I was nosing around the Internet looking for optimal angle calculators for solar panels. I'm not sure I found any that were worth using. They typically ask your location and then come up with angles that vary with the month. But they don't ask about the angle your home faces. They also vary by as much as 10 degrees, so clearly they are using different calculations or assumptions.
My place faces nearly due SW and so will not get much morning sun, but will get sun until sun down. This is good for mitigating the power peak curve. I understand some utilities pay more for panels that are oriented this way. I can't find any calculations that take azimuth into account. It would seem the optimal elevation angle would be lower than panels pointed due south.
Spherical trig isn't that hard. The power output of a panel scales with the cos of the angle between the normal to its surface and the sun.
There is a fudge factor for the typical weather behaviour of fair weather clouds in the afternoon in the UK. Not sure how well that applies in continental USA if at all.
Loss of efficiency roughly scales as 1 - x^2/2
Where x is the angle in radians between the normal to collector and the sun. Provided that you are aligned within 0.15 radian ~9 degrees of the optimum the difference in efficiency is barely noticeable ( <1%).
It takes a 26 degree pointing error to be down to 90% yeild.
In the UK the optimum for total power is around a SSE facing roof with an slope angle around 45-50 degrees which isn't far off the norm here. It varies with latitude (ie with maximum transit altitude of the sun).
You can mock up the integrals in a spreadsheet pretty easily as the sun moves along the ecliptic. It really isn't rocket science. Any basic astronomy text will show you how to compute the suns position.
The hard part is predicting local seasonal variations and insolation - that is far more important than the geometrical considerations.
There are also competing diffuse light effects that favour a more shallow angle than the one for optimum direct solar capture. Different calculators are including different models of how the power is collected. In the UK it is an even split between diffuse and direct.
It is a bit long in the tooth now but this book isn't a bad introduction to optimising a solar configurations. It dates from the first OPEC induced energy crisis and solar enthusiasm:
Sun Power: Introduction to the Applications of Solar Energy J. C. McVeigh ISBN 10: 0080208622 / ISBN 13: 9780080208626 Published by Pergamon Press, 1977
The fundamentals haven't changed but the cost of PV solar panels has.
It is basic spherical trig - work out the unit normal to your roof surface and then compute the position of the sun. Their dot product is the cos of the angle between them which is the answer you want.
There is an additional factor due to extinction as the altitude of the sun gets very low. That only really hurts us in the UK where in winter the sun barely gets out of the strongly attenuated band <5 degrees.
It isn't really worth obsessing about optimal angles unless you intend to have a system that can alter its angle of tilt with the seasons.
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