# Evaluating Glare from Roof-Mounted PV Arrays: Page 2 of 3

## Mathematics of Glare

Glare studies are seldom, if ever, required in residential settings. However, it is not uncommon for neighbors to express concerns about potential glare or reflectance related to a proposed PV installation. While these concerns are understandable, they are also unfounded. Using basic physics, math and trigonometry, you can show that even if a PV array reflects some sunlight, it is highly unlikely that a third-party observer will see glare effects, especially if the potential viewer is located on an abutting property. Sunlight reflected off a residential roof-mounted PV array is most likely to travel skyward, up and over adjacent structures.

Law of reflection. Sunlight striking a smooth surface behaves in a predictable manner according to the law of reflection. As illustrated in Figure 2, the law of reflection states that when sunlight strikes a flat surface, the angle of incidence equals the angle of reflectance, as measured on either side of the line that is normal (perpendicular) to the reflecting surface. In effect, the direction of the reflected light mirrors that of the incoming light.

Location of sun. For viewers to experience glare from the reflected sunlight in Figure 2, they would have to be located in or near the direct path of reflection. The location of the sun is a primary variable in any glare hazard analysis. The altitude angle of the sun determines the altitude angle of the reflection, according to the law of reflection, as measured off a line normal to the surface of the array. Further, the solar azimuth angle determines the plane along which the reflected light travels.

One of the simplest ways to identify the location of the sun for a glare hazard analysis is to use the University of Oregon Solar Radiation Monitoring Laboratory (SRML) sun path chart program (solardat.uoregon.edu/SoftwareTools.html). You can generate an annual sun path chart for a specific location by simply entering a zip code or the site latitude and longitude. Figure 3 is a sample sun path chart generated for Belmont, Massachusetts.

Angle of reflectance. The altitude angle of the sun varies according to the time of day and year. The lowest altitude angle occurs daily at sunrise and sunset; the highest altitude angle occurs at solar noon on the summer solstice. A glare hazard analysis for a full year typically includes altitude angle calculations for reflected sunlight at representative times of the day (sunrise, solar noon, sunset) and year (spring equinox, summer solstice, fall equinox, winter solstice). Since most residential roof-mounted PV arrays are installed at a tilt angle rather than horizontally, you must account for this tilt angle in your calculations. One way to do this is to use basic trigonometry.

Figure 4, for example, assumes an array tilt angle of 25° and a solar altitude angle of 30°. Because all the angles in a triangle add up to 180°, we know that the angle between the incident light and the back of the module equals 125° (180° − 25° − 30°). Since the angles that make up a straight line also equal 180°, we know that the angle between the incident light and the front of the PV array equals 55° (180° − 125°). The law of reflection dictates that the reflected light and the plane of the array mirror this 55° angle. Because opposite angles resulting from intersecting straight lines are congruent, two opposite angles on the backside of the PV array both equal 55°. You now have all the information needed to solve for x, which is the angle of the reflected light as measured off the horizon line. In this example, y equals 100° (180° − 25° − 55°), which means that x, the angle of reflected sunlight relative to an abutting property, is 80°.

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