The recent announcement of Elon Musk caused quite the stir. The founder of Paypal, SpaceX and Tesla Motors proposed a public transit system dubbed the "Hyperloop" to connect Los Angeles and San Francisco. The premise of Hyperloop is based on a low-pressure tube which will act as the conduit for pods carrying passengers at speeds exceeding 700 mph.While near-supersonic travel in a tube may not be everyone's cup of tea, from our perspective one of the most interesting aspects of this concept is the central role of solar energy. Musk's proposed concept envisions covering the top of the Hyperloop with solar panels, and harnessing the sun's rays as the principal power source for this transportation system.

Image credit: SpaceX / Tesla

Image credit: SpaceX / Tesla

As outlined in his working paper, Musk states that "...by placing solar panels on top of the tube, the Hyperloop can generate far in excess of the energy needed to operate. This takes into account storing enough energy in battery packs to operate at night and for periods of extended cloudy weather". Since we are always interested in innovative ways to use solar energy, we decided to lift the hood and take a peek at the details of his plan.

Hyperloop has a very large surface area and the proposed location has very favorable solar radiation conditions. The total surface area is 4.25 meters wide and about 560 kilometers long. The proposed concept assumes a maximum solar power output on the order of 120 watts/m2. Given a surface area of 2.38 million square meters and a solar energy potential of 120 watts per meter squared, this corresponds to a whopping 285 megawatts of energy. Musk qualifies this calculation further by saying that this is the amount that can be achieved at "peak solar activity".

While the scale of Hyperloop is much bigger than a typical residential solar panel installation, the steps to check its feasibility are exactly the same.

Image credit: SpaceX / Tesla

Image credit: SpaceX / Tesla

Checking the Solar Resource

For a quick, back of the envelope calculation, we can use Sunmetrix Discover to assess the solar energy potential in  Los Angeles and San Francisco. LA has a Solar Score of 81 and a corresponding average hourly insolation of about 222 watts/m2. San Franscisco, on the other hand, has a Solar Score of 75 and an average hourly insolation of about 211 watts/m2. We should note that these figures denote the inputs or "fuel" of solar panels under average climatic conditions during the year, while the 120 watts/m2 figure mentioned above is the output estimate under cloudless skies around noon. So how do we get from the inputs to the outputs?

Determining the Electrical Output

A conventional 250 watt capacity solar panel has a surface area of about 1.5 m2. This corresponds to about 460 kWh of electrical output for LA, and 438 kWh for San Francisco in a given year (assuming that the panels are installed flat on the Hyperloop). Let's assume that we'll average about 450 kWh of output for a whole year along the entire Los Angeles - San Francisco corridor. This corresponds to about 50 watts of output per hour (and a very respectable capacity factor of about 20%). Another way to interpret these numbers is as follows: for a desired level of output, we need to install a total capacity of 5 times the output itself.

Although exact panel dimensions vary from one model to another, conventional solar panels are about 1.5 meters high and 1 meter wide. Thus, the Hyperloop tube can accommodate 3-4 panels side by side along its 560 kilometer track. This corresponds to between 1.1 to 1.5 million solar panels for the whole system. Therefore, the total annual output of such a solar installation, on average, would be in the range of 450 kWh * 1.1 to 1.5 million = 495,000 MWh to 675,000 MWh if we were to cover it entirely by solar panels. Finally, if we divide this by the number of hours in a year (8760), we get the instantaneous output of  56 to 77 megawatts of power.

Checking the Cost Estimates

The baseline solar energy system for the Hyperloop has an average output of 21 megawatts. Using our 1 to 5 ratio above, we can estimate the installed capacity at around 100 megawatts (or about 400,000 of the 250 watt solar panels we mentioned above). It seems that, instead of covering the entire length of the tube, less than half of the total surface area on top of the tube will be covered in solar panels. The Solar Energy Industries Association (SEIA) estimates that utility-scale solar energy installations cost about $2 per installed watt (based on Q1 2013 numbers).  Taking this number as the basis of our cost estimate, the total cost of installation of the solar energy system (without the batteries) would be around $200 million. Taking into account inflation and other expenses, this figure is likely to be higher in the future. Musk's cost estimate? $210 million plus a margin of about 10%. Bang on.

Comparing our numbers

Musk's Hyperloop concept can generate about 21 megawatts of power from the solar panels, on average. However, the system actually requires an average power of 6 megawatts when it is cruising. This power will be drawn from an energy storage system that uses the same lithium ion technology available in the Tesla Model S. By acting as a buffer, the energy storage system will help balance out the fluctuations in solar energy output and enable continuity of service during the night. With an average generation of 21 megawatts and an average output of 6 megawatts, we see no reason why the storage system wouldn't work. Furthermore, designing and building a 100 megawatt (installed capacity) system is not an enormous challenge by itself. According to the SEIA, a total of 723 megawatts of solar energy was installed in the US in the first three months of 2013.

Our verdict

It seems like Elon Musk has done it again. Although we cannot comment on the areas beyond our solar expertise (such as the concept of the air cushion, safety statistics, etc.) when it comes to the solar energy output estimates for this location, and the costing, we were very pleased to see a well-designed system. It's clear that Hyperloop will face many technical, economic and regulatory challenges, but solar energy is not one of them. If anything, such an innovative and daring project would help the solar energy industry itself and promote the vision of a sustainable future where public transit is powered by a clean and abundant energy source.