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I was very interested in doing as many calculations as possible in my original design. One of these calculations was finding the best angle to mount the solar panels at for optimum power generation. The best angle is perpendicular to the sun's rays. Since the angle of the sun moves during the year and the sheer number of summer noon hours more than doubles the winter noon hours, I chose to optimize for winter sun.
Per the recommendation of several websites and The Solar Electric House, the optimal winter angle is found by adding 15 degrees to the latitude and the optimal summer angle by subtracting 15 degrees. The latitude at the barn is approximates 39 degrees. The optimal winter angle is then 39 + 15 = 54 degrees.
If mounted at 54 degrees, then there is an energy loss due to angles during the summer. The optimal summer angle is 24 degrees. For a given area of 1 square meter perpendicular to the sun's rays, an area at an angle of x degrees from the original square must be (1 square meter)/(cos(x)) in size in order to produce the same energy.
Using this formula and an angle difference of 54 - 34 = 30 degrees, 1/(cos(30)) = 1.155 square meters.
1 square meter divided by the 1.155 square meters gives the percentage of area that the original is of the larger: 1 / 1.155 = 0.866 = 86.6%. Therefore, there is an energy loss of 100% - 86.6% = 13.4% due to the angle.
There are 3 winter noon hours and 7 summer noon hours. So summer hours are 233.3% that of winter. This more than makes up for the loss due to angles.
Despite all these wonderful calculations which made sense and were fun to do, mounting the panels at an angle proved such an inconvenience due to high winds and available materials, that I installed the panels at the angle of the roof which is 36 degrees. Although not optimized for winter any longer, the energy loss for winter only comes to 4.8%.
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