# Stepping round a circle



## savarin (Jun 24, 2021)

Ever since I was a kid in school too many years ago to mention I have never been able to accurately step the radius around a circle thus dividing it into 6 equal parts.
I have tried many times and used quality compasses and dividers all to no avail.
There is always a tiny discrepancy.
Is there a better more accurate method of subdividing up a circle?
I will have a go with a protractor and see if that gets better.


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## Mike_Mac (Jun 24, 2021)

It is because pie is 22/7 and not exactly 3. Therefore, the circumference is not 6 times the radius.


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## brino (Jun 24, 2021)

Mike_Mac said:


> It is because pie is 22/7 and not exactly 3. Therefore, the circumference is not 6 times the radius.



......well pi is really not 22/7......that's just another estimate!

-brino


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## savarin (Jun 24, 2021)

Technically it should work, every instruction states thats the method to use.
No matter how careful I have been it has never worked for me.
I will purchase a large protractor and mark it out on a large circle and then draw the smaller circle inside it.
That should work.
Just talking about it has given me the idea


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## KyleG (Jun 24, 2021)

Mike_Mac said:


> It is because pie is 22/7 and not exactly 3. Therefore, the circumference is not 6 times the radius.



He’s erecting six chords, which should perfectly divide the circle and land where he started. If he was wrapping around the circumference, then he would have the issue you’re describing.


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## KyleG (Jun 24, 2021)

Savarin, are you running into this issue at the drafting table or doing layout on metal? (Or some other situation?)


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## savarin (Jun 24, 2021)

Eventually on metal, just never got it to work on paper.
Sounds silly for something so fundamental.
I am assuming its a problem with the point of the dividers/compass wobbling


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## brino (Jun 24, 2021)

Charles,

Is this your normal sequence:




From Machinery's Handbook, 30th edition page 66.

-brino


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## savarin (Jun 24, 2021)

not quite, I draw the circle then step round with the radius.


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## Liljoebrshooter (Jun 24, 2021)

I found a chart for cordial factor on the net.  

Joe


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## brino (Jun 24, 2021)

Perhaps this method would at least split your error in two.
Rather than have the full error at the end you'd have two "half errors" split between two semi-circles.

-brino


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## savarin (Jun 24, 2021)

thats the way I usually go Brino and also eyeball it to make the error even smaller. But why do I find it so damn difficult to get it spot on..
All of this is to mark out a bunch of holes for the the focusser units for the bino so they track perfectly in use. (more on this in the bino thread later)


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## Iceberg86300 (Jun 24, 2021)

savarin said:


> thats the way I usually go Brino and also eyeball it to make the error even smaller. But why do I find it so damn difficult to get it spot on..
> All of this is to mark out a bunch of holes for the the focusser units for the bino so they track perfectly in use. (more on this in the bino thread later)


Seems like calculating the coordinates of each point out to 5-6 places would serve you better.

Just dial them up on the dro.

Or handwheels.

Or use some calipers to set your compass.

Or use some calipers sacrilegiously as a scribe/compass in conjunction with a square.

But the method shown above for a hex inside a circle should work just as well with with an accurately set compass on paper.


ETA: Stepping around isn't a very good way to go b/c as you progress each point is going to include the error of each previous point.



Sent from my SM-N975U using Tapatalk


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## RJSakowski (Jun 24, 2021)

Using a compass or dividers set to the radius will divide a circle into exactly six equal parts.  The error that you see is due to the point of the compass slipping slightly as you scribe the arc.  Shop dividers rarely have needle sharp points.  Compasses  from drafting sets usually have very fine needle with a blunt shoulder just above to keep the point from digging too deeply into the paper.  They also can have a hinged arm so the point can be set perpendicular to the paper. 

For scribing on metal or plastic, I will make a light punch mark with a sharp punch for the tip to sit in which prevents skating on the surface. For this purpose, I make punches out of old chain saw files with the tip ground with a 30 -30º angle.  ( I cut the file in half and anneal the struck end).  You do have to take care not to disturbe the divider setting while scribing the arcs. With practice, you should be able to come very close to six equal divisions.


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## RJSakowski (Jun 24, 2021)

Division of a circle into six sectors by scribing is limited by the operator's ability to visually locate a mark on a scribe line and position a divider point at that location.  If your error is .010", conceivably you could be off by .060" on the last scribe line.

For better accuracy, an RT will work well.  If you have a DRO, then calculation to the coordinates will locate points to the accuracy of the DRO.  A spin indexer will divide a circle into six equal parts. A 5C hex collet block will also work.


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## benmychree (Jun 24, 2021)

brino said:


> Charles,
> 
> Is this your normal sequence:
> 
> ...


This method eliminates accumulated error, which I think is Savarin's problem.


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## tjb (Jun 24, 2021)

I may totally be misunderstanding what you're trying to accomplish, but I've laid out holes on the perimeters of circles many times using a rotary table.  Center the rotary table and the piece on it; move off-center by exactly the radius; drill/mill/whatever; advance 60 degrees; repeat for all six holes.  No guess work.  (That is, if you have a good rotary table.)

Regards,
Terry


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## Shotgun (Jun 24, 2021)

If it were up to me, I'd draw it up on a computer and then use a spray glue to attach it to the part.  Made a lot of airplane parts for a Dyke Delta that way.


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## Lo-Fi (Jun 24, 2021)

I do as Shotgun suggests all the time, it's absolutely foolproof and super quick. CAD is also useful for giving coordinate points from whatever datum you might choose. Even to the point where it's time efficient to redraw a print just so you can choose where all your measurements originate. Saves an absolute ton of noodling and many mistakes.


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## hman (Jun 24, 2021)

I've had varying success striking chords.  Sometimes it's non-sharp points, sometimes it's non-rigidity of the compass, sometimes it's "missing the point."  Other times, it's right on.

Depending on the diameter of your protractor and the diameter of the circle you're trying to divide, the protractor method should be very good.  If you can find a protractor that's larger than your target circle, all the better.


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## RJSakowski (Jun 24, 2021)

Rather than use a protractor, I would use my drafting T square and 30/60/90 triangle.


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## Mitch Alsup (Jun 24, 2021)

savarin said:


> not quite, I draw the circle then step round with the radius.



And that is where the error is arising. Each step adds to the error.

Brino's method (i.e., machinery handbook) draws the diameter line first, then sets a radius and draws the circle. At both places where the circle intersects the diameter draw an arc that also intersects the circle. The only error is in setting the radius at C and at A and finally at B. This method only has direct error and not accumulated error.


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## Bi11Hudson (Jun 24, 2021)

*Pie are NOT squared, pie are round. Cornbread are squared*. . . So speaks the backwoods hillbilly of long ago.

22/7 is also an approximation. For me the easiest method is with a straight edge and a dividers. Pick a point on the line and strike a center. Using that center, draw a circle. At both points where the line and circle intersect, draw an arc from that  point to where the arc intersects the circle. That will give the six desired points, based on the radius of the circle. There is no "exact" answer otherwise, Pi is an "irrational(?)" number. It cannot be defined. The last time I followed the theory, 30-40 years ago, it had been calculated to 50K decimal places. I lost interest at that point, It works essentially unit-less. A string and a couple of sticks will give the same results on a larger scale.

.


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## savarin (Jun 25, 2021)

Followed Brinos method and got what I wanted, what looks like an exact intersection, first time ever.
Now I just have to figure out how to fabricate this on a little chunk of aluminium.
(see https://www.hobby-machinist.com/threads/the-giant-binocular.55688/page-24)


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## Ken226 (Jun 27, 2021)

For stuff like this, if I'm not feeling lazy enough to resort to CAD or the DROs bolt circle function, I'd use a trig right triangle formula.

For even segments, you'd only need to use the center as zero and calculate a set of coordinates for the first point.

After,  you can just alternate the negative sign from x to y coordinates to plot the other points.

For example,  if I wanted the coordinates for 6 points around a 4" diameter circle:

Assuming the center is zero, the only calculations needed would be for the 1st point.   6 points around a circle means 60° slices of the pie, and the radius is 2".

For X of the first point, cos60° times the radius.
  So,   (Cos60°)(2)=1  so X=1    


And y for the 1st point,  Tan60° times X
       (Tan60°)(1)=1.732051

So, right off the bat, I can plot the left and right most points as  x=2, y=0 and x=-2, y=0.

And the other 4 points, from the calculations above, just by swapping the order of the coordinates, to place them symmetrically in their respective quadrants using + and - of the coordinates calculated from the 1st quadrant.

  So,  coordinates for all points going counterclockwise from 3 o'clock.

1.    X2,   y0
2.    X1,   y1.732051
3.    X-1,  y1.732051
4.    X-2,  y0
5.    X-1,  y-1.732051
6.    X1,   y-1.732051.

To verify my work, I google a quick internet plotter and plot the points:





It'll work for any size circle and even numbers of points, as long as they're evenly spaced and symmetric in orientation.   Uneven or an odd number and you'd have to calculate each point individually. Also not difficult.

   If there's more that 1 point per quadrant,  you have to do a seperate calculation for each point in the quadrant.



Or, is this totally not at all what he was talking about?  I was a little confused about the purpose.


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## Liljoebrshooter (Jun 27, 2021)

Here is the chart I found online. 
Joe


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## Illinoyance (Jun 30, 2021)

If you start by laying out chords successively around the circle the last chord WILL end at the starting point.  The fact that you are having trouble making it come out balls on means an accumulation of small errors, probably not getting the point of the divider exactly on the last arc scribed.  Try making a light prick punch mark at each chord/circle intersection.  If the punch mark is off a bit you should "walk" it to where it is supposed to be.  Then scribe the next arc.  Rinse and repeat.

I you do the layout according to brino's diagram you will not have the problem of accumulating errors.

On any circle six chords each equal to the radius will fit EXACYLY.  If it doesn't you have introduced errors. The most likely one is not setting the divider leg exactly where it is supposed to be.  I am assuming you did not disturb the divider setting from when you scribed the circle.
Pi is not involved.


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## savarin (Jun 30, 2021)

Using a magnifier its easy to see its all me.
Problem solved
Thanks everyone


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