Trigonometry problem

Desert Rat

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).

Wheelman55

Mr. Rat. This might help…I once used it to calculate awning depth. 

https://susdesign.com/overhang/

Wheelman55

GW. Here’s another link:

https://www.borstengineeringconstruction.com/Calculators.html

MichaelK

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 to-scale drawing on a sheet of typing paper with a protractor and just measuring the length of the shadow with your ruler.

Desert Rat

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)

Midday sun angle at winter solstice = 90⁰ - (latitude degrees + 23.5⁰)

Here's an online calculator:
https://calculator.academy/shadow-length-calculator/

RCinFLA

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.

mvas

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

Marc Kurth

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.

Wow, Tim Wilhelm! I haven't spoken with him in years. Tim is a good man who generously and tirelessly guided people with their wind and solar projects while teaching classes in those subjects. It wasn't just theory for him - he is a hands-on practical engineer who designed and built successful solar and wind systems.

Dave Angelini

"Measure with micrometer, mark with chalk, cut with an axe"   

Marc Kurth

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.

Miller_Ranch

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