM # ADS
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  3. 21st May 2010, 10:41 PM #2
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    Default

    I think this is what you mean. Anyway, see piccy and see if it helps. Cheers.
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  4. 21st May 2010, 11:10 PM #3
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    I interpret your "circumradius" to be the radius of the circle through the points, so:

    The point of the pyramid is the same for both the faces and the ridges. Use the ridges to employ whole numbers (the circumradii). To find the height of the point above the top (z), observe that 80:z = 95:680, so z = 572.6, for a total height of 1252.6mm. (95 is the excess over 80, 175-80).

    The face radius of an octagon is R cos 22.5 degrees, 161.7mm for the base. The triangle through the face and the axis has a small angle of arc tan 161.7/1252.6 = 7.35 degrees, which is the same as the angle of the base with the face, or 97.35 degrees outer angle.

    Cheers,
    Joe
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    Fiction has to make sense. - Mark Twain
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  5. 22nd May 2010, 08:08 AM #4
    whitewood
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    Default A new angle on the forum

    I believe this thread is a great example of what makes this forum worth reading and members special.

    Why would Rod want to know such an obscure piece of information.

    Why would Durdge and Joe Greiner go to such trouble to draw / work out this complex problem for a complete stranger.

    That such level of help is available for no cost is priceless.

    John
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  6. 22nd May 2010, 09:14 AM #5
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    Default

    and just to point out that Durge and Joe are both correct even though there's two different answers. Durge's angle is the angle of the ridge to the base along a line intersecting with the opposite point on the octagon. Joe's is the angle of a face to the base perpendicular to the face.

    Cheers
    Michael
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  7. 22nd May 2010, 11:23 AM #6
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    Adding on to Joe's info, this spreadsheet will calculate the angles for the mitres on each side. Enter the blue values. One is the number of sides, the other is the tilt angle of the side. The yellow numbers are the ones you want.
    Spreadsheet originally courtesy of Zenwood.
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  8. 22nd May 2010, 04:28 PM #7
    Rod Martin
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    Default dumbfounded...

    I can't believe I got such thorough help in no time at all.

    Durdge, your picture is exactly what I had in mind; Joe and Alex, your help was fantastic too.

    You're right John...this help is absolutely priceless.

    Very much appreciated everyone...sincerely.

    Cheers,
    Rod

    nb. Still in shock!

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  9. 23rd May 2010, 08:48 AM #8
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    Perhaps this formular could be added to the Library also

    cheers
    pal
    Learn from yesterday, live for today, hope for tomorrow. The important thing is not to stop questioning.

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