About Equinox Humps

Looking back at the equation, I believe this phenomenon is due to the difference between the sunrise/sunset times seen by a horizontal surface, and those times seen by the tilted array.

It is easy to imagine an abbreviated summer solar day on a tilted surface simply because the solar path has northerly segments at the extremes of the day that are behind the plane of the tilted array. So the sun "rises" on the tilted surface some time after it rises from the horizon. And it "sets" on the tilted surface some time before it sets on the horizon.

The winter mechanics are less easily imagined. From the curve, they would seem to require an extended solar day on the tilted array, implying an earlier sunrise and a later sunset on the tilted array than at the horizons. Consider this:

At the moment of winter sunrise, the sun's rays are parallel to a horizontal surface and no energy impinges the surface. But they are not parallel to a  south-facing tilted surface so the energy falling on that surface is suddenly greater than zero. The extreme of course would occur if the surface was tilted vertical.

Sunrise, governed by the horizon, occurs simultaneously on both surfaces, but the tilted surface has a head start up the cosine curve. Similarly, when sunset occurs simultaneously on both surfaces, incident energy has already tapered to zero on the horizontal surface but drops from a finite value to zero on the tilted surface.

Simply stated, summer mechanics impose a contracted day length whereas winter mechanics impose an enhanced intensity level. The summer contraction is reduced as the summer solstice is approached and the panel tilt approaches horizontal. The winter enhancement is increased as the winter solstice is approached and the tilt angle approaches vertical.

And since the total energy magnitudes are greater during the summer cycle, one might expect the summer peak-to-trough magnitude to be greater. In fact, it is.

The day-length contraction for any given summer day is a function of the tilt angle set for that day. It probably reaches a minimum at the summer solstice when the tilt angle is near zero.

The intensity-level enhancement for any given winter day is also a function of the tilt angle set for that day. It probably reaches a maximum at the winter solstice when the tilt angle is near 62 degrees.

Implied are the crossover points where the mechanics change from contraction to enhancement and back again. I don't know where these occur, but I will try to locate them and publish here at some future time.

Another contribution to this phenomenon, albeit minor, might be the divergence between the north or south component of the incident angles between solar noon and sunrise/sunset. On the equinoxes there is no divergence, hence a tilt setting for these days is optimum without compromise. On any other days, the solstices being the extremes, incident radiation is off-normal except for two moments in the day. Hence the single optimum setting involves compromise.

There is one final thing to notice. The curve discussed here is displayed with an expanded vertical scale. The perturbations, while noticeable and interesting, are of pretty small magnitude. This also seems to be in alignment with the small energy variations that would be expected from sunrise/sunset variations.




May 13, 2002. Sunset was 18:51.

Sunset observed on the array tilted at 23.6 degrees was 18:34.