solarEbike wrote: ↑
Aug 20 2018 12:37pm
wturber wrote: ↑
Aug 10 2018 8:18pm
I'd consider adding a bit more distance between the solar trailer and bike as well.
For the final build... I'll move it a little further back. I'll still get the same shadow but it will be later/earlier in the day.
Previously, I had posted anecdotal evidence along the lines of "When I'm riding toward the sun early and late in the day, my head and torso cast a shadow on the solar array. This makes me sad."
Sure, moving the array further back decreases the shading problem but how much is enough? If I double the distance to height ratio of the shading obstruction, will that cut the shading in half? Most of my solar energy capture happens 3-4 hours before and after solar noon when the head shading is not a problem so how much are those early and late hours really worth? Moving the array further back creates a longer trailer which affects handling and maneuverability so ideally I want to make it as long as it needs to be and not an inch longer.
So, I ran a 3D solar shading simulation. I don't know why I didn't think to do this earlier but now that I've done it, the results are glorious.
This shows every travel direction at once so it may take a little work to parse but I think it's worth the effort.
The white cylinders in the center represent the head and torso of the rider on a recumbent bike, simplified to present the same shading profile in every direction. The little yellow/orange squares are 5" (125 mm) SunPower solar cells. The analysis takes into account local weather using a statistically-derived typical meteorological year and calculates the position of the sun for every hour of every day of the year. The numbers on the cells are annual shading derates for a non-tilting array located in Oakland, California. "100" means no shading on that cell. "90" means that cell gets 90% of the energy of an unshaded cell at the same tilt and azimuth.
If you're in the southern hemisphere, you'll need to swap north and south. If you live close to 38° latitude anywhere in the world, your numbers should look very similar to this. If you're much closer or further from the equator, your numbers will look quite different. If you're optimizing only for summer travel rather than year-round, your numbers will also be different.
So what does this tell us?
If you're traveling due north all day in California, all your cells are in rectangle (1)
. The sun rises to your right and sets to your left and is pretty much behind you all day so your head never casts a shadow on the array. You can put the array as close to the bike as you want. If you look closely, you'll notice some 98's and 97's for the cells closest to the rider. That's because on the summer solstice, the sun rises and sets 31° north of east and west at this latitude meaning the sun is in front of you at sunrise/sunset so you lose a few rays in the summer.
If you're traveling due south, all your cells are in rectangle (2)
. The sun rises to your left and sets to your right and is pretty much in your eyes all day. Your head casts no shadow on the array early and late in the day but it does cause shading problems in the middle part of the day. Since the sun's elevation is lower in winter, the problem is much worse in the winter because you cast a longer shadow at noon. If you maintain a 1:1 ratio of distance to height from the array to your head, you can limit your year-round losses to 5% (100-95 on the worst cells). Move the array just a little further back and your losses drop to 1-2%. Much better.
Things get much worse when you're traveling east (3)
or west (4)
. You're now traveling directly toward/away from the sun early/late in the day. At a 1:1 ratio, your losses are 10%. At 2:1 they're only 2%. Not linear at all.
If we assume all travel directions are equally likely, the average losses of the closest cell at 1:1 is (0+5+10+10)/4 = 6.2%. If we assume the worst case scenario that a couple of shaded cells can knock out the whole module and we have four modules then the overall self-shading loss is only 1.6% which sounds pretty good to me.
Incidentally, a single-axis sun-tracking system with the axis parallel to the direction of travel provides the most benefit when traveling north/south and the least when traveling earth/west but that's a topic for a future post.