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Geometrically Analyzing Solar Reflections

October 17, 2013
Initial view

Fig.1 Initial view of the problem: a flight controller standing in a control tower with a solar array to the north potentially reflecting the sun back at him.

Ten arcs are created over the solar season centered at the flight controller's viewpoint and showing the sun's annual movement range.

Fig. 2 Ten arcs centered at the flight controller’s viewpoint show the sun’s annual movement range.

In an NPR interview discussed here recently, MIT’s Christoph Reinhart briefly described a solar design problem he had worked on at a “nearby airport.” Using Radiance, Reinhart’s team made an in-depth study of the specular effects of different PV manufacturers in order to determine whether reflections from a nearby PV array would cause glare issues for a person standing in the control tower.

Lets back up for a moment and take a look at the overall problem of identifying when reflections would be in the flight controller’s view. To do this, I’ve recreated the scenario in the Rhino image shown above (Fig. 1). I’ve placed the model here in Portland, Oregon, at approximately 45 degrees north latitude. I have correspondingly angled the solar array at 45 degrees towards the south.

The windows surrounding the flight controller are projected onto the celestial sphere and the arcs divided into orange segments when the sun is visible and blue when it is shaded.

Fig.3 The windows surrounding the flight controller are projected onto the celestial sphere. Orange segments show when the sun is visible, blue when it is shaded.

First, I create a series of arcs showing the sun’s path relative to the controller’s viewpoint (Fig. 2).  Using the Heliotrope plugin I developed for Grasshopper, I generated ten arcs and evenly spread them between the winter solstice at the bottom and summer solstice at the top. The arcs lie on a sphere centered at the controller’s viewpoint.  When the solar paths (in orange) are flattened out onto a plane at the viewer’s height (shown in green), we get the same arcs shown in classical 2D Pilkington Sun Path Charts traditionally used in hand drawn solar analyses.

Let’s ignore the solar panel for a moment and first analyze the tower windows surrounding the viewer. From his viewpoint, we can project the window borders, along with the arcs, onto the solar sphere. This projection (Fig. 3) is done using the virtual heliodon component in Heliotrope. The periods in which the arcs appear in the window tell precisely when the sun will be directly in the controller’s view.

From the point of view, create vectors to the corners of the solar panel and reflect them upward to the sky using the reflection component in Heliotrope.

Fig.4 Using the reflection component in Heliotrope, we project vectors from the controller’s point of view to the corners of the solar panel and reflect them upward to the sky.

The orange arc segments now show when the sun is in the controller’s view and blue segments show when it is shaded by the surrounding walls. Of course this is an excellent starting point for determining when additional shade devices are needed to protect the viewer.

So far, so good. However, understanding when the sun will reflect off the solar panel to the viewer is a slightly more complicated problem. The first step here is to project vectors from the viewer’s eye point to the corners of the solar panel and reflect them towards the sky as shown in Fig.4.  As with the projected windows, these reflected vectors point toward the days and times when the sun will be reflected up to the viewer. Because they are now separated out to different base locations, however, it is unclear how to transfer that information onto our solar sphere.

To do so, we must remember that we are visualizing the sun as infinitely far away, using a Ptolemaic view in which the universe is not just earth centric, but in fact centered right on us!  With this assumption, we can move the base points of the reflected vectors wherever we like and assume they are still pointing to where the sun’s reflection will become problematic.

In the final picture (Fig. 5) we group the vectors together at the controller’s viewpoint, project them out onto the celestial sphere, and again split the solar arcs into hidden and exposed portions that now tell us when the sun’s reflection will appear in the viewer’s eyes. To the uninitiated this may appear confusing since it seems to say that the sun is coming directly through the tower roof.  What it correctly tells us, however, is that during the dates and times the sun appears in those positions on the solar arcs, it will also reflect off the PV panel to the controller’s viewpoint. I’ll leave it as an exercise for the reader to add the window and additional shade elements into the multi-legged reflection path.

The reflections of the solar vectors are clustered to the viewer's eye point and projected onto the celestial sphere, showing when the sun's reflections will be a problem in the flight controller's view.

Fig. 5 The reflections of the solar vectors are clustered to the viewer’s eye point and projected onto the celestial sphere, showing when the sun’s reflections will be a problem in the flight controller’s view.

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