The Physics Police

The Physics Police

Saturday, December 21, 2013

Solar Power the World

Renewable energy is great. Producing more of the world's energy from renewable sources is crucial to reducing carbon emissions. In the long run, as fossil fuel prices rise, investments made in renewable energy will pay off.

Solar power is a promising renewable energy source. The last decade has seen a lot of investment in solar power. It has even been encouraged by government refunds here in the US. This has been especially effective, because it lessens the prohibitive up-front cost.

There's this popular info-graphic depicting the surface area required to power the wold with solar.

The first problem I'd point out is that the image is an equirectangular projection, which means it skews the relative area of different points. That's quite the wrong choice of map projection!

Second, this comical depiction ignores the problem of transmission. By concentrating the solar power generation far from population centers, loss during transmission would be staggering. Also, why not piggyback on the existing power grid infrastructure?

Pedantry aside, as I mentioned above, the challenge facing solar clearly isn't limited surface area, but up-front cost.

I gathered some statistics and did a little linear interpolation in order to hazard a guess at the price of photovoltaic solar panels per square foot in 2030, as indicated in green on this info-graphic.

((2030 - 2009) * ($2.90 - $1.94) / (1990 - 2009)) + $1.94 = $0.88

Then I calculated the cost in today's dollars to place an order for enough solar panels to power the world in 2030.

($0.88 ft-2) * (496805 km2) = $4.71 trillion

That sounds like a lot, but it's only a quarter of the projected GDP of China by that date.

Another important challenge to solar powering the world would be what to do about night time. Maybe we can all get electric cars. They could store power by day, and releasing some back into the grid at night.

This would, however, depends on significant improvements made in electric battery and/or fuel cell technology. While I think these are hugely worthy research goals, I can't help but think of the energy storage biology has already invented.

The cost to produce a calorie of heat from ethanol is about 1.01 calories of input in the form of farming, transportation, processing, etc. If those inputs could be supplied by photovoltaic power during the day, they would drain half of produced electricity, but provide a supply of ethanol to be burnt, carbon neutral, during nighttime.

This is also too good to be true, because you'd finally run into that surface area problem. There may be plenty of land available for photovoltaic, but presumably not enough land to grow crops enough to produce all that ethanol.

I guess we'll have to keep our fingers crossed for that energy storage breakthrough.

Actually, I've heard of one clever idea called solar thermal, where mirrors reflect sunlight to heat a giant tank of water, which is large enough to stay hot and provide some power throughout the night.


  1. I like that you address this. The smart grid idea could work better with other methods of storage, such as flywheels (concrete and bearings are cheap to make slow-turning flywheels), pumped water or pressurized air (I'm not a fan of the losses on this unless the compressor is used to heat a home and the depressurization loss is used for refrigeration). The electric car-on-grid-at-night idea fails to some degree with the idea that people need their cars during the day, so they are charging at night, not discharging into the grid. It kind of depends on charging the cars at work and after work at home before the sun goes down, with enough stored energy to run the grid all night and still drive to work in the dark in the morning....Maybe just put batteries in people's houses when the solar panels are installed with the next roof replacement (solar shingles, etc.)? There's also the possibility of using the solar power to store hot water in the basement for heating the houses, thus freeing up more petrol for other uses at night until more storage is installed, more houses are built with passive solar and much better insulation/earth works. With more people telecommuting, there is also the possibility of a migrating society that doesn't live where buildings have to be heated in winter/cooled in summer.

  2. Actually, the electric car-on-grid-at-night idea is plausible, even with current technology.

    The Tesla can charge 98.7 kWh (300 miles) in 5 hours 6 minutes.
    This charging can be done at work, during the daylight hours.
    Let's assume a commute of 50 miles (round trip) per day.
    How much additional charge a Tesla owner budget for one day?

    (98.7 kWh) * ((300-50)/300) = 82.25 kWh

    Way more than the 30.9 kWh used in the average home per day.