<p>As I said in my comment, you appear to be using an Azimuth system different from what most astronomy programs will return it in.  As long as you're consistent, it won't matter, but double check to make sure.</p>
<p>To make the problem easier, subtract off the target's Alt and Az from the Sun's
Alt and Az, so that the target is the 0,0 point.</p>
<p>After that, the correct angle is simply 1/2 Alt, and 1/2 Az.  To convert that back into Alt/Az coordinates, add 30 to the Alt, and 90 to Az.</p>
<p>So, if the Sun is at 50 Alt, 40 Az.  Subtract off the target's coordinates to get 20, -50.  Divide by two: 10, -25.  Add back the target's coordinates to get the correct Alt/Az for the mirror: 40Alt, 65Az.</p>

CC BY-SA 4.0
2022-04-26T02:42:33.973Z
2022-04-26T02:42:33.973Z
Greg Miller
<p>for the control of a heliostat I have a program for the calculation of azimuth and elevation.
Now I am still missing the calculation of azimuth angle and elevation angle for setting the mirror. While searching for examples, I discovered this post here.
<a href="https://astronomy.stackexchange.com/a/43318/46036">https://astronomy.stackexchange.com/a/43318/46036</a>
My prototype is located in the northern hemisphere and is aligned in north-south direction.
In the rest position, the mirror points to the south (azimuth 90°, elevation 0°).
The target is 55° southwest and 30° above the mirror horizon.</p>
<p>Can you tell me with what calculations I can determine azimuth angle and elevation angle of the mirror?</p>
<p>Many thanks in advance!
Itsme</p>
<p><a href="https://i.sstatic.net/RSUG6.jpg" rel="nofollow noreferrer">enter image description here</a>
<a href="https://i.sstatic.net/Bdsr0.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Bdsr0.jpg" alt="enter image description here" /></a></p>
<hr />
<p>Miller,</p>
<p>thank you very much. Your answer helped me a lot to realize my mistake. I had to remove a servo from the prototype that was a solar tracker and replace it with a stepper motor. Due to carelessness, I positioned the angle sensor incorrectly. Please excuse my incorrect description of the angle position with which I caused corrections of the calculation. After the correct positioning of the angle sensor it now looks like this.</p>
<p>My prototype is located in the northern hemisphere and is aligned in north-south direction.
In the rest position the mirror points to the south (azimuth 180°, elevation 0°).
The target is 55° southwest and 30° above the mirror horizon.</p>
<p>Now it should be possible with the example from the contribution
<a href="https://astronomy.stackexchange.com/a/43318/46036">https://astronomy.stackexchange.com/a/43318/46036</a>
it should be possible to implement the correct calculation.</p>
<p>Is the following calculation correct?</p>
<p>mirrorAz = 55° + (SunAz - 55°) / 2</p>
<p>mirrorAlt = 30° + (SunAlt - 30°) / 2</p>
<p><strong>Added 04/27/2022</strong></p>
<p>The azimuth axis currently has the following orientation.
North = 0°
East = 90°
South = 180°
West = 270°</p>
<p>At my location it was very cloudy yesterday. In the short cloud gaps I could test the calculations in the afternoon.
At that time the SunAz = 213.51° and the SunAlt = 50.18°. These values correspond to the NOAA table.</p>
<p>mirrorAz = 55° + (213,51° - 55°) / 2 = 134,26°</p>
<p>mirrorAlt = 30° + (50,18° - 30°) / 2 = 40,09°</p>
<p>The mirror reflection mirrorAlt reached 30° relatively accurately but mirrorAz is far off.
The value of mirrorAz should actually be about 226°.</p>
<p>How can this large mirrorAz difference occur?</p>
<p>With best regards
Itsme</p>

CC BY-SA 4.0
2022-04-26T00:10:53.130Z
You az angles seem non-standard.  Usually 0 is North, 90 is East, and South would be 180.  Based on the angles you gave it seems like your 0 point is West, and 90 is South.  Just looking for confirmation you meant to do it that way.  Also, if your mirror doesn't rotate about the center of the mirror, that will change things too.
Greg Miller
CC BY-SA 4.0
2022-04-27T03:17:49.277Z
It looks like you have the right idea.  I'm still not sure about the Azimuth system you're using, but as long as you understand it, that's all that matters.
Greg Miller
CC BY-SA 4.0
2022-04-27T09:49:49.583Z
After correction mirrorAlt is ok but not mirrorAz. See above
Itsme
CC BY-SA 4.0
2022-04-27T13:06:50.610Z
You keep saying your target is 55deg SouthWest, but 55deg is NorthEast. So that is likely where the issue lies.
Greg Miller
CC BY-SA 4.0
2022-04-29T09:22:21.460Z
That was exactly my problem. Thank you very much, you have helped me a lot.
It is not 55°. Correct is 235°.

I was confused by this description.
[link] (https://web.archive.org/web/20170618104429/http://www.cerebralmeltdown.com/understanding-heliostat-targets/)
Itsme
<the-sun><mathematics><azimuth>
Azimuth angle and elevation angle of a heliostat mirror
Itsme
# Azimuth angle and elevation angle of a heliostat mirror

(Asked by: username_0 on 2022-04-25)

for the control of a heliostat I have a program for the calculation of azimuth and elevation.
Now I am still missing the calculation of azimuth angle and elevation angle for setting the mirror. While searching for examples, I discovered this post here.
<https://astronomy.stackexchange.com/a/43318/46036>
My prototype is located in the northern hemisphere and is aligned in north-south direction.
In the rest position, the mirror points to the south (azimuth 90°, elevation 0°).
The target is 55° southwest and 30° above the mirror horizon.

Can you tell me with what calculations I can determine azimuth angle and elevation angle of the mirror?

Many thanks in advance!
Itsme

[enter image description here](https://i.sstatic.net/RSUG6.jpg)
[![enter image description here](https://i.sstatic.net/Bdsr0.jpg)](https://i.sstatic.net/Bdsr0.jpg)

---

Miller,

thank you very much. Your answer helped me a lot to realize my mistake. I had to remove a servo from the prototype that was a solar tracker and replace it with a stepper motor. Due to carelessness, I positioned the angle sensor incorrectly. Please excuse my incorrect description of the angle position with which I caused corrections of the calculation. After the correct positioning of the angle sensor it now looks like this.

My prototype is located in the northern hemisphere and is aligned in north-south direction.
In the rest position the mirror points to the south (azimuth 180°, elevation 0°).
The target is 55° southwest and 30° above the mirror horizon.

Now it should be possible with the example from the contribution
<https://astronomy.stackexchange.com/a/43318/46036>
it should be possible to implement the correct calculation.

Is the following calculation correct?

mirrorAz = 55° + (SunAz - 55°) / 2

mirrorAlt = 30° + (SunAlt - 30°) / 2

**Added 04/27/2022**

The azimuth axis currently has the following orientation.
North = 0°
East = 90°
South = 180°
West = 270°

At my location it was very cloudy yesterday. In the short cloud gaps I could test the calculations in the afternoon.
At that time the SunAz = 213.51° and the SunAlt = 50.18°. These values correspond to the NOAA table.

mirrorAz = 55° + (213,51° - 55°) / 2 = 134,26°

mirrorAlt = 30° + (50,18° - 30°) / 2 = 40,09°

The mirror reflection mirrorAlt reached 30° relatively accurately but mirrorAz is far off.
The value of mirrorAz should actually be about 226°.

How can this large mirrorAz difference occur?

With best regards
Itsme

**Tags:** the-sun, mathematics, azimuth
> **Comments:**
> **username_1**: You az angles seem non-standard.  Usually 0 is North, 90 is East, and South would be 180.  Based on the angles you gave it seems like your 0 point is West, and 90 is South.  Just looking for confirmation you meant to do it that way.  Also, if your mirror doesn't rotate about the center of the mirror, that will change things too.  
> **username_1**: It looks like you have the right idea.  I'm still not sure about the Azimuth system you're using, but as long as you understand it, that's all that matters.  
> **username_0**: After correction mirrorAlt is ok but not mirrorAz. See above  
> **username_1**: You keep saying your target is 55deg SouthWest, but 55deg is NorthEast. So that is likely where the issue lies.  
> **username_0**: That was exactly my problem. Thank you very much, you have helped me a lot. It is not 55°. Correct is 235°.  I was confused by this description. [link] (https://web.archive.org/web/20170618104429/http://www.cerebralmeltdown.com/understanding-heliostat-targets/)  

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## 1 answers

### Answer by username_1 on 2022-04-26. Score: 3

As I said in my comment, you appear to be using an Azimuth system different from what most astronomy programs will return it in. As long as you're consistent, it won't matter, but double check to make sure.

To make the problem easier, subtract off the target's Alt and Az from the Sun's
Alt and Az, so that the target is the 0,0 point.

After that, the correct angle is simply 1/2 Alt, and 1/2 Az. To convert that back into Alt/Az coordinates, add 30 to the Alt, and 90 to Az.

So, if the Sun is at 50 Alt, 40 Az. Subtract off the target's coordinates to get 20, -50. Divide by two: 10, -25. Add back the target's coordinates to get the correct Alt/Az for the mirror: 40Alt, 65Az.


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