It is incorrect to consider tidal power as renewable energy. Harnessing tidal energy will pose more severe problems than using fossil fuels. This study provides quantitative estimates to show how using tidal energy can destroy the environment in a short amount of time. Tides are induced by the rotation of the Earth with respect to the gravity of the Moon and Sun. The rotational energy of the Earth is naturally dissipated by tides slowly. Consuming tidal energy further reduces the rotational energy, accelerates the energy loss rate, and decelerates the rotation of the Earth. Based on the average pace of world energy consumption over the last 50 years, if we were to extract the rotational energy just to supply 1% of the world’s energy consumption, the rotation of the Earth would lock to the Moon in about 1000 years. As a consequence, one side of the Earth would be exposed to the Sun for a much longer period of time than it is today. The temperature would rise extremely high on that side and drop extremely low on the other side. The environment would become intolerable, and most life on Earth could be wiped out.
Oopsie
The author is saying if we use tidal energy to cover 1% of our total energy usage AND if we assume our energy usage will increase exponentially year by year, after 1000 years we’ll stop the earth spinning.
No shit.
If we sap an exponentially growing amount of energy from the earth’s inertia, at some point in the future it will stop because the amount of energy feeding into the system (sun) is relatively fixed in value.
If I was to bet, this paper was tongue in cheek joke between the student and their instructor.
Its a pretty good joke though, you gotta admit. Nothing like someone with a phd and the knowledge to mess with people not literate in the subject matter. Kudos to dr liu.
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You’re hearing about it for the first time, because it’s not a realistic issue. The math is (I assume) correct, but the circumstances describe are impossible.
If you boil down the authors claim, it comes down to:
If you extract energy from a system, with a finite rate of replenishment, at an exponentially growing rate, eventually all of the energy will be absorbed.
To me, that’s a ‘no shit’ sorta thing.
There is another problem with tidal power. A big tidal project can change the tidal range over large geographic areas. There was a plan to do a tidal project in the Bay of Fundy in Maine in the 1970s. The study showed is would change tides as far away as Washington, DC. It was scrapped.
Based on the average pace of world energy consumption over the last 50 years, if we were to extract the rotational energy just to supply 1% of the world’s energy consumption, the rotation of the Earth would lock to the Moon in about 1000 years.
That sounds unlikely to me.
Can you post your equations proving this?
Or better still, link to a peer reviewed paper proving this?
This paper from the royal society estimates the earth’s rotation is slowing at 1.8 milliseconds per century.
So you claim that humans use of tidal energy will increase this (over 1000 years) from 18 milliseconds to 31,536,000 seconds.
That is an increase of about 1 x 10^10
From what I can see with some back of the envelope maths is that your claim is pure horse shit.
So the Stanford post assumes that we continue to consume roughly 2% more energy per year. At that rate, in 1000 years we would go from consuming 1.753×10^13 W to consuming 6.98×10^21 W. This would be 40,000 times the energy the sun puts on the Earth. Because most energy quickly turns into heat, this would heat up the entire surface of the Earth to the point where it is uninhabitable. I feel that tidal locking would be the least of our concerns at that point.
Professor Liu seems to have made a simple mistake: What his model showed was unsustainable was not tidal energy, but actually his assumed exponential growth rate of energy consumption to ludicrous levels, levels that would spell disaster for the Earth.
That said, the website’s math checks out. The linear approach is a very basic year 1 physics problem that can be quickly confirmed.
The values we need for this calculation:
The mass of the earth (M) is: 5.97×10^24 kg
The radius of the earth (R) is 6.37×10^6 m
The angular velocity of the earth (w) is 7.29×10^-5 rad/sec
The current total worldwide primary energy consumption is 1.753 × 10^13 W. This is pretty close to the article’s assumption
The equations necessary:
The moment of inertia of a solid sphere of uniform density is: 2/5 MR^2
Rotational kinetic energy is calculated by: 1/2 I w^2
After some very basic plug-and-chug:
This provides a moment of inertia of the earth (I) of: 9.69×10^37 kilogram meters squared
And a total rotational kinetic energy of: 2.575×10^29 kg m^2 /s^2 This is pretty close to what the Stanford website calculated.
So if we used the suggested 1% here, it would take around 5.0 x 10^10 years to tidally lock the earth to the moon with our current energy consumption. But that’s not what was assumed in the article. It was also assumed that we would continue to expand our energy consumption by a constant 2% per year. This requires basic calculus.
We have energy consumption that starts at the previously mentioned: 1.753 × 10^13 W
Below, n is equal to the number of years.
This leads us to a consumption growth formula of: 1.753×10^13 * 1.02^n
To indefinitely integrate that formula, we simply divide it by ln(1.02), which gives us: 8.85236×10^14 1.02^n (we will drop the +c because it’s not necessary here)
And now we just need to solve the following equation for n: 2.575×10^29 = 8.85236×10^14 1.02^n
Solving gives us a real solution of: around 1681 years. This is close enough for me to say that the math checks out, considering that I didn’t start with exactly the same base formulas. But ultimately this is besides the point. The math is right, but the premise of a constant 2% growth is ultimately unsustainable. Short of building planet-scale radiators to shed heat, the earth would become uninhabitable by virtue of the sheer energy consumption alone.
Thanks for taking the time for the in depth analysis.
Yes, the 2% increase assumption is insane.
Brilliant
The linked article does provide calculations. The main assumption for such a short prediction appears to be that the rate of energy consumption will continue to grow exponentially, which to me seems unsustainable regardless of the production method.
This is BS
The moon is too small and too far away to cause the earth to stop spinning no matter what we do with the water from the tides. With his kind of reasoning, the water held in reservoirs from daming rivers would have stopped the earth from spinning and windmills (and sail boats) would have stopped the wind from blowing.
Actually the axis of the earth has shifted a measureable amount due to groundwater exploitation by humans shifting around the weight distribution of earth.
Also in your comparision to windmills you need to consider the very strong difference, that the wind is generated by the heat energy that comes from the sun, whereas earths spinning has no external energy source to maintain it.
Funny enough, if harvesting tidal energy were enough to stop the Earth’s rotation, then a civilization advanced enough to use all that energy without burning the planet to a crisp should easilly be able to restart the rotation or even pause the slowing long before it becomes a real issue.
We could intentionally force a 24hr day, and/or a 365.25 day year at that point, because fuck it, why not? Show Mars and Venus what happens if they don’t get with the program, right quick.
It’s a bit of a moot point anyway right? Tidal energy generation requires resonably specific geography to work. While it can probably generate a respectable amount of energy, you can’t just install it everywhere.
On one hand, this follows roughly the same logic as saying wind turbines will use up all the wind.
On the other hand, tidal locking is such a cool premise for a sci-fi dystopia.
That reminds me, ‘The Tides Return Forever’ is a cracking album by German prog band Eloy. I’m now going to be playing that this week 😉
