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Matthew Traum

Simple Trig Explains the Value of Sun Tracking Solar Panels

Sometimes after I stare at a problem long enough, the solution finally jumps out and bites me. I have been staring at the same solar energy problem on and off for seven years, and this week, I finally figured it out.

Before becoming a professor, I worked in the solar industry, and now I am responsible to teach college students about alternative energy. So, I have known for a long time that a sun-illuminated flat solar panel fixed in its orientation with respect to the sky generates power at different rates as the sun traverses overhead. The Ameco Solar Company has posted an excellent example daily flat solar panel output profile on their Web site.

What I could never figure out was the physical mechanism underlying this result. I have heard many explanations, several of which are probably partly true. Some say that when the sun nears the horizon its rays must penetrate more of the atmosphere than when it is overhead. The photon-absorbing properties of the atmosphere reduce the energy reaching the panel. To some extent this observation is true, but it doesn’t explain why a solar panel pointed directly at the sunset collects more energy than a fixed flat panel at a non-ideal orientation.

I have also heard that more sunlight is reflected by a solar panel when the light arrives at an angle. Reflected photons clearly don’t get converted to energy. To some extent, this phenomenon also exists, but it does not explain the rounded profile of the daily solar panel output. If reflection were the main solar profile culprit, the profile would be a linear function of the time of day, not a smooth curve.

So what is the underlying mechanism?

It turns out that Isaac Newton’s inverse square law applies to this situation in a roundabout way. When cast in terms of gravity, electric field, and radiation, the inverse square law states that the intensity of a field emanating from a point source falls off according to the source strength divided by the area of the sphere of radius R from the point source.

In other words, solar energy density is a function of the sun’s output divided by the intersecting area. By analogy, when the sun is not directly overhead, its rays are forced to spread over a larger surface area defined by the angle the sun makes to a flat panel facing straight up. This phenomenon is beautifully illustrated on the Windows to the Universe Web site.

Thus, after a little trigonometry, it becomes obvious why solar panels set up to track the sun can collect so much more energy in a single day than their flat-mounted counterparts. Tracking panels always face the sun; so the absorbed light does not spread out and diminish its energy density.

This point may be trivial, but it is a phenomenon I can finally claim to understand after 7 years of staring at it.