# Polar Array Angles

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Hi Guys

Been working on some landscaping projects recently that use circular arrays of paving stones.

The gaps between each paving stone should be a specific distance (In this case 30mm).

I normally do this by drawing circles at the corner of the paving stone at 30mm radius that gives me the correct spacing for the next.

I then mirror this around which takes an eternity.

I'm trying to work out to use a polar array to do this.

I can get the gap close to 30mm using this method but it's a couple of decimal places off.

I have the angle between the stones that needs to be achieved but cant work out how to get this to work with an array.

I've attached a screenshot to try and illustrate what I am trying to achieve.

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14 minutes ago, james 172 said:

Hi Guys

Been working on some landscaping projects recently that use circular arrays of paving stones.

The gaps between each paving stone should be a specific distance (In this case 30mm).

I normally do this by drawing circles at the corner of the paving stone at 30mm radius that gives me the correct spacing for the next.

I then mirror this around which takes an eternity.

I'm trying to work out to use a polar array to do this.

I can get the gap close to 30mm using this method but it's a couple of decimal places off.

I have the angle between the stones that needs to be achieved but cant work out how to get this to work with an array.

I've attached a screenshot to try and illustrate what I am trying to achieve.

And what is the gap mid paving slab and on the inner edge?

The gap is always going to be different on the inner edge and outer edge, its the nature of trying to fit a square object in a circular pattern.

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I'm not concerned with the dimension mid paving slab.

I understand that it's different on the inner and outer edge, I just need the outer edge dimension to be exactly 30mm.

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Use ARRAY / path. Select the circle as a path and then you can specify the distance between the stones.

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I assume you understand that 30.2996 to two decimal places is 30.00. What is the dimensional tolerance to the size of the paving stones?  I am sure it is more than 0.01mm. I’d accept the solution you are getting as being more than good enough unless you are dealing with a math problem and not a real world construction task.  There is no “exact” for measurements in the real worls.

For an interesting read on the error in measurement check out The Measure of All Things  .  It documents the realization that measurements are not exact and the introduction of how to handle data error.

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37 minutes ago, guran said:

Use ARRAY / path. Select the circle as a path and then you can specify the distance between the stones.

Thank you that's perfect, exactly what I was looking for!

That will save me literally hours on these particular projects.

Thanks to all who responded, haven't used the site for a while but as ever it's come up with the goods.

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7 minutes ago, lrm said:

I assume you understand that 30.2996 to two decimal places is 30.00. What is the dimensional tolerance to the size of the paving stones?  I am sure it is more than 0.01mm. I’d accept the solution you are getting as being more than good enough unless you are dealing with a math problem and not a real world construction task.  There is no “exact” for measurements in the real worls.

For an interesting read on the error in measurement check out The Measure of All Things  .  It documents the realization that measurements are not exact and the introduction of how to handle data error.

Yeah I understand that it's a crazy degree of accuracy (unachievable in the real world) I'm chasing but if I do it manually I can get it to 30.00. Just looking for a more efficient way to do it.

Thanks for the book recommendation too, I'll definitely take a look.

It is easy to get caught up in numbers when staring at a screen!

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I expect that you would have good results using the command Measure.

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Look into gear design it takes into account the pitch radius which is similar to what your trying to do its some simple maths where your gear tooth is a paver for a given radius and angle of fill.

If you have 150mm paver and want on inside radius say a 5mm gap then your chord is 160mm and needs to be reworked out for spacing given an arc length and radius.

now its 1/2 chord length then the angle where did I put that formula ?

1/2 chord/sin ang= rad/sin 90 solve for sin ang.

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Array to path is a great tool, I've used it on Keyscape 2014, but alas, we no longer can have it.  So, I'm back to using my AutoCAD LT 2010, which doesn't appear to have the option , so, if you too haven't got an 'Array to path' option, then this work-around might help:

If I want 300mm square pavers with a 30mm gap, on a 5m radius circle...

1. Draw one paver, 300mm x 300mm and place it into position on the circle
2. Decide how far apart the mortar gap will be; say 30mm at widest.  Paver 300mm + gap 30mm = chord of 330mm.
3. Simply divide the circle circumference by one chord to find how many chords you can get in your full circle. Mine was 95.6 chords...you can round that chord down to a whole number to keep it simple and keep pavers all whole and even... 95 chords = 95 pavers with gaps. Done! Now let's set it up that array for our 95 pavers around that circle...
4. Click ARRAY>polar array>select object (click on your paver)
5. Still in ARRAY: select your centre point (if you can't see where the centre of your circle is, hover your mouse over the edge of the circle to get the centre X to show up, click it)
6. Still in ARRAY: change Method to 'Total number of items and Angle to fill'
7. Still in ARRAY: select 'Total number of items' (total chords, mine was 95 chords)
8. Still in ARRAY: select 'Angle to fill' as 360 degrees.
9. Still in ARRAY: check the 'Rotate items as copied' box is ticked
10. Press OK

Voila!  Your pavers are now symmetrically arranged quite beautifully around the circle

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I believe Array Path didn't come with AutoCad LT until the 2012 release.

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As you have LT you can write something in excel that uses a start point an arc and as already mentioned how many chords  working out the insertion point and a angle of rotation. Then just insert Just requires a cut and paste of the ID of start point and nominate arc length radius etc.  just copy and paste the resulting column

-Insert "paver" x,y 1 ang

Edited by BIGAL