Cosine loss

Cosine loss is the term for the energy you lose by not facing the sun's rays directly. For example, if you face a 1 square meter solar panel directly at the sun, meaning perpendicular to the incoming rays, you get all the energy available to that collection area (about 1kW). If the panel is at an angle to the sun, you get some fraction less of the available energy which is a function of the cosine of angle away from being perpendicular to the suns rays. See drawing below.

It's an obvious concept but under-discussed, probably because it results in lost power. If you think about it a bit, it explains a lot about configuration of solar collection systems. It is why all power towers are tall and the mirrors face South (in the Northern hemisphere). Since the sun's path through the sky varies across 47 degrees over the year, you'd want to put the target in the middle of that, so your cosine loss never exceeded 23.5 degrees. Cos(23.5) = .917, so you only lose about 8% energy in the worst case.

In the video below, my target is on a South facing roof with a 30 degree pitch. If there were solar panels on that roof, they would suffer least cosine loss when the sun is at a 60 degree altitude (measured from ground), around April 1 and mid-Sept -- that's when the runs rays would hit them dead on. Where I live, in mid-November, the sun is at about 40 degrees altitude (measured from ground). So a solar panel on my roof is about 20 degrees out of ideal this time of year, about 6% cosine loss. My heliostat was angled about 10 degrees, so actually my mirror suffered significantly more cosine loss than would a panel, about 60 degrees out of ideal, which is a 50% loss, given the target (assuming the target is perfectly hit).

The reason for bringing this up is that supplementing a residential solar panel installation probably provides the best return on investment for a cheap heliostat. That is, if you already have a solar panel installation, there is an excellent chance it is underutilized and a $500 investment in heliostats could deliver 10% returns in energy savings. It's not a particularly "efficient" use of the heliostat. The ideal residential installation would have a well placed target, ideally a solar panel that could handle multiple suns. Then again, power is as pure a commodity as there is, and 10% ROI is 10%. Still, it's worth keeping in mind.

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Some additional description:

This is an image from Power From The Sun (Chapter 2). Their description is this

"An instructional concept, and one often used in solar irradiance models, is that of the extraterrestrial solar irradiance falling on a horizontal surface. Consider a flat surface just outside the earth’s atmosphere and parallel to the earth’s surface below. When this surface faces the sun (normal to a central ray), the solar irradiance falling on it will be I_o , the maximum

possible solar irradiance. If the surface is not normal to the sun, the solar irradiance falling on it will be reduced by the cosine of the angle between the surface normal and a central ray from the sun."