## Math involved in finding the optimal angle of placing a solar panel

I want to write a 3500 - 4000 word research paper on the best angle to place a solar panel to optimize solar collection throughout the year. I was thinking of using planes in 3D and probability distribution for the cloud amount for different times of the year. There has to be a primary focus on math though. So my question is, is there enough math involved in this topic? If so, what math is involved? Thanks! (BTW, this is my first post, so hope this goes well).
 Recognitions: Homework Help Science Advisor Plenty, if you like 3D trig. Should also look at the value of the electricity produced (I assume this is PV). It can vary with time of day. Different types of panel cope differently with oblique angles. Main problem for the math may be that the best way is to simulate a year. Getting any kind of algebraic closed form to apply some calculus to might be impossible.
 Hey gokuls and welcome to the forums. To build on the advice of haruspex, you might want to create random variables for the intensity and other parameters and then get a mean and variance for the distribution of total collection input.

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## Math involved in finding the optimal angle of placing a solar panel

Might need to do various takes on accounting for cloudy weather, too. Not much point in optimising the angle for best autumn incidence if autumn is typically 80% rainy. (Then again, that might be the very reason for optimising it for autumn, esp where you are reliant on solar panel for your autumn energy.)

 Quote by haruspex Plenty, if you like 3D trig. Should also look at the value of the electricity produced (I assume this is PV). It can vary with time of day. Different types of panel cope differently with oblique angles. Main problem for the math may be that the best way is to simulate a year. Getting any kind of algebraic closed form to apply some calculus to might be impossible.
Thank you all for your respones!

haruspex I don't quite follow when you say "simulate a year", do you mean the orbit of the earth or amount of cloud cover. Could you please elaborate a bit? Other than that thank you, but I am still a bit worried if I can write for 3500+ words!
 Recognitions: Homework Help Science Advisor Yes, I meant the track of the sun and feeding in info re the value of power generated at different times of day and seasons. You could also randomise day to day for weather conditions.
 I actually know a guy that has built his own solar panel that moves throughout the day to be positioned to look at the Sun. If you would like to talk to someone who as actually built one, and programmed it himself PM me. I know for a fact there was a ton of math involved. But in the end be for practical purposes estimations were quicker and easier given the hardware he was using.
 I am interested in learning the math behind solar panel tilting optimization. I am trying to know how to start with monitoring the radiation data in my region and how to use the data. My learning is more on the data side. May i request you to contact me too.

 Quote by Diffy I actually know a guy that has built his own solar panel that moves throughout the day to be positioned to look at the Sun. If you would like to talk to someone who as actually built one, and programmed it himself PM me. I know for a fact there was a ton of math involved. But in the end be for practical purposes estimations were quicker and easier given the hardware he was using.
I am interested in learning the math behind solar panel tilting optimization.

I am trying to know how to start with monitoring the radiation data in my region and how to use the data. My learning is more on the data side.

May i request you to contact me too.

 Tags optimization, solar panel