# Musings about calculations of angle of solar impact.

cdherman
Solar Expert Posts:

**27**✭
So, it occurs to me that only on 2 days a year, will there be a moment where the sun is striking my panels at exactly 90 deg NS and EW.

For instance, in KC (39 deg lat), on April 23rd and August 18, the Sun will be at 64 degree elevation at solar noon (180 deg south)

My array is facing due south (180) and is tilted 26 degrees. So on those two days, the sun will strike it perfectly perpendicular at solar noon.

On all other days between 4/23 and 8/19, the suns elevation reaches 64 before solar noon, and when the sun finally does reach 180, the other axis will be higher.

For instance, on Jun22 the max elevation is 74.5 here ( 90- (39-23.5)). The elevation reaches 64 degree already at 10:42AM and returns there at 1:59PM. Between those times, the sun is higher then the NS angle of my panels.

This of course, brings back memories of trigenometry, but those 30 year old memries from high school trig are pretty faded and useing complex geometry to calculate the angle of impact of a ray of sun on a plane (panel) involves some serious use of a calculator and (sin cosin, tan????) that I have forgotten.

Specifically:

Anyone know of a calculator out there that does this nicely, online?

Anyone really care, except me??:D

I find it fascinating. I mean, we all should understand some basic insolation priciples I think, as knowing what angle the sun is striking the array at any given time helps you spot malfunctions quickly. Simply knowing the elevation of the sun does NOT give the full picture. You have to know elevation, azimuth both, as well as the NS and EW orientation of the panel and only can it be calculated. (if you know how......)

For instance, in KC (39 deg lat), on April 23rd and August 18, the Sun will be at 64 degree elevation at solar noon (180 deg south)

My array is facing due south (180) and is tilted 26 degrees. So on those two days, the sun will strike it perfectly perpendicular at solar noon.

On all other days between 4/23 and 8/19, the suns elevation reaches 64 before solar noon, and when the sun finally does reach 180, the other axis will be higher.

For instance, on Jun22 the max elevation is 74.5 here ( 90- (39-23.5)). The elevation reaches 64 degree already at 10:42AM and returns there at 1:59PM. Between those times, the sun is higher then the NS angle of my panels.

This of course, brings back memories of trigenometry, but those 30 year old memries from high school trig are pretty faded and useing complex geometry to calculate the angle of impact of a ray of sun on a plane (panel) involves some serious use of a calculator and (sin cosin, tan????) that I have forgotten.

Specifically:

Anyone know of a calculator out there that does this nicely, online?

Anyone really care, except me??:D

I find it fascinating. I mean, we all should understand some basic insolation priciples I think, as knowing what angle the sun is striking the array at any given time helps you spot malfunctions quickly. Simply knowing the elevation of the sun does NOT give the full picture. You have to know elevation, azimuth both, as well as the NS and EW orientation of the panel and only can it be calculated. (if you know how......)

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## Comments

30,738adminThe folks who provide PV Watts (which can give you hour by hour predicted output based on local measured/averaged weather conditions) also have open source for the math behind the software.

Cosine will work fine--and if you are "flat" within 10 degrees:

- Cos (10 degrees) = 0.985 (or 1.5% loss due to geometry)

-Bill10,300✭✭✭✭"Anyone really care, except me??:D"

now that's a bit unfair to say that now isn't it?

some of what you said you lost me on, but the summary i am assuming you to say is that you don't want to design for the peak sun angle for the rest of the time it will be lower in the sky and i agree to a point. it will also be further off east or west too and yup you need to do the math to figure it for anytime of the year.

to be sure we are on the same page we recommend starting off with your latitude as the starting angle to use. 0° at the equator would mean the pv is flat on the ground and is said to be 0° from the ground standpoint and this is at the equinoxes so it is the average. now if you say you are at 39° latitude this means 39° off of the horizontal. (do note that if you are at 26° then you may want to adjust the angle upward.) now that 39° is for the peak or solar noon at equinox and you want to harvest better when the sun is lower in the sky and not just at solar noon so upping the angle is warranted and we usually go up to about 15° more. added to the 39° gives you a 54° angle and that would also help for winter collection when it's worse overall. from what i figure is that you may have subtracted about 13° rather than add it to come up with 26°. there is obviously a limit to going higher as the sun winds up being off many degrees east or west and not just in altitude.

i hope i addressed what you were driving at.

27✭The "anyone care but me" quip was not meant to annoy -- I honestly think I am spending too much effort messing with this. It was meant more self-deprecating that anything else.

The installation is finished -- I am just kind of mentally going over angles and when maximum production will occur. 26 deg is where my roof is at and I am not doing anything fancy.

Calculating the angle at which the suns rays hit a tilted panel is not easy. I will have to explore how Cos works again.....