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  1. #1
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    Default Diameter Of A Circle

    I would like to ask the assistance of the Forum with a mathematical problem I have, I just cannot get my head around it at this time so I seek some assistance.
    I need to know the diameter of a circle that needs to be divided into 18mm sections, I attach a rough diagram to help illustrate what I am saying.
    If someone can help me out and save me going mad from trying to figure it out I would be most appreciative.

    Keith_W
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    There isnt enough info.
    Cant be answered without knowing the number of holes or the dia.

    Stuart

    if you mean 16 holes
    (18+18)*16=576
    576/3.14= 183.44 dia

    I think

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    You need to specify how many holes, the size could be based on 4 holes or 100.....

    As you have drawn it with 16 the diameter to the center of the holes will be R 92.26, so a diameter of 184.52mm

    Ew

    Stu, you can't just go 32x16 cause the 18mm spaces are chords not arcs....though it seems to have made SFA difference.
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    Quote Originally Posted by Ueee View Post
    Stu, you can't just go 32x16 cause the 18mm spaces are chords not arcs....though it seems to have made SFA difference.
    Yes and No

    I did ask in my first post how close he wanted to get......I deleted it as on first read I thought he wanted 18 holes.
    I'm not sure its as simple as chords because of the 18mm between holes........

    Stuart

    p.s show your workings
    Last edited by Stustoys; 22nd May 2014 at 05:50 PM. Reason: p.s. and bit about chords

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    Thanks Sustoys & Ueee for a quick response.
    The number of holes was not really critical so I just picked 16 to do the drawing. The diameter is not know as the critical part was the 18mm between each hole.
    I can run with the 184mm diameter and 16 holes now, thanks again for your help, really appreciated it.

    Keith_W

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    Default

    It's 2*pi*r = 18*2*n where n is the number of holes, the *2 is to allow for a space between the holes.

    so re-arranging r = 18*n/pi if n = 16, then r = 91.661mm or diameter = 183.3

    Ray

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    you might find this handy if you bookmark it for the future . you just change the number values for what you require then you can print it out what ever size you want .

    http://www.cgtk.co.uk/metalwork/divider

    johno
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    Quote Originally Posted by RayG View Post
    It's 2*pi*r = 18*2*n where n is the number of holes, the *2 is to allow for a space between the holes.

    so re-arranging r = 18*n/pi if n = 16, then r = 91.661mm or diameter = 183.3

    Ray
    I disagree because like Stu you have worked it out as if the 18mm segments are arcs not chords. I Stuffed up too as i worked it out as 16 segments of 36mm, where i should have worked out 32 segments of 18mm. R should be 91.82, do D is 183.64

    Ray your number is what Stu's would have been if he did not round pi to 2 places....maybe not

    Ew

    Workings.....its just a triangle with one side 18 and angles of 360/32 and 2 equals.
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    Thats not right either, there is another very flat triangle to solve inside the hole too.....

    Ew
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    ok I think I've worked out where the error I'm thinking of comes from.
    Take 32 lines 18mm long and call them Ewan's chords . In a straight line they are 576mm long. In a circle you'd have a diameter of 184.52mm.
    The same doesnt apply to balls as they no longer touch on the "center line".
    or does it? or is it so small to not be worth bothering about?(most likely)

    Stuart

    p.s. it was nice of the OP to make the hole dia and distance between holes the same.
    Last edited by Stustoys; 22nd May 2014 at 06:33 PM. Reason: p.s.

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    Quote Originally Posted by Stustoys View Post
    ok I think I've worked out where the error I'm thinking of comes from.
    Take 32 lines 18mm long and call them Ewan's chords . In a straight line they are 576mm long. In a circle you'd have a diameter of 184.52mm.
    The same doesnt apply to balls as they no long touch on the "center line".
    or does it? or is it so small to not be worth bothering about?(most likely)

    Stuart

    p.s. it was nice of the OP to make the hole dia and distance between holes the same.
    Yes and no, as i see it its not really a circle we are after, its a 16 or 32 sided shape, with each side being either 18 or 36mm.just looking at it i thing the 16 sided dimension was right.....

    As we have seen our answers are within a pretty small range so it really depends on how accurate Keith needs as to whether we are right or not.....

    Yes having 18 and 18 is nice and "easy"


    Ew
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    Default Marv Klotz's Utilities

    You could also try Marv Klotz's utilities. A number of useful tools there.

    http://www.myvirtualnetwork.com/mklotz/

    If you have a newer computer with Win 7 or Win 8 in 64 bit, you will need to download and install DosBox - this will also work for Linux.

    Findlay.

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    Trying to correct for arc length vs chord length get's a bit messy, we know the hole diameters are 18 mm, and we assume the hole centers are on the diameter, so we have a 2n sided polygon which just encloses a circle of radius r.

    So the circle is divided into 2n equal angles, so each angle is 2pi/2n or pi/n radians

    Taking n=32 the circle is divided into 32 segments forming a 32 sided polygon where the sides are all 18mm and the center of every second side is the center of an 18 mm hole

    each of the 32 segments is an angle of 2pi/32 = 0.196 radians each, and forms a triangle with base 18mm and height r so tan of half the angle will be 9/r and tan (0.196/2) = 0.098, so r = 9/0.098 = 91.83 or d=183.6

    simple...

    Ray

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    Hi Ray,
    If only I understood your last post completely....

    Having said that I think if you just run the numbers as 16 chords.
    If you call base of this triangle is 36mm long.....doesnt that give the OP what his is after? removing the error I talked about in my last post lol

    Stuart
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    Last edited by Stustoys; 22nd May 2014 at 11:09 PM. Reason: Fixed up my wording. lucky Ewan worked out what I meant

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    That is exactly what i have been thinking, and was how i got my first answer. I get the feeling if i worked it out on 32 segments and then worked out the triangle inside each circle i would end up with the same answer.

    Ew
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