Author Topic: mirror not located on rotational axis  (Read 1487 times)

ben

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mirror not located on rotational axis
« on: September 09, 2015, 09:02:59 AM »
Hi All,

I think it would be very important to have the mirror located centrally at the intersection of both the axis of rotations.

I have seen many designs where the elevation axis is located behind the mirror.
Similarly, and possibly as a consequence, the azimuth axis does not intersect the middle of the mirror.

Can anyone please describe how this affects the ability to accurately point to a target?

My understanding is that unless this "offset" is accounted for in software, then when you control the mirror to a desired location, the reflected beam is not in the desired location.

I have read through a number of designs and seen somewhere where this phenomenon was discussed. I cannot find this discussion now, so thats why I wanted to start this thread and highlight it as an important (or trivial) design consideration.
Anyway, regarding the previous discussion on this topic, I thought that the conclusion was that "its not so critical" or something.
Later I read that people are having drift in the afternoons. I say that probably the drift is related to their mirror not being centrally located at the intersection of the two axis.

Can anyone who has experience with this please comment?
Ben.
« Last Edit: September 09, 2015, 09:09:42 AM by ben »


ben

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Re: mirror not located on rotational axis
« Reply #1 on: September 09, 2015, 09:20:10 AM »
imagine mirror[1] located at the origin, rotated at some angle.
and mirror[2] located a distance away from the origin, rotated about the origin the same angle.

Q: would the reflected ray from the mirror[2] be at the same location as the reflected ray from mirror[1]?
A: ???

I created the image below from a spreadsheet.
Once I develop this further, I will attach.
Ben.


Gabriel

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Re: mirror not located on rotational axis
« Reply #2 on: September 10, 2015, 03:11:11 PM »
Hi Ben,

This is actually something I have on the list of things to add to the updated version of the program. I have tried to figure out the math for this, but haven't had much luck yet. I actually had a picture drawn that looked a lot like yours.

The complicated bit is that it seems that the distance to the target also comes into the calculations (in addition to the distance from the center of rotation of the machine to the mirror). Also, if you take into account the fact that the program is set up so that there can be multiple heliostats, each with multiple targets, the number of parameters that a person must input increases considerably.

Finally, the way the targets can be set up using the joystick wouldn't technically yield correct tracking.
In general, it's a lot easier to just either live with the error or build the machine with the mirror close to the center of rotation. It still would be nice to have the code available for anyone who might need it.

The processing program I have been working on actually has the ability to model this error, so it can be used to test any potential fixes.

I know the heliostat project that Google has floating around the web had the math for this error. I looked at it, but it didn't seem to help much.

Gabriel

ben

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Re: mirror not located on rotational axis
« Reply #3 on: September 13, 2015, 04:38:42 AM »
Hi,

From my calculations and spreadsheet, I should be able to provide a 'formula' used to specify this error.
In my opinion, designing a machine with this offset (between mirror and axis) is sub-standard (sorry to be so harsh).

I agree that this error could be accounted for in the program, but I am opposed to that. As you say, and I agree, there are so many parameters already.

My thoughts are that anyone considering building a heliostat (or suntracker) should be aware of this concept and make it a design consideration.

Its best to start with a solid design, instead of making compensations later down the track.

Ben.

ben

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Re: mirror not located on rotational axis
« Reply #4 on: September 13, 2015, 04:52:51 AM »
Attached is a spreadsheet saved in three different formats:
- CSV, just a plain text file
- ODS, open office with graph embedded
- XLS, excel 97/2000/XP with graph embedded (saveas'ed within openoffice)
I use open office.

The text file is there for those worried about embedded macros (or whatever).
You need to graph columns B and C, using X-Y scatter.
comments are made throughout the file to explain what I have done.

This is my version#2 of this file.

Rows 17,18,19,21 have values that can me modified by the user

If anyone opens the ODS or XLS files, can they please verify they are harmless?


ben

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Re: mirror not located on rotational axis
« Reply #5 on: September 13, 2015, 05:06:22 AM »
oops, the CSV didnt save the formulas. I will redo later, unless someone can verify the ODS or XLS.
dare you... ;)

From the image, to me it seems the distance-to-target does not come into the calculation, because the reflected rays from the axis-mirror and offset-mirror are parallel,. Because they are parallel, the distance-of-target does not amplify the error.

This setup places the mirrors at both the same angle of rotation (about themself).
what moves is, the offset-mirror not only rotates about itself, but also about the axis-of-rotation (0,0 in the diagram).
or another way to put it , is that it rotates and translates

Imagine a rotation-angle of 45deg. the reflected rays would be straight up at 90 deg.
The center of the reflected ray from the axis-mirror would be at x=0.
The center of the reflected ray from the offset-mirror would be at "cos(45)xOFFSET"
= 0.707 x offsetDistance.

Does this seem correct?
Ben,

Gabriel

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Re: mirror not located on rotational axis
« Reply #6 on: September 21, 2015, 07:14:45 PM »
I'm not 100% sure the distance to the target doesn't come into play.

If you imagine a heliostat with a mirror that is offset from the center, and also imagine it tilting backward and forward, you will notice that the mirror is also moving "up" and "down" as it does this.

The target is of course not moving, so the the target's altitude in relation to the center of the mirror is decreasing and increasing. If the target is close to the mirror, then the change in altitude is more extreme than if that same target is further away.

That's how I think of it anyway. I've learned that it is best not to assume that I'm right though until I've actually tried it out in the real world, or at least a computer simulation. :)