Open source code for the maths behind a heliostat?

Question

Theoretically, using a Raspberry Pi, (at least) one mirror, and two motors, one should be able to build a heliostat, i.e. a device which redirects sunlight to a fixed spot, like a scrub in the shadow of a building.

I am now searching for heliostat (open) source code, ideally in python, hopefully with enough comments. Also: Is my following rough approach correct?

1. We need to know the exact geographical location of the mirror in terms of longitude, latitude. For simplicity, we assume that the mirror itself always has an obstacle-free view of the sun.
2. For a given time, we can use celestrial mechanics to calculate the path of the sun on the sky.
3. Using the reflection law from geometrical optics, we can determine the position of the mirror, since we know the vector from the mirror position to the spot we want to direct light to.

That sound simple enough, at least theoretically. I read that for step 2, many use precalculated tables. Why? Is it numerically so challenging?

References

• https://www.sunearthtools.com/dp/tools/pos_sun.php
• Jon Henley: Rjukan sun: the Norwegian town that does it with mirrors
• Renard Bleu: ICARUS: the Analog Heliostat
• Raspberry Forum: 2 axis Heliostat
• Open Source Sun Tracking Skylight
• Sadly mostly offline, but everybody is linking there: http://www.cerebralmeltdown.com/

Answer 1

I wrote the source you need some years ago:

https://jumpjack.wixsite.com/progetti/sorgenti-ipsun

The Arduino/Processing version was just a demo program to manually control a TENVIS camera by multiple buttons, it lacks the "astronomical algorithm".

The Javascript version contains astronomical calculations and a demo page which connects to a local TENVIS camera.

I also built a prototype...

https://jumpjack.wixsite.com/progetti/ipsun

...then I found, at MakerFairRome 2016, a maker which sold on Kickstarter a ready-made heliostat, initially named "Lucy", then renamed "Caia"... but 5 years passed and it has not yet been born... so I think I'll have to go back to my project and develop my own heliostat.

But in the meantime I found this page about a "static heliostat", and now I am trying to reverse-engineer it to figure out if it could be easier/cheaper:

http://cleardomesolar.com/solareflexpanels.html

Additional resource with dozens of links to heliostats, coelostats, and whatelse...:

http://www.redrok.com/main.htm#gsc.tab=0

Answer 2

Assuming you know Sun Altitude/Elevation and Azimuth at a given location on Earth (you can calculate it using any astronomy library, such as suncalc.js), and the Altitude/Elevation and Azimuth of target w.r.t mirror, the mirror must point toward this direction:

mirrorAz = TargetAz + (SunAz - TargetAz) / 2
mirrorAlt = TargetAlt + (SunAlt - TargetAlt) / 2

Answer 3

I just discovered that a lot less math is needed to build an heliostat:

• in '800 somebody "discovered" that you don't need any un-existing sun-sensor or un-existing computer to continuously track the sun moving in the sky: you just need a clock; but a special clock, which rotates at specific speed. Rotating at this speed a properly oriented mirror, it will reflect the sun in the same direction for whole day, but in slightly different directions on next days; the device was indeed designed to work only for some hours, during optics lessons. There are several variants of these devices, currently I am focusing on Silbermann heliostat buit by Louis-Jules Duboscq; with this device you don't need to know/do maths: somebody did it for you 250 years ago; I think the right speed is half the sun speed and is constant along the day, but I am still working on this: the box of Silbermann heliostat looks too big to be so simple.
  • Original description of working mechanism
  • Modern description of working mechanism

• there is a "werid way" to look at how a parabolic mirror reflects rays;
  • classic way: all rays coming from same direction (a satellite) are reflected to same point:
  • alternate way: wherever a ray comes from, it will be always redirected in same direction (as long as it passes through focus):

Does this mean that wherever the sun is in the sky, it will be always reflected in same direction along the day?!?

So I did a real life test: I took a parabolic antenna, I painted it in reflective coat, I placed it the sun, in front of my north-oriented window. Result: a whole wall of the room which had never seen the sun before was filled by natural sun light!! My experiment lasted only 1h15m because I started it late, while sun was going to set (in that point the sun arrived today only at 16:00, and it set at 17:15 behind buildings). During this time, a flat mirror placed on the illuminated wall reflected light to a constant position on another wall.

The light was not as bright as the sun, because the mirror is just around 0.33 m2 and the wall is 6m2, so I think I observed a collateral effect: if reflective coating is not perfect but a little coarse, you get this effect:

And probably:

So you can decide:

• if you want intense reflection, you need a "perfect" mirror (next test will be to glue mirror mosaic tiles to the parabolic antenna), but it will be as large as the mirror itself.
• If light widespread all over the wall is enough, you can use a reflective coating.

Further experiments will follow.

In the meantime , you can play with this 2d optics simulator:

https://phydemo.app/ray-optics/simulator/