# Angle of Sun

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Hello,

I am trying to compute solar efficiency and need to convert the angle of incidence of the sun to the solar panel. The panel is elevated off the ground by 37 degrees and at any given time, I know the angle of the sun from the zenith straight above and the angle from south which is the direction towards which the solar panel is tilted.

Can anyone help me with the math to convert the two angles into a single angle of incidence on the panel? I imagine it is some kind of trigonometric computation, but it is eluding me so far. I can subtract the tilt angle from the zenith angle to get one dimension and the angle from south like a clock is the second angle. How can I combine these perpendicular angles to get a single angle which is the angle of incidence?

Thanks for your help.

-William

• Solar Expert Posts: 60 ✭✭
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Re: Angle of Sun

The calculator on this website does that. It's based on material in the book posted there, where you will probably find the equations you're looking for.

Hope this helps,
--
Moe
• Registered Users, Solar Expert Posts: 1,832 ✭✭✭✭
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Re: Angle of Sun

William,

The type of loss you’re researching is called “cosine error”. For example, if azimuth angle of incidence is off by 30 degrees from perpendicular, and the cos of 30 degrees is 0.866, then the performance would be 86.6% of optimal.

For errors in both tilt and azimuth, and everything else being equal, you just need to multiply the two cosine errors together. For example, if both the tilt alignment and the azimuth alignment are each off by 30 degrees, then the performance would by 86.6% x 86.6% = 75% .

Changes in array output current are the best indicators of this behavior.

HTH,
Jim / crewzer
• Solar Expert Posts: 60 ✭✭
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Re: Angle of Sun
crewzer wrote: »
...if both the tilt alignment and the azimuth alignment are each off by 30 degrees, then the performance would by 86.6% x 86.6% = 75%...

So to find the angle of incidence in your example, it would be the inverse cosine of .75 = 41.4º?
• Registered Users, Solar Expert Posts: 1,832 ✭✭✭✭
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Re: Angle of Sun
So to find the angle of incidence in your example, it would be the inverse cosine of .75 = 41.4º?
Hmmm... been a while since I studied solid geometry... I'll have to try to remember to sketch this out while sitting in one of five airports on this week's travel itinerary!

Regards,
Jim / crewzer