# Calculating circle composed of individual segments

Hi there, I need to calculate the curving (in degrees °) of a circular ledwall, composed of individual ledpanels 500x500mm. We can bend them from 0° to 20° on each side: see picture.

I would like to know how many of these panels I need and in what curving I need to bend them to obtain a circle with a 2 meter radius. I’m trying to use Sketchup to help me with that but I just can’t seem to find a way. Can someone help me with this? Much appreciated!

By my calculation you would need 25 panels curved at 14.4 deg
But I may well be wrong.

3.14 x 2 x 2 = 12.56
12.56 / .5 = 25.1
360 / 25 = 14.4

I have rounded slightly.

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A default circle has 24 segments and with a radius of 2m each segment would be ~522mm
Increase the number of segments by 1 to 25 and the segment length would now be ~501mm

Now you can measure the angle over just one segment … to be 14.4 degrees.

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Here’s a quicky version of how to model it, I’ve made them 20mm thick, they are no doubt thicker. I’ve used 250 for the circle to make it divisible by 25 so that you get a 10 segment curve for both sides of the panel.

Following on from Box’s & Wo3Dan’s explanations, I did a similar thing but using true bend to make the panel fit the 2m radius. I agree with the number of panels required and the centre angle of approx 14.4º.

I don’t know how or where your panels actually bend but this what I came up with as a “bend angle” if I’m reading the request correctly.

The angle in the measurements box is difficult to read but is approx 3.7º.

Isn’t that 5 segments on both sides, meaning on either side of the center line?
Or do I need an extra cup of coffee?

Added. No coffee involved but I guess you meant inner and outer curve.

Yes in that sense, 5 and 5 make 10 and both the inner and outer ring both have 10 segments, 5 either side of the center line. Meaning the vertices line up and the segments are equally sized, so it is a section of a wedge.

Perhaps it’s the whisky I’m drinking that is confusing you.

How could that be, being on the other side of the globe?

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Thanks for the clip. But I’m still not sure how many degrees I have to bend the panels. Someone said 14,4° but isn’t that just the length/place of the circel (360°) each panel takes? Or is this also the curving of a panel (meaning I have to curve them 7,2° on eacht side?)

Yes that is basically correct, 14.4 or 7.2 a side on 25 panels should give you a 2m radius circle with a tiny bit of gap between them. There is a tolerance that is unavoidable, either there is a gap or the radius is smaller.
25 panels at 14.4 is as close as the hardware works.
If you need it to be absolutely exact and the panels can be adjust to such a fine degree you need to do the calculations without any rounding.

As I showed above
2 x pi x r will give you the Circumference. Edited to the correct formular C/o @slbaumgartner
Divide the circumference by the panel size will give you the number of panels
Divide the number of degrees in a circle by the number of panels will give you the degree of bend for each panel.

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Must be the whisky: pi x r**2 is the area of a circle. The circumference is 2 x pi x r.

No doubt it’s the whisky and a coincidence of the radius.
In this case 3.14 x 2 x 2 works, or was as close to a sketchup circle that I accepted it.

I did say in my original reply…

Click in sequence on the scenes tabs of this SU file for a quick analysis.

Number of panels in a circle.skp (242.2 KB)

The conclusion is that if you want to use whole panels, you will get a radius of less that 2 meters with 24 panels and more than 2 meters with 25 panels.

If you want absolutely 2 meters as the radius, you will need to trim the panels. In such a case, draw a 2 m radius circle with 25 segments to get the required width of each panel. This doesn’t consider the panel thickness. In such a case, the angle will be 360° divided by 25 or 14.4°.