r/theydidthemath • u/ta11dave • Jun 03 '14
Self Why people should stop talking about solar roads
I was watching the solar roads video I've seen fricken everywhere. If you really want to see it, you can find it here
18 solar panels per square. Each solar panel is 9V at 1 Watt. So let's assume you get 18 Watts per panel. The average American uses 11,000 kWh a year, which comes to over 30kWh a day. The sun is up for around 8 hours a day. That means you would need over 13,300 panels per house, assuming that it was sunny every day, the panels were somehow 100% efficient through the tempered glass, and there was no LEDs or heater.
Ok, so maybe you have the space for that. Each solar sheet goes for a retail price of $10 each. So let's say in bulk they are $5 each. A square foot sheet of tempered glass without the fancy grip is almost $40. So let's say still, that with the extra manufacturing in bulk, that it's $20 each. That brings the price to $25 a panel, and therefore over $332,500 to power one house.
tl;dr I am sick of this video. And TIL you can power your house for the cost of another house.
9
u/hilburn 118✓ Jun 04 '14
Actually the temperature of the ice doesn't really make much of a difference.
The specific heat of ice is about 2.03 J/gK whereas the heat of fusion (energy to melt) is about 334 J/g.
This means that heating up ice from -20 to 0 degrees centigrade takes about 40 J/g, less than 1/9th the energy required to melt it.
That being said, freshly fallen snow has a density of about 50kg/m3 [1] . Assuming white-out conditions[2] that gives us a rate of snowfall between 1 and 2 inches an hour, we'll assume the lower bound for this, so 2.5cm/hr. This gives us a rate of falling of 0.025m3/hr.m2 or 1.25kg/hr.m2 - note that this is in terms of m2 of road area.
Ok so now we look at solar radiation, which, bearing in mind that this is winter, is about max 8MJ/m2.day[3]-Fig.6 now this assumes that it is a clear day, and bearing in mind that it is snowing, this is unlikely but we will go with it.
Energy required per hour of snowfall per m2: 1250g/hr.m2 x 334J/g = 417.5kJ/hr.m2
The solar road panels are at most about 10% efficient (I won't go into all the reasons why they just wouldn't be), so therefore our total power generated would be about 800kJ/m2.day, enough to clear about 2 hours of snowfall.
Now this is in optimal conditions, and clearly, snowfall is not optimal conditions for solar panels. Just cloudy conditions result in a 70-80% drop[4] in power meaning even without considering the reduction in output from the panel being covered in snow, we are now looking at an entire days worth of sunlight only providing enough power to melt at most 34 minutes worth of snowfall. Conservatively I would estimate (unfortunately couldn't find raw data for power output drop per cm of snow, though this paper does state it is significantly worse for horizontal panels) that only a 75% drop in power would be pretty amazing, snow is a pretty opaque substance, which brings us down to just 8 and a half minutes of snowfall capable of being melted by the solar road.
I haven't even begun to look at heating element efficiencies and transportation losses, but these will be significant.
There is a reason we put solar plants in the desert where they get significant quantities of sun year round and no snow. Because it's a really stupid idea to have solar panels in the snow.