Published on February 22nd, 2019 | by Michael Barnard
February 22nd, 2019 by Michael Barnard
Over on Quora, someone brought up the question about whether human kinetic energy could somehow be contributing to global warming. To assist them to understand the sheer absurd scale of the energy already flowing around in the environment, I worked up the potential and kinetic energy in a square mile of rain vs the energy produced by an average wind turbine in an hour. Warning: math and units follow.
A standardized raindrop is considered to have a mass of 4 milligrams (mg). Rain typically falls from lower height clouds, but forms in the interior of the cloud, not at the cloud base. For a napkin calculation, we’ll use 2,000 meters.
Potential energy is calculated with the formula GPE = mgh, so 0.004 * 9.8 * 2000 or 78.4 joules. Of course, most of that energy is consumed by air friction. The terminal velocity of the average raindrop is around 9 meters per second (m/s). Energy is equal to 0.5 * mass * velocity squared, so when the raindrop hits its energy is 0.5 * 0.004 * 9^2 or 0.162 joules. That means that about 78.2 joules of energy was dissipated as friction aka heat during the fall of a single raindrop.
In a heavy rainstorm about 1,580,088,782,700 raindrops fall in a square mile in five minutes, so that’s about 1.2 * 10^14 joules of energy in those rain drops. Let’s take that up to an hour to make a comparison, so that’s 24 * 10^14 joules in an hour.
A megawatt hour (MWH) is 3.6 gigajoules (gj). Modern wind turbines are in the range of 95% of the Betz Limit of 59.3% of energy from the wind being harvested, and are typically about 2.5 MW in capacity at present. 3.6 gj times 2.5 divided by 95% then divided by 59.3% again gives us about 15.8 gigajoules in the wind flowing through a turbine for an hour. The wind turbine is harvesting about 9 gigajoules of that.
A gigajoule is 10^9 joules. That’s a lot less than 10^14, obviously, five orders of magnitude. The wind turbine would have to turn nonstop for 2,700,000 hours or 112,500 days or 308 years in order to produce the same energy as the kinetic energy in a square mile of heavy rain.
Of course, onshore wind turbines are typically in the range of 40% capacity factors, which means that they generate 40% of the potential maximum electricity if they operated full time for a year. But the wind doesn’t blow at optimal speeds all the time and there’s maintenance. So let’s make these numbers more realistic.
The wind turbine would have to operate for 6,750,000 hours or 281,250 days or 771 years in order to produce the equivalent potential energy of a single hour of heavy rain in a single square mile.
If we wanted to quibble, we could look at how many square miles a wind turbine takes and divide it out. Turns out it’s about 10 MW per square mile so our hypothetical 2.5 MW turbine would only occupy about a quarter of a square mile. If you wanted to divide by four, you’d find that it still took about 200 years of operation to generate the same energy as in a single hour of rain.
One of the things about nature is that most people have no idea how incredibly big and energetic it is. That’s part of the reason why carbon capture and sequestration initiatives are failing: the size of the problem is too big for us to manage. The only solution is to stop emitting CO2e and let the biggest machine we have access to — nature — do its work.
It’s also the reason why many people think that renewables can’t possibly work, that they aren’t sufficient to power the world. We are barely touching the tiniest shred of a single thread of the energy flowing in the Earth’s atmosphere at present and yet we are already over 25% of global electrical supply from renewables.
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