Solar_Panel_v1
Solar Panel Configuration:
A solar panel is supported on beams whose ends are associated with the following points of a three-dimensional system: A (0,0,3), B (3,0,2), C (3,5,2); What is the general equation of the plane p that passes through these 3 points?
CALCULATION:
The formula I will use is this one (AP = r):
(I) AP.n = 0
This means that any vector of the plane p cross vector with its normal vector is equal to one (projection of n vector in r is null).
1) Let’s use the three points given, two by two, and make two vectors (v and u):
v = AC = C -A = (3,5,2)-(0,0,3) = (3,5,-1)
u =AB = B - A = (3,0,2)-(0,0,3) = (3,0,-1)
2) Calculating cross product of v x u; so n( i, j, k ) is equal to:
n = v x u = [ i j k i j ]
[ 3 0 -1 3 0 ] = 0i - 3j + 15k + 5i +3j - 0k = (5,0,15)
[ 3 5 -1 3 5 ]
3 ) Choose any vector that passes through point A:
AP = P - A
AP = (x,y,z)-(0,0,3)
AP = (x-0, y-0, z-z)
AP = (x,y,z-3)
4) So, let’s substitute the values to the equation (I):
AP.n = 0 (I)
(x,y,z-3)(5,0,15)=0
5x + 0 + 15z - 45 = 0 (5)
x + 3z -9 = 0
x - 3z = 9
Answer: The equation of the plane (p) is, therefore:
p: x - 3z = 9
Please see the graph solution:)
This means that any vector of the plane p cross vector with its normal vector is equal to one (projection of n vector in r is null).
1) Let’s use the three points given, two by two, and make two vectors (v and u):
v = AC = C -A = (3,5,2)-(0,0,3) = (3,5,-1)
u =AB = B - A = (3,0,2)-(0,0,3) = (3,0,-1)
2) Calculating cross product of v x u; so n( i, j, k ) is equal to:
n = v x u = [ i j k i j ]
[ 3 0 -1 3 0 ] = 0i - 3j + 15k + 5i +3j - 0k = (5,0,15)
[ 3 5 -1 3 5 ]
3 ) Choose any vector that passes through point A:
AP = P - A
AP = (x,y,z)-(0,0,3)
AP = (x-0, y-0, z-z)
AP = (x,y,z-3)
4) So, let’s substitute the values to the equation (I):
AP.n = 0 (I)
(x,y,z-3)(5,0,15)=0
5x + 0 + 15z - 45 = 0 (5)
x + 3z -9 = 0
x - 3z = 9
Answer: The equation of the plane (p) is, therefore:
p: x - 3z = 9
Please see the graph solution:)
Panel Localization:
If we had a mobile panel, we would make it follow the sun, like a sunflower.
I have a post on the jungletronics channel with Arduino that does just that, check it out for yourself: https://medium.com/jungletronics/solar-turret-v-1-1-6a5283023104
But the solution presented here has the fixed panel. So the best location of the panel is with its compliance aligned with the east-west axis as you can see in the gif below (simulation one_solar_day).
We make a compass-rose localization for this solar panel :).realize that during the day we will not have a constant amount of energy generated. We will need servos to make the panel follow the sun, but this is a post for another day:)
Thank you!
Credits:
Ricardo Zanardini - https://youtu.be/K7BL01Ce1tY (thank you, man!)
A nice sun_tracking_day :)
![[url=https://medium.com/jungletronics/solar-turret-v-1-2-113fc9723f81]https://medium.com/jungletronics/solar-turret-v-1-2-113fc9723f81[/url]](https://www.geogebra.org/resource/vfjpbw77/VyYj8i5Bm1Cye4ui/material-vfjpbw77.png)