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
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.