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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

sunstrip

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 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://www.geogebra.org/m/ukkrcv3c

Optgeo example:

Optego example

Maybe Sunpath3d page can help:

Sunpath 3d

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

Also this page may be useful:

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

sun calc

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    $\begingroup$ 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! $\endgroup$
    – uhoh
    Mar 26, 2021 at 14:15
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    $\begingroup$ it is less easy than it seems :-( $\endgroup$
    – jumpjack
    Mar 27, 2021 at 8:10
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    $\begingroup$ 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? I'll add a simple calculation for a conic section mirror in 1D soon but using normal math/python, not Blender. $\endgroup$
    – uhoh
    Mar 27, 2021 at 9:11
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    $\begingroup$ 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: geogebra.org/classic/xg9uqpqn $\endgroup$
    – jumpjack
    Mar 29, 2021 at 19:09
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    $\begingroup$ 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: geogebra.org/m/w6sfffwk $\endgroup$
    – jumpjack
    Apr 12, 2021 at 11:02

2 Answers 2

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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, 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.

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    $\begingroup$ 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. $\endgroup$
    – jumpjack
    Jan 23, 2022 at 6:49
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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

sunset

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

small radius

big radius

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!)

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