### Can solar roads be cost effective?

6/22/2014 03:51:00 PM
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Here's a slightly mathematical doodle on the feasibility of solar roads.

The cost-benefit comparison most commentators are implicitly doing here is asking whethter the value of the electricity generated by the solar road exceeds the extra cost of building the solar road versus a standard asphalt road. This depends on a lot of variables: how long the roads last, the difference in cost between solar roads and asphalt roads, how much electricity the solar panels produce, how much electricity the solar panels consume (you can't paint on glass, so the lines have to be displayed by electric-powered LEDs; you can't plow glass, so the ice has to be melted off by electric-powered heaters), and how much energy is lost during transmission (most of our interstate surface area isn't near cities!), what times people consume the most electricity (we can't store unused electricity, nor can we control when solar panels generate the most electricity!), and related to the last point, what the price of electricity is.

But, this is not the right calculation to do. This kind of math is what led people to erroneously think that proton-beam therapies were a cost effective cancer treatment in adults. To explain my analogy, proton-beam therapies are enormously expensive, but do save lives by killing cancer, meaning that the total benefits they provide would be worth the high cost. BUT, it turns out that we already have an alternative cancer treatments--traditional radiation therapies--that provide the same benefits at a fraction of the cost. The lesson here is that you can't compare total benefits to total cost, you have to compare added benefit to added cost compared to the best alternative.

Which brings me back to solar roads. Solar roads are a difficult and expensive option in a world that has tons and tons of cheap, more effective alternatives. For example, hardly any buildings in the US have solar panels on their roofs. Putting solar panels on roofs would eliminate all of the technological limitations of the solar road: they wouldn't need to have tempered-glass surfaces capable of holding semi-trucks; they wouldn't need LED displays; they wouldn't need to be heated to clear the ice; they wouldn't need to be textured to provide traction for cars; they could be angled to maximize the amount of direct sunlight; they'd be located closer to where the electicity is needed, so less transmission losses. All of these are things that would not only allow the panels to generate more electricity, but also reduce the cost of making the solar panels. And this retains the main advantage of solar roads: we wouldn't need to spoil unused land to install these panels.

So let's do a little math. Let $C_{sr}$ represent the cost of, say, a square meter of solar road, while $C_{r}$ is the cost of a square meter of asphalt, non-solar road, and $C_{s}$ is the cost of a square meter of solar panel installed on a roof (for our purposes, it will suffice to assume that these quantities are the summed discounted costs over all future periods--including both upfront building and future maintenence). Furthermore, let $W_{sr}$ be the energy produced by a sqare meter of solar road, compared to $W_s$ units of energy produced by a square meter of solar panels installed on a roof (for our purposes it will suffice to say that energy is the usuable power output over the course of, say, a representative year). There are a couple of postulates that I think should be uncontroversial:
1. $W_{sr} \lt W_s$
2. $C_{sr} \geq C_r+C_s$
The first postulate is the direct statment of all the things summarized in the previous paragraph--for lots of reasons, solar roads generate less electricity per unit of area than a solar panel on a roof. The second postulate is a bit less obvious but an approximate proof would be as follows:
a solar road's functions can be decomposed into a solar panel function and a road function. The "road cost" portion of the cost of the solar road is what it would cost to surface a road using the solar-road technology but leaving off all of the components of the solar road panels that are used for generation of electricity (so, no silicon, no circuitry etc, can use cheaper surface than the tempered glass because transparency isn't needed, with different surface we could paint lines rather than use leds, etc). What remains after the solar panel functions are stripped away must be less than or equal to the cost of building a road under the alternative, because if it wasn't cheaper we could just use this--solar road without the solar panel--in the alternative. The "solar cost" is what it would cost to build a solar road without any of the components needed to make it drivable (no tempered glass, no load-bearing foundations, no LEDs or heaters. Again, this must be less than or equal to the cost of building a solar panel in the alternative, because at the very least we can use a solar road without the road as a solar panel. This leaves us with two additional terms in our decomposition: first, there are many things which are necessary in the solar road (the LEDs, the heating system, the tempered glass) which aren't counted in either the "solar cost" or the "road cost" components, and these are extremely expensive things. Second, there may be some components that are counted in both the "road cost" and the "solar cost"--for example, solar cells on the roof still require some kind of protective case--perhaps made of plain glass on the front and plastic on the sides and back--that would be rendered redundant when merged with the solar road, which has it's own much more expensive protective case of tempered glass and steel(?) foundations. So we shouldn't count the cheap glass and plastic case on the roof-installed solar cell. This is actually where the key assumption of this postulate lies: the redundancies that could be eliminated by merging the road and solar cell are far cheaper than the extra costs that would be required in neither if they were separate.
With that established, we can proceed.

From the first postulate we know that $\frac{W_{sr}}{W_s} \lt 1$ which implies by way of the second postulate that $$C_{sr} \gt \frac{W_{sr}}{W_s}\left(C_r+C_s\right)$$ which implies that $$\frac{C_{sr}}{W_{sr}} \gt \frac{C_r+C_s}{W_s}.$$ Note that the left hand side is the cost per unit of energy of the solar road, and the right hand side is the cost per unit of energy under the best alternative. Solar roads are cost inefficient whenever my postulates are true. Case closed.
Mangosteen Juice 6/24/2014 02:18:00 AM
Solar road is a very interesting concept but it is not practical. During monsoon season when there is no light due to clouds, the solar road won't get its energy leaving the purpose of its creation in vain.

Regards,
Lucas Moore
anniebaker 7/10/2016 08:58:00 AM
Great blog by the way read my last article.