<p>My guess is the reflector is shaped in a parabolic curve. The reason is that if you look at the inversed problem for sunlight concentrators as shown in the figure <a href="https://courses.lumenlearning.com/ivytech-collegealgebra/chapter/solving-applied-problems-involving-parabolas/" rel="nofollow noreferrer">here</a>, the sunlight will be focused to a point. Now, let's image the sunlight is shining from the other side of the reflector in the same figure, then the reflected light will be lines extended straightforward from the focused lines from the previous case. So, regardless of the angle of the sun, all reflected lines are shotting from the same focal point and would yield the result we want!</p>
<p>If you want to keep the bright band of the reflected light at the same position in your roof over seasons, the only thing you need to do is to tilt the parabolic reflector over some angle accumulately. The change will be very small day over day, but considerable over seasons.</p>

CC BY-SA 4.0
2022-01-23T06:49:45.397Z
real challenges are: demonstrate it geometrically/dinamically in geogebra; verify if/how also season changes can be taken into account in the 3d geometry of the mirror.
jumpjack
CC BY-SA 4.0
2022-01-22T18:59:36.927Z
2022-01-22T18:59:36.927Z
Xiaodong Qi
<p>A little anti-intuitive, but it looks that a convex circular mirror could keep the sun reflected on a target for all along the day:</p>
<p><a href="https://i.sstatic.net/2jx4I.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/2jx4I.png" alt="sunrise" /></a></p>
<p><a href="https://i.sstatic.net/whl1A.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/whl1A.png" alt="sunset" /></a></p>
<p>Smaller radius result in wider reflection, i.e. longer availability of light on target:</p>
<p><a href="https://i.sstatic.net/fZgtd.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/fZgtd.png" alt="small radius" /></a></p>
<p><a href="https://i.sstatic.net/7Lj40.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/7Lj40.png" alt="big radius" /></a></p>
<p>So probably the cleardome design is based on double curvature: small one determines strip length, big one determines strip thickness.</p>
<p>Probably a configurable mirror made of multiple tiny mirros would be better, allowing customization for everybody needs (but it would be very hard to build!)</p>

CC BY-SA 4.0
2024-03-13T09:25:04.730Z
2024-03-13T09:25:04.730Z
jumpjack
<p>An heliostat is a device capable of reflecting the sun in a fixed point while the sun itself moves into the sky, thanks to a moving mirror.</p>
<p>But this company astonished me with its invention: a static heliostat! Rather than mounting a mirror on a pan&amp;tilt mechanism, they designed a curved mirror which, at any time in the day, reflects sun in a same point (actually same strip).</p>
<p><a href="http://cleardomesolar.com/solareflexpanels.html" rel="nofollow noreferrer">http://cleardomesolar.com/solareflexpanels.html</a></p>
<p><a href="https://i.sstatic.net/bCpTe.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/bCpTe.png" alt="Static heliostat" /></a></p>
<p><a href="https://i.sstatic.net/SZPej.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/SZPej.png" alt="sunstrip" /></a></p>
<p>How can I design a static mirror which reflects a sun-strip over a wall all along a day? Let's suppose I have these data:</p>
<ul>
<li>Wall exposed to North.</li>
<li>Mirror 5 meters away.</li>
<li>Apprximate location: 42N, 12E.</li>
</ul>
<p>I am trying experimenting with Geogebra and <a href="http://jeanmarie.biansan.free.fr/optgeo.html" rel="nofollow noreferrer">OptGeo</a> but with no luck so far.</p>
<p>I can reorient the mirror by hand every week or month, but I don't want to have to reorient it hour by hour!</p>
<p>Geogebra example:</p>
<p><a href="https://i.sstatic.net/6NG0j.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/6NG0j.png" alt="Geogebra example" /></a></p>
<p><a href="https://www.geogebra.org/m/ukkrcv3c" rel="nofollow noreferrer">https://www.geogebra.org/m/ukkrcv3c</a></p>
<p>Optgeo example:</p>
<p><a href="https://i.sstatic.net/6GIwv.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/6GIwv.png" alt="Optego example" /></a></p>
<p>Maybe Sunpath3d page can help:</p>
<p><a href="https://i.sstatic.net/AESy9.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/AESy9.png" alt="Sunpath 3d" /></a></p>
<p><a href="http://andrewmarsh.com/apps/staging/sunpath3d.html" rel="nofollow noreferrer">http://andrewmarsh.com/apps/staging/sunpath3d.html</a></p>
<p>Also this page may be useful:</p>
<p><a href="https://www.sunearthtools.com/dp/tools/pos_sun.php" rel="nofollow noreferrer">https://www.sunearthtools.com/dp/tools/pos_sun.php</a></p>
<p><a href="https://i.sstatic.net/bVH1r.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/bVH1r.png" alt="sun calc" /></a></p>

CC BY-SA 4.0
2021-03-26T14:15:07.123Z
The exit is fantastic, thanks! I'll delete my old answer and if there's not already a great answer in the morning or if there is and I have something to add, I'll post something  new. Thanks!
uhoh
CC BY-SA 4.0
2021-03-27T08:10:23.233Z
it is less easy than it seems :-(
jumpjack
CC BY-SA 4.0
2021-03-27T09:11:10.363Z
It would be trivial in Blender, but I'm not good at it yet. See answer(s) to [How to simulate reflection of people in a 4 meter parabolic mirror to show that they won't appear upside down?](https://blender.stackexchange.com/q/204499/5334) I'll add a simple calculation for a conic section mirror in 1D soon but using normal math/python, not Blender.
uhoh
CC BY-SA 4.0
2021-03-29T19:09:32.860Z
This is still in draft, but the simulator allows viewing how sun is reflected along a wall during the day (sunAngle parameter) and during the year (seasonAngle parameter). It's weird to notice how on some specific positions of mirror, the line representing how it moves along the wall rotates along the year, but it always pass in one some point. If it's true and it's not a geometry error, it could be very important for an heliostat.    Geogebra project:   https://www.geogebra.org/classic/xg9uqpqn
jumpjack
CC BY-SA 4.0
2021-04-12T11:02:27.193Z
This new project shows how a circular mirror (seen from above) could produce a sunstrip covering a wide angle, depending on circle radius and target distance: https://www.geogebra.org/m/w6sfffwk
jumpjack
CC BY-SA 4.0
2022-01-22T18:21:09.017Z
@jumpjack Have you figured it out? Very interesting fact, but I don't understand what you have drawn on geogebra. Can you explain a bit more?
Xiaodong Qi
CC BY-SA 4.0
2022-01-22T18:34:12.517Z
@XiaodongQi no I didn't figure out it yet. Geogebra sketch should show how the edges of sun reflection should move along the day, i.e. how the area covered by sun reflection moves around along the day.
jumpjack
CC BY-SA 4.0
2022-01-22T18:59:29.713Z
@jumpjack My guess is the reflector is shaped in a parabolic curve. Let me write my comment as an answer...
Xiaodong Qi
CC BY-SA 4.0
2024-09-13T11:59:15.783Z
After some simulations with ray optics simulator ( https://phydemo.app/ray-optics/simulator/ ) I found that any curved surface can generate a wide reflections; this means that a simple sphere covered with reflecting film can act as a "stationary heliostat"; I also calculated which portion of the sphere is actually needed to reflect sun un one direction all along the day: a 90° section of the sphere is enough; thismeans that from each sphere you can ger 4 mirrors; and, the bigger is the radius, the bigger is the sun image visibile in the mirror, with the biggest one when the mirror is flat.
jumpjack
<the-sun><tracker>
How to design a static heliostat?
jumpjack
# How to design a static heliostat?

(Asked by: username_0 on 2021-03-24)

An heliostat is a device capable of reflecting the sun in a fixed point while the sun itself moves into the sky, thanks to a moving mirror.

But this company astonished me with its invention: a static heliostat! Rather than mounting a mirror on a pan&tilt mechanism, they designed a curved mirror which, at any time in the day, reflects sun in a same point (actually same strip).

<http://cleardomesolar.com/solareflexpanels.html>

[![Static heliostat](https://i.sstatic.net/bCpTe.png)](https://i.sstatic.net/bCpTe.png)

[![sunstrip](https://i.sstatic.net/SZPej.png)](https://i.sstatic.net/SZPej.png)

How can I design a static mirror which reflects a sun-strip over a wall all along a day? Let's suppose I have these data:

* Wall exposed to North.
* Mirror 5 meters away.
* Apprximate location: 42N, 12E.

I am trying experimenting with Geogebra and [OptGeo](http://jeanmarie.biansan.free.fr/optgeo.html) but with no luck so far.

I can reorient the mirror by hand every week or month, but I don't want to have to reorient it hour by hour!

Geogebra example:

[![Geogebra example](https://i.sstatic.net/6NG0j.png)](https://i.sstatic.net/6NG0j.png)

<https://www.geogebra.org/m/ukkrcv3c>

Optgeo example:

[![Optego example](https://i.sstatic.net/6GIwv.png)](https://i.sstatic.net/6GIwv.png)

Maybe Sunpath3d page can help:

[![Sunpath 3d](https://i.sstatic.net/AESy9.png)](https://i.sstatic.net/AESy9.png)

<http://andrewmarsh.com/apps/staging/sunpath3d.html>

Also this page may be useful:

<https://www.sunearthtools.com/dp/tools/pos_sun.php>

[![sun calc](https://i.sstatic.net/bVH1r.png)](https://i.sstatic.net/bVH1r.png)

**Tags:** the-sun, tracker
> **Comments:**
> **username_1**: The exit is fantastic, thanks! I'll delete my old answer and if there's not already a great answer in the morning or if there is and I have something to add, I'll post something  new. Thanks!  
> **username_0**: it is less easy than it seems :-(  
> **username_1**: It would be trivial in Blender, but I'm not good at it yet. See answer(s) to [How to simulate reflection of people in a 4 meter parabolic mirror to show that they won't appear upside down?](https://blender.stackexchange.com/q/204499/5334) I'll add a simple calculation for a conic section mirror in 1D soon but using normal math/python, not Blender.  
> **username_0**: This is still in draft, but the simulator allows viewing how sun is reflected along a wall during the day (sunAngle parameter) and during the year (seasonAngle parameter). It's weird to notice how on some specific positions of mirror, the line representing how it moves along the wall rotates along the year, but it always pass in one some point. If it's true and it's not a geometry error, it could be very important for an heliostat.    Geogebra project:   https://www.geogebra.org/classic/xg9uqpqn  
> **username_0**: This new project shows how a circular mirror (seen from above) could produce a sunstrip covering a wide angle, depending on circle radius and target distance: https://www.geogebra.org/m/w6sfffwk  
> **username_2**: @jumpjack Have you figured it out? Very interesting fact, but I don't understand what you have drawn on geogebra. Can you explain a bit more?  
> **username_0**: @XiaodongQi no I didn't figure out it yet. Geogebra sketch should show how the edges of sun reflection should move along the day, i.e. how the area covered by sun reflection moves around along the day.  
> **username_2**: @jumpjack My guess is the reflector is shaped in a parabolic curve. Let me write my comment as an answer...  
> **username_0**: After some simulations with ray optics simulator ( https://phydemo.app/ray-optics/simulator/ ) I found that any curved surface can generate a wide reflections; this means that a simple sphere covered with reflecting film can act as a "stationary heliostat"; I also calculated which portion of the sphere is actually needed to reflect sun un one direction all along the day: a 90° section of the sphere is enough; thismeans that from each sphere you can ger 4 mirrors; and, the bigger is the radius, the bigger is the sun image visibile in the mirror, with the biggest one when the mirror is flat.  

---

## 2 answers

### Answer by username_2 on 2022-01-22. Score: 3

My guess is the reflector is shaped in a parabolic curve. The reason is that if you look at the inversed problem for sunlight concentrators as shown in the figure [here](https://courses.lumenlearning.com/ivytech-collegealgebra/chapter/solving-applied-problems-involving-parabolas/), the sunlight will be focused to a point. Now, let's image the sunlight is shining from the other side of the reflector in the same figure, then the reflected light will be lines extended straightforward from the focused lines from the previous case. So, regardless of the angle of the sun, all reflected lines are shotting from the same focal point and would yield the result we want!

If you want to keep the bright band of the reflected light at the same position in your roof over seasons, the only thing you need to do is to tilt the parabolic reflector over some angle accumulately. The change will be very small day over day, but considerable over seasons.

> **Comments:**
> **username_0**: real challenges are: demonstrate it geometrically/dinamically in geogebra; verify if/how also season changes can be taken into account in the 3d geometry of the mirror.  

---

### Answer by username_0 on 2024-03-13. Score: 2

A little anti-intuitive, but it looks that a convex circular mirror could keep the sun reflected on a target for all along the day:

[![sunrise](https://i.sstatic.net/2jx4I.png)](https://i.sstatic.net/2jx4I.png)

[![sunset](https://i.sstatic.net/whl1A.png)](https://i.sstatic.net/whl1A.png)

Smaller radius result in wider reflection, i.e. longer availability of light on target:

[![small radius](https://i.sstatic.net/fZgtd.png)](https://i.sstatic.net/fZgtd.png)

[![big radius](https://i.sstatic.net/7Lj40.png)](https://i.sstatic.net/7Lj40.png)

So probably the cleardome design is based on double curvature: small one determines strip length, big one determines strip thickness.

Probably a configurable mirror made of multiple tiny mirros would be better, allowing customization for everybody needs (but it would be very hard to build!)


---

