There have been some commercials that talk about the idea that all the energy needed to power human endeavor falls on the surface of the earth from the sun in a few minutes each day. Let’s examine this claim more critically and see where it takes us.

First, let’s get the definition of renewable clearly in mind. As I understand the argument it is power that is “constantly renewed.” Since the only energy coming INTO the earth’s system comes from the sun, I must conclude that fundamentally renewable power is related to the amount of power coming from the sun within a short time period. On that basis, this discussion will work exclusively with the amount of power the sun imparts to the earth. Whether it is harvested via solar panels, windmills, biomass, or wave machines, is merely a matter of efficiency and convenience.

I’ve posted on this topic before (Solar Panels – the Math), but in the interest of readability, I will repeat the physics here.

Sunlight on average, at sea level, bombards the earth with about 1.3 KW per square meter. In one hour, that means that one square meter of sunlight generates 1.3 KWh. Pretty straight forward. According to the US EIA, in 2006 total world energy consumption was 472 quadrillion BTU. If I did the math right that works out to 1.38E14 kWh/year or 3.8E11 KWh/day.

So, let’s assume, generously, that this 1.3 KW falls on a square meter for 6 hours/day. This means that 48,500 square kilometers of earth’s surface is needed to generate all of the power needed to run the activity of the entire human race.

Wait, I forgot to account for efficiency of conversion of one form of energy to another.  Let’s be generous and say we can achieve a 30% conversion efficiency. Remember that we are including solar, wind, biomass, etc.  So we need to use the sunlight that hits about 162,000 square kilometers of the earth’s surface each day to meet our immediate energy needs.

Just how big is 162,000 square kilometers? It’s about 62,500 square miles, bigger than the state of Georgia. Of course, I’ve neglected the infrastructure requirements around such facilities: the area required for stored energy when sun driven energy forms are not available, maintenance facilities, transmission lines, etc, etc. For the US, we consume about 15% of the total, so we would only need to use land the equivalent of New Hampshire or about 0.25% of the land mass.

So what? nuclear power requires space too! Power density is the key here. Nuclear power is simply star power from billions of years ago, stored within the atoms at an immensely compressed scale.

OK, the math… One uranium atom produces about  188MeV of heat or 8.4E-15 WH. So 1 KWH of heat requires about 1.2E17 atoms or about 5 micrograms of uranium.  Using the same 50% efficiency granted to renewables, to generate 5.4E11KWH/day using uranium alone would require approximately 50 metric tons of U per day. Uranium is a heavy metal, heavier than lead. So, total volume of uranium consumed each day would be about 2.7 cubic meters, that’s a cube that is about 1.4 meters (4.5 feet) per side. But this is an unfair comparison, nuclear power requires more than just a cube of uranium to generate electricity. I include this discussion to help everyone understand the fundamental scale of nuclear power.

So how much physical land would all of this take? Again, ignoring all infrastructure beyond the energy created, just like was granted renewables, a typical 1000 MW(electric) core is about 16 square meters. Most 1000 MW(e) nuclear power plants operating today sit on about 2 square kilometers of land, or so. The nuclear reactor, control room, and everything else supporting the nuclear reactor (called the nuclear island) is a small fraction of the nuclear power plant site (less than 20%), the rest is taken up by turbine, transmission and other non-generation specific needs. In fact, significant portions of the land are unused to exist as a required buffer for the community; these spaces have become nature preserves in many cases. However, in order to account for the land use that exists outside the actual creation of energy, let’s assume that the entire 2 square kilometers are required for a nuclear facility of 1000 MW. This accounts for mining, processing and storage – more than reasonable given that currently all spent fuel is being stored on site.

In 1 day a 1000 MW plant generates on average, 21.6E6 KWh, assuming a 90% capacity factor. To generate 3.8E11KWH would require about 35,000 square kilometers, or about 20% of the space required for renewables as defined above.

So, what does all this mean? It means that, setting aside technology issues related to energy storage, renewable energy as defined above requires significant areas of the world to be set aside for energy generation. Nuclear power can reduce that footprint and resulting impact by 5X.

Next myth: Uranium mining is dirty and leaves radioactive waste in its wake.


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