Trigonometry problem
Desert Rat
Solar Expert Posts: 147 ✭✭✭
I don't remember any of my high school trigonometry, so here's what I'm looking for:
How to figure the length of a shadow cast by a solar array, given latitude and distance from grade to highest point on solar panels.
Assuming south facing ground mounted panels, level ground, lowest point of sun (winter solstice).
How to figure the length of a shadow cast by a solar array, given latitude and distance from grade to highest point on solar panels.
Assuming south facing ground mounted panels, level ground, lowest point of sun (winter solstice).
Comments

Mr. Rat. This might help…I once used it to calculate awning depth.OffGrid in Terlingua, TX
5,000 watt array  14 CS 370 watt modules. HZLA horizontal tracker. Schneider: XW6048NA+, Mini PDP, MPPT 80600, SCP. 390ah LiFeP04 battery bank  3 Discover AES 42486650 48 volt 130ah LiFePO4 batteries 
OffGrid in Terlingua, TX
5,000 watt array  14 CS 370 watt modules. HZLA horizontal tracker. Schneider: XW6048NA+, Mini PDP, MPPT 80600, SCP. 390ah LiFeP04 battery bank  3 Discover AES 42486650 48 volt 130ah LiFePO4 batteries 
Although I have used the trig functions on my calculator to do that, what I've found to be the most expedient way to figure that out is to draw a toscale drawing on a sheet of typing paper with a protractor and just measuring the length of the shadow with your ruler.
System 1) 15 Renogy 300w + 4 250W Astronergy panels, Midnight 200 CC, 8 Trojan L16 bat., Schneider XW6848 NA inverter, ACDelco 6000w gen.System 2) 8 YingLi 250W panels, Midnight 200CC, three 8V Rolls batteries, Schneider Conext 4024 inverter (workshop) 
Thanks for the links, Mr. 55
I also found this:The following formula is used to calculate the length of a shadow cast by an object.
L=H/tan(a)
 Where L is the length of the shadow
 H is the height of the object
 a is the angle to the source of light (typically the sun)
Here's an online calculator:
https://calculator.academy/shadowlengthcalculator/

Likely you will have to be concerned with a longer shadow cast range than highest winter solar noon angle above horizon over the day with lower sun angles above horizon toward morning and afternoon.

Here is an educational video explaining how to do the calculations. Note: I said ... "calculations" = plural. As there are actually two calculations. The single formula for shadow length = height x tan(angle) is only applicable at solar noon. You need the longer shadow length from 9am and 3pm, not just the shortest shadow at solar noon.
https://youtu.be/TvToXfN9Jsc

mvas said:Here is an educational video explaining how to do the calculations. Note: I said ... "calculations" = plural. As there are actually two calculations. The single formula for shadow length = height x tan(angle) is only applicable at solar noon. You need the longer shadow length from 9am and 3pm, not just the shortest shadow at solar noon.
I always have more questions than answers. That's the nature of life. 
"Measure with micrometer, mark with chalk, cut with an axe""we go where power lines don't" Sierra Nevada mountain area
htps://offgridsolar1.com/
Email offgridsolar@sti.net 
Dave Angelini said:"Measure with micrometer, mark with chalk, cut with an axe"
Yep, that's Tim. He is lucky to be alive. About 12 years ago a Dodge pickup truck ran over him in front of his home one night then left him for dead. Damages were severe and permanent, but he labeled himself as RAM Tough because of his sense of humor. He must be 72 or 73 years old now.
I always have more questions than answers. That's the nature of life. 
Dave Angelini said:"Measure with micrometer, mark with chalk, cut with an axe"
I cut it twice and it's still too short !!!
Pythagorean theorem,
This is petty simple and might help you.
a, squared + b, squared = c, squared
plug in numbers as needed
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