I have never been to the equator, but I’m pretty sure that vehicle is not at a location on the equator. Take that back. A quick spin around the globe and I see there’s a desert in Kenya right about at the equator, but given the stickers are en Español… ?

Let us hark back to our middle school Earth Science class. The only times and places where the sun’s angle of incidence on the earth is 90° are March and September equinoxes at the equator, and during the solstices at latitudes +/- 23.5°. (Spain occupies a region just greater than 35° and just less than 45°N. So still wrong.)

If you were going to spend $200 on a portable solar solar panel, presumably in addition to $140 – 250 for a power station, wouldn’t you want your panel to be as efficient as possible? As it is, the cell efficiency is 19-21%. But think of all that sunshine that’s going to waste by not having the panel angled properly!

I’m going to build and adjustable stand for my small RavPower 24W solar panel. (It’s not the one pictured. Need to save up more egg money for that!)

If you cannot decipher my little plans, here is the idea. The solar panel sits on a platform that’s hinged to a base. Directly above the hinges is a piece of moulding that keeps the panel from sliding off. The base is wider than the platform. At the back of, and attached to the base are two poles on either side. The poles have three sets of hooks at various heights. A dowel rod lays across a set of hooks. The top of the platform (with solar panel) rests on the dowel rod.

The heights of the hooks, of course, correspond to the optimal angles of incidence for winter, spring/fall, and summer. The whole contraption will be painted white to reflect heat. Devises connected to the panel’s USB ports will be placed underneath, in the shade of the platform, while they recharge.

If you are interested in building your own, or have an interest this particular problem space of lengths and angles &c. (you know who you are!) instructions are below the fold.

1. Collect data

Determine your latitude (LAT) using GoogleEarth, LatLon, or a map.

Find the dimensions of your panel (owner’s manual)

2. Calculate optimal angles of incidence 

That’s the angle that your solar panel needs to be tilted such that the sun’s rays hit your panel directly during the winter, the summer, and spring & fall (the same).

Using one of the methods above, calculate the three angles for your latitude (or the latitude you’re traveling to if you are a hiker or camper). If you’re unfamiliar with the notation, the asterisk means to multiply.

3. Solving for triangle values

Seen from the side, the solar panel stand is a right triangle. Using the Rule of Sines, the Pythagorean Theorem, and the dimensions of the solar panel, we’ll determine the dimensions of the stand’s components.

I want to know three things.

• How tall do the poles need to be?
• How long does the platform need to be. (I know it’s going to be longer than the length of the base.)
• What heights correspond to my optimal angles of incidence?

My panel is 34″ wide, and 12″ high, and that’s the way it’s going to lay on the platform. I want the platform to be slightly larger than the height of the panel, so side ‘a’ =15″. 

The poles need to be tall enough for me to put hooks in (for the dowel rod) that would correspond to the greatest angle the panel needs to be tilted– the winter angle, 53.6°.  

I know all three angles.

<C = 90°

<A = 53° (Dang. Why did I round down? Stupid.)

<B = 37° (180-90-53=37)

I know that side ‘a’ =15″. I can use the Rule of Sines to first determine the length of side ‘b’ (height of the poles).

So the highest hook is at 11″, meaning the poles need to be about 12″.

I now know the lengths of two of the sides so…

Side ‘c’ = 18.5″ so the platform needs to be about 19″ (with 1/2″ extending beyond the dowel rod).

Apply the Law of Sines to the other two optimal angles (summer, spring/fall), remembering to recalculate the value of <B, to determine where to place the other two sets of hooks.

That was fun! Heh. Already had a tag, “math.” Good for me.