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

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Discussion Overview

The discussion focuses on the mathematical considerations involved in determining the optimal angle for solar panel placement to maximize solar energy collection throughout the year. Participants explore various mathematical approaches, including 3D trigonometry and probability distributions related to cloud cover and solar intensity.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant suggests that there is significant math involved, particularly in 3D trigonometry, and mentions the variability of electricity production based on time of day and panel type.
  • Another participant proposes creating random variables for solar intensity and other parameters to calculate mean and variance for total solar collection.
  • Concerns are raised about the impact of cloudy weather on optimizing angles, with a suggestion that optimizing for specific seasons may not be effective if weather conditions are unfavorable.
  • One participant mentions the challenges of finding an algebraic closed form for calculations, suggesting that simulating a year may be necessary.
  • A participant shares an anecdote about a person who built a solar panel that tracks the sun, indicating that while there was a lot of math involved, practical estimations were often more efficient.
  • Another participant expresses interest in learning about the math behind solar panel tilting optimization and seeks guidance on monitoring radiation data.

Areas of Agreement / Disagreement

Participants generally agree that there is a substantial amount of math involved in the topic, but there are multiple competing views on the best approaches to take, particularly regarding the impact of weather and the feasibility of simulations versus closed-form solutions. The discussion remains unresolved on several points, including the specifics of the mathematical methods to be used.

Contextual Notes

Limitations include potential dependencies on specific definitions of solar intensity and cloud cover, as well as the unresolved nature of how to effectively simulate weather conditions over a year.

Who May Find This Useful

This discussion may be useful for individuals interested in solar energy optimization, mathematical modeling, and those looking to understand the practical applications of mathematics in renewable energy technologies.

gokuls
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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).
 
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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.
 
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.)
 
haruspex said:
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!
 
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.
 
Diffy said:
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.
 

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