You remember, of course, all the trigonometry you learned in school, and its practical applications to daily life. Well, here's another example:

The solar panel is at its peak efficiency when directly facing the sun: that is, when the panel is perpendicular to the rays from the sun. This corresponds to the sine value of 1.0 for a 90° angle, as the graph illustrates. When the panel is parallel to the rays of the sun (0°), or away from the sun, the efficiency drops off to practically nothing. At angles between these two extremes, the maximum relative efficiency changes as a sine function of the angle. For example, sin(65)=.9063, so at an angle of 65° the maximum potential efficiency of the panel will be a bit more than 90%.

The practical importance is that I can expect to harvest more of the sun's light if I can keep my panel facing the sun, like a sunflower. It needn't be exactly 90°; anything close to the top curvature in the graph will be fine. The aforementioned 65° sounds like a reasonable goal. If my panel never strays more than 25° in any direction from the sun, that gives me 50 total degrees of tolerance for inexactitude, while still attaining 90% efficiency or better.

Now, this is fun math, but only as an approximation or a hypothetical ideal. Even on a sunny cloudless day, earth's atmosphere diffuses a certain percentage of the sun's light, so that light is coming from all directions, not just from the point of the sun. Were it not so, our sky would be completely black, as in outer space. So the efficiency is not 100% at 90°, and is not zero at 0°. On overcast or rainy days (LOTS of those in Nicaragua), the diffusion is even greater and the efficiency curve much flatter. Nevertheless, this seems to be an idea worth pursuing. I hope to follow with another blog article or two, in trying to implement the above to improve my solar panel system.

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