Fun With the Sun

Playing with the Numbers on Solar Energy

Jan 03, 2022

Most countries have pledged to switch to electric-only vehicle production by 2040.

The total amount of solar energy reaching the Earth is 8000 times the annual global energy consumption of all fuels (oil, gas, coal, nuclear, and renewables).

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Put those three facts together (sources are listed below) and it appears we may be moving rapidly towards the all-electric, zero-carbon economy envisioned by Bill Gates in How to Avoid a Climate Disaster.

In an earlier essay, we sounded a cautionary note about how limitations on the grid that moves electricity around might be a pinch point in achieving even just the all-electric vehicles part of Mr. Gates’ plan. Let’s turn that around now and have some fun thinking about possibilities, and play with some of the numbers on solar energy potential.

What we will do here is definitely in the nature of those quick sketches on a napkin, or back-of-the-envelope calculations, that have been memorialized by institutions and on the web, and that occasionally lead to major breakthroughs We will compute some approximate numbers and sketch one intriguing idea that might help visualize our potential all-solar-electric future.

We’ll start with that 8000-times number. It’s real, and impressive, but there are lots of steps between solar energy at the top of the atmosphere and what arrives at the plug in your home.

The top bar in this figure is that huge number for total energy received in sunlight (all numbers are in terawatts -TW or trillions of watts – but don’t worry about the units, just focus on the relative numbers).

The atmosphere sits between the sun and our solar collectors on the ground, and absorbs or reflects ~46% of incoming radiation, leaving ~93,600 TW reaching the surface (approximate calculations are perfectly appropriate when you are scribbling on a napkin, or an envelope).

We will be conservative here and say our solar farms will only be feasible on land, 29% of Earth’s surface, and that brings us down to ~27,000 TW. Let’s also say that collectors on the ice fields of Antarctica and Greenland are also unlikely (~10% of the land surface). That brings us to ~24,000 TW.

Solar collectors are not 100% efficient at converting sunlight to electricity (nothing is). There are a number of estimates out there, and a number of competing technologies, but the numbers tend to cluster between 20 and 30%. Let’s use 25%, which then brings us all the way down to about 6,000 TW.

We have “lost” a lot of energy along the way, but the bottom line is how this compares with total global energy consumption. That number would not even show up on this figure (although I have put in a small line) - It is about 20 TW. Knowing that this rough calculation gives a number for available solar energy that is 300 times global demand leaves a lot of room for economic, social and regulatory limitations. Mr. Gates should be pleased.

Solar collectors can take up a lot of space, so since we are talking fun-with-numbers here, let’s use the U.S. as an example and sketch how much land would be needed to capture enough energy to meet national needs. Keep in mind here that we are talking not just about electricity, but all energy gained from oil, coal, gas, nuclear and renewables.

Here is a fairly complicated look at the U.S. energy economy that tracks the type of energy used and in which sector (would not fit on a napkin! – again, ignore the units).

The left hand bar shows how much energy is consumed from all sources (101.3). The right hand bar is total energy actually put to work (75.9). The discrepancy is the difference between the amount of energy used to produce electricity (38.3), and that amount actually delivered (13.0). A sizeable amount of energy is lost in the burning of fuels to produce electricity and in moving those electrons along the grid. Units here are Quads or Quadrillion BTUs – but again, the relative numbers are what matters.

Since we have already included the efficiency of solar collectors in the top figure, we can use the 75.9 number on the right as our target for total energy capture from the sun for the U.S. Through the maze of energy conversion tables (why do different organizations use so many different units?), that 75.9 becomes about 2.54 TW (or about 13% of total global energy usage). We’ll be conservative again and limit the construction of solar farms to the contiguous 48 states, which together represent ~5% of the land area of the Earth. Five percent of 6000 TW (first figure) gives us about 300 TW to play with. So acquiring 2.54 TW for all U.S. energy needs would require (back-of-the envelope) about (2.54/300), or less than 1% (actually about 0.85%) of the total land area of those 48 states. That would be about one acre out of every 118.

Now we can have some fun with that number by asking how that “less than 1%” of all land area relates to current land uses in the U.S.

There are estimates of the total areal coverage of, and potential energy capture from, rooftops and parking lots across the country. Those numbers (far right column) are less than total energy demand, but could provide 37% of that total, or about twice the current total consumption of electricity alone. With direct, local uses like these (we’ll imagine an example below) this source could reduce the need for the major upgrades to the current electric grid system that will be required to handle an all-electric economy that relied on large-scale, remote solar farms.

Given current land area estimates, either about 2% of all farmland or about 5% of all desert and semi-arid lands (37% and 16% of total U.S. land cover, respectively) could meet the demand. That huge solar farm in California (there is a link to the story under Sources below) is one example of placement in a semi-arid area.

Farmland planted in corn for ethanol is a particularly intriguing number. By federal law and rules, 10% of gas at the pump has to be ethanol. The conversion to all-electric vehicles might become the fastest part of the transition toward the all-electric economy. As we reduce the number of gasoline-powered cars, we reduce the need for ethanol. Converting just over one-half of the current corn-for-ethanol farmland to solar farms could meet national energy needs.

OK - so if the capacity is there, why haven’t we all gone totally solar? There are lots of economic, policy and regulatory roadblocks, but those are not topics for this Substack site – we just deal here with science and technology. And besides we are just having some fun with the numbers on our envelopes and napkins (digital ones now, of course!).

The primary technical limitation to high dependence on solar power is that it is not always available – no energy at night or on cloudy days. The quick answer to that problem is energy storage, and there are a number of proposals for that. Batteries come to mind, but wouldn’t they have to be of unimaginable capacity to store energy for, say a small town?

Large, yes, but not unimaginable. Briefly, Tesla has applied the battery know-how derived in part from their electric car products to produce battery “megapacks” that might handle the job. One installation is in place in Australia, and, despite some setbacks, appears to be viable. A number of other installations are set to occur in California, including one at a solar energy farm built by Apple.

We are starting to get too serious here. The fun part of this fun-with-the-sun, back-of-the envelope approach is envisioning what might be, with just a few, rough calculations to see if we are totally off-base. So far we seem to be hitting home runs.

Here is a mental romp on a distributed (decentralized) system that combines solar energy and electric cars and battery storage and your daily home and transportation needs (and thanks to my colleague Cameron Wake for introducing me to this system-level energy solution).

E-cars, or total electric cars, seem to be the wave of the future. Major automakers are advancing this transition from gasoline at warp speed. Bill Gates says this transition is one of the first key steps toward the all-electric economy.

Increasingly, there is talk of the feasibility of battery systems in E-cars that can provide as well as accept electrons. This becomes the key link in this fun-with-the-sun scenario.

Let’s say your daily driving destinations build solar panel “canopies” over their parking lots and make the energy captured available to recharge E-car batteries (our local town library already does this from roof-top panels!). If you are mostly at home, either a community solar farm or the panels on your home or building can charge your car during the day. At night, or, better still, during power outages, your car batteries become your local reserve and power your home. Reliance on the grid and large utilities would be greatly reduced.

Could this work? Some steps are being taken. The University of Massachusetts Amherst campus is installing solar canopies over some parking lots (linked to a Tesla battery storage system). Solar collectors at the building or community level is an area of rapid growth. And look again for those online discussions of reversible E-car battery systems.

But we need some numbers to play with. Those same E-car sites give estimates of storage capacity of up to 200 kilowatt-hours. Average daily home electricity usage is about 30 kilowatt-hours. Excess storage capacity would mean that you would not have to fully recharge the car each day. Those 200 kWh car systems have a predicted driving range of over 300 miles on a single charge, so your daily driving needs might not make a big dent in stored energy.

Here is a fun back-of-the envelope calculation. There are about 250 million cars and light-duty trucks (like pickups and vans) on the road in the U.S.. If these were all electric and could store 200 kilowatt hours of electricity each, the total storage capacity would be about 50 billion kilowatt-hours. Daily electric consumption in the U.S. is about 10 billion kilowatt-hours and residential use is about 4 billion. If we could even partially recharge all those vehicles each day….

I realize that this solar panel/car/home energy system will not be feasible for the 3% of the U.S. land area that is densely urban (and the 60% of the population that lives there), or for those who do not have cars. This is really just one idea that might help make a dent in our dependence on carbon-based fuels. We will need several others, but it seems that the energy resource (the sun) might not be the factor limiting our journey to the all-electric future. Creative solutions needed!

So, I have had fun playing with the numbers and seeing what we might learn from our envelope and napkin approximations. They all seem to tell us that there is a huge untapped potential to use the sun to power Mr. Gates’ all-electric economy.

Sources

The link to the story on the large solar farms in California is here:

https://www.nytimes.com/2021/12/21/climate/solar-power-federal-land-california.html?searchResultPosition=1

A release on the international agreement on non-carbon-fuel-based vehicles out of COP26 is here:

https://www.gov.uk/government/publications/cop26-declaration-zero-emission-cars-and-vans/cop26-declaration-on-accelerating-the-transition-to-100-zero-emission-cars-and-vans

The image of the solar farm, located at the Kennedy Space Center, is from:

https://www.nasa.gov/feature/kennedy-ready-to-plant-new-solar-farms

The reference to the book by Bill Gates is:

Gates, B. 2021. How to Avoid a Climate Disaster: The Solutions We Have and the Breakthroughs We Need. Alfred A Knopf. 257pp.

This NASA site is the source for the amount of solar energy received from the sun and the amount absorbed by the atmosphere:

https://earthobservatory.nasa.gov/features/EnergyBalance

That earlier essay on electric cars and the grid is here: