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Thread: Diameter Of A Circle
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23rd May 2014, 10:46 PM #31
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23rd May 2014 10:46 PM # ADSGoogle Adsense Advertisement
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24th May 2014, 10:02 AM #32GOLD MEMBER
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24th May 2014, 10:40 AM #331915 17"x50" LeBlond heavy duty Lathe, 24" Queen city shaper, 1970's G Vernier FV.3.TO Universal Mill, 1958 Blohm HFS 6 surface grinder, 1942 Rivett 715 Lathe, 14"x40" Antrac Lathe, Startrite H225 Bandsaw, 1949 Hercus Camelback Drill press, 1947 Holbrook C10 Lathe.
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24th May 2014, 11:00 AM #34.
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24th May 2014, 01:05 PM #35
It's also the solution that converges quickest to the "natural" solution of just dividing the circumference into 2n segments x h wide.
Here is the third solution, which is the one Ueee and Stuart liked.
So the three versions.. are
D= h/sin(pi/2n) h=18mm n=16 holes D = 183.84 mm
D= h/tan(pi/2n) h=18mm n=16 holes D = 182.76 mm
D= 2h/sin(pi/n) h=18mm n=16 holes D = 184.53 mm
D= 2hn/pi h=18mm n=16 holes D = 183.32 mm ( arc length version )
since sin(pi/2n) converges on pi/2n for large values of n, likewise tan(pi/2n)=pi/2n, and sin(pi/n)=pi/n
All end up with D=2hn/pi funny that..
On tattslotto... my son reckons tattslotto is a TAX on people who are bad at maths.. doesn't stop me buying tickets though.
Ray
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24th May 2014, 06:32 PM #36GOLD MEMBER
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Oh ruddy hell!!!....... just when I thought you guys had it all sorted out as to why how when and which way is correct????
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24th May 2014, 06:38 PM #37
It just goes to show that there are more than one way to skin a cat... Or what ever you skin down there
Best Regards:
BaronJ.
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24th May 2014, 06:45 PM #38GOLD MEMBER
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25th May 2014, 12:49 AM #39
Ueee and Stuart might like their solution, but I think it really only works for small values of n
when n is moderately large I think RayG's 2nd option looks best -- and is the easiest to set out !
although when the hole diameter is small and n gets very large there's no real difference between RayG's solution 1 and 2.
There's a very simple explanation why that is so, would anyone care to say why?regards from Alberta, Canada
ian
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25th May 2014, 08:47 AM #40
This might also come in handy for working out circle divisions and increments.
http://www.blocklayer.com/circle-divider.aspx
Might even add a second inner circle with option of smaller circles (holes) centered on the inner circle circumference increments?
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25th May 2014, 09:29 AM #41GOLD MEMBER
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Thats because its the only one that gives 18mm between the holes(though there is another)
How so?
how does that come into it? once your picked your answer the set out is the same.
Sooner or later you end up with an "almost" straight line and(I think) all the while Rays solutions move closer to the U and S solution?
Given its likely a critical application like form work for a birdbath I think we have it close enough to be "fit for purpose". Though I think I have another answer but the best my maths ability can do is say its "something less than 183.346mm"
Stuart
lots of "I think"s. its early and I'm in a hurry... its been fun
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25th May 2014, 12:13 PM #42
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25th May 2014, 12:59 PM #43GOLD MEMBER
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No but I'll butcher one of yours.
Now I'm not even 100% sure this isnt one of your methods.
Take the OPs drawing to mean 18mm measured on the arch. So the first part is easy. 16*18= pretty much half the circumference. But how do you work out the length of the arch "through the hole" until you know the diameter? Its not an 18mm chord..... to top that off I've changed my mind, it has to be "something MORE than 183.346mm" lol
Time for calculus?
Perfection is a pita lol
Stuart
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25th May 2014, 01:31 PM #44
Hi Stuart,
The arc length is just arc_length = radius * angle in radians
So..
angle = 2pi/2n --> angle = pi/n
h = r * angle
D = 2r = 2*h*n/pi for h=18, n=16 D = 183.32
That's the one I called the "natural solution" earlier.. Of course, you could mix and match hole versus space methods...
Ray
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25th May 2014, 02:08 PM #45GOLD MEMBER
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Hi Ray,
I thought that might be the one... but the bit I'm not getting is.
Any arch draw through the center of a circle has to be longer than the diameter of the circle.
So the 16 spaces are 18mm. The 16 archs are "more than 18mm".
So the diameter has to be more than 32*18/pi... doesn't it?
Stuart
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