TRACKING THE SUN
A solar panel that is sitting on a surface like a roof often receives sunlight at an angle. Solar intensity is at its maximum when it strikes a surface perpendicularly, so a solar panel that is receiving most of its sunlight at an angle is not obtaining all the energy it could. It would be ideal for solar panels to always be directly perpendicular to the sun's rays. The solution to this problem, though it may be complex in execution, is simple in concept: a solar panel that changes angle with the sun.
A solar panel that is sitting on a surface like a roof often receives sunlight at an angle. Solar intensity is at its maximum when it strikes a surface perpendicularly, so a solar panel that is receiving most of its sunlight at an angle is not obtaining all the energy it could. It would be ideal for solar panels to always be directly perpendicular to the sun's rays. The solution to this problem, though it may be complex in execution, is simple in concept: a solar panel that changes angle with the sun.
The study of atmospheric sciences allows us to determine the exact position of the sun at any time in any location. The sun's position can be very basically broken down into two angles: solar hour angle and solar elevation.
In this project, I took advantage of these easily calculable angles. Combining them with some basic mechatronics allowed me to come up with the following solution:
The sun-tracking solar panel is a mechanical base with a solar panel mounted on two axes of motion. The base itself is a plate with a mounted breadboard (more specifically a Board Of Education breadboard), a battery pack, and a servo. 
This lower servo is the "hour angle servo", and it rotates parallel to the base plate from East to West. A second servo, the "solar elevation angle servo" is mounted on top of the hour angle servo. The solar elevation angle servo rotates perpendicularly to the base plate, from the horizon to ninety degrees above the horizon.
All the components of the base are put together with screws and nuts, and the servos and battery pack are connected to the breadboard.
The solar panel itself is made up of six six-volt solar modules. The modules are hot glued to a piece of foam-core, with holes drilled in it for the wires. The solar modules are connected in parallel, and the wires are soldered together. The whole solar panel is attached to a metal plate, which is in tern attached to the solar elevation angle servo. The solar panel is also connected to a separate breadboard for testing purposes.
The sun-tracking solar panel can be coded in two ways: to change the angles every our, or to continuously change angles. 
Hourly changes are quite simple to achieve, since dimensional analysis will tell you how much to move the hour angle servo. In this case, the servo needed to move 83 steps for every fifteen degrees, which is the amount the angle changes every hour.
Solar elevation is more complicated, being nonlinear. When the servo was calibrated with a level, the position 780 corresponded to zero degrees and the position 330 corresponded to ninety degrees. So, the solar elevation angle for each hour was converted to a servo position using:
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀Servo Position = 780 - ( 5 x Solar Elevation Angle )

Continuous tracking requires establishing a new variable (k) that can move through the entire range of the servo (1 - 2000). The position of the hour angle can then be calculated by:
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀Position = 1200 - (k/2)
The equation that determines the position of the solar elevation angle, thus causing the servo to move smoothly is:
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀Position = Initial Angle - (Δangle x Δk) / 167
To justify putting the work into developing sun-tracking solar panels, I also calculated the difference in energy produced by a stationary panel (at the best possible angle), a panel that tracks every hour, and a panel that tracks continuously. Although the numbers are based on ideal conditions, the results from just the month of January show what a difference this kind of technology can make:
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