# Check My Math

What Slope For Solar Panels?

When told south-facing solar panels should be mounted with a slope of 20-40 degrees (my latitude=42 degrees), I wondered why the angle shouldn't be midway between the sun's noon altitude at winter solstice and at summer solstice. I think the reason is to maximize the concentration of sunlight (when the rays are nearest perpendicular to the panel) during the longer days of summer. Still, 20 degrees is not much slope.

As I understand it, the savings from generating more energy than you consume is counted over a year. You can bank a lot of credit over the summer months and use that credit in the winter months. In Indiana you get a 1:1 credit for what you generate in excess of your use and send to the grid.

So how high and low does the sun get at local noon? I didn't have two paper plates to determine the Altitude of the Noon Sun, so I illustrated the north celestial pole (N) as up, and Celestial Equator (CE) 90 degrees to the right. From the Celestial Equator I marked 23+ degrees north and 23+ degrees south to denote the tropics, which correspond to the sun's location at the solstices as a result of the earth's tilt (23.5 degrees).

To the left of my origin point I marked a line 42 degrees from north, which would be my horizon, for the altitude of the north star is equal to my latitude. From 180 degrees--my horizon illustrated to the left and to the right--I subtract 42 (my latitude) and 90 (N to CE) and 23 (south of the CE) to derive 25 degrees (the sun's approximate altitude at winter solstice). From that low, it moves up over 46 degrees (23+23) for a total solar altitude of about 72 degrees at the summer solstice.

As shown in the smaller diagram, perpendicular to 72 degrees (the summer solstice altitude) on the right is 18 degrees (the best slope for the solar panel then) on the left; perpendicular to 25 degrees (the winter solstice altitude) on the right is 65 degrees (the best slope for the solar panel then) on the left.

That is, the summer solstice slope is best at 18 degrees and the winter solstice slope peaks at 65 degrees. The recommended 20-40 degree slope therefore reflects the greater emphasis on trying to maximize energy captured from the summer sun. You concede the winter months, knowing that you'll get more bang for your buck by maximizing solar capture in the summer.

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