# B Long term sustainable energy bounds

#### lavinia

Gold Member
Is there an upper bound on the amount of sustainable energy/unit time that could ever be made useful to mankind?

For instance, if we imagine that the entire surface area of the earth were covered with deserts and no cloud ever appeared in the sky and then computed the rate of sunlight energy hitting the planet that would seem to be way above any realistic bound on the amount of usable solar energy per unit time. There must be some reasonable calculations that allow for a relatively small usable surface area and for normal weather conditions and for an upper bound on the efficiency of possible solar collectors.

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#### russ_watters

Mentor
For instance, if we imagine that the entire surface area of the earth were covered with deserts and no cloud ever appeared in the sky and then computed the rate of sunlight energy hitting the planet that would seem to be way above any realistic bound on the amount of usable solar energy per unit time. There must be some reasonable calculations that allow for a relatively small usable surface area and for normal weather conditions and for an upper bound on the efficiency of possible solar collectors.
I'm not sure, but I would think this shouldn't be difficult to ballpark yourself. Sort of a Drake equation for solar energy.

#### fresh_42

Mentor
2018 Award
Well, it's a physical forum, so I'm probably not allowed to make the mathematical comment: A trivial upper bound is the amount of available solar radiation as it is basically the only intake of an otherwise more or less conservative system.

#### Bandersnatch

Well, it's a physical forum, so I'm probably not allowed to make the mathematical comment: A trivial upper bound is the amount of available solar radiation as it is basically the only intake of an otherwise more or less conservative system.
It's not true, though. There's also orbital and rotational energy that is transferred into the Earth system by tidal interactions. Kinetic energy of impactors is another input, if less usable.

#### fresh_42

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2018 Award
It's not true, though. There's also orbital and rotational energy that is transferred into the Earth system by tidal interactions. Kinetic energy of impactors is another input, if less usable.
I know, that's why I said more or less, but I assume those other factors: loss of atmosphere, losses due to rockets, impacts can be neglected; maybe the contribution of the moon is another essential factor, but I'm not sure about the net balance of its interactions.

#### tech99

Gold Member
For the UK where I live, we are at this moment using 35GW. The government use a "capacity factor" of 9.4%. So with 22GW of installed capacity by 2020 we will only meet a few percent of annual energy usage. If we could store the energy to use at night, we would need to cover an area the size of a big city with solar panels. This will not necessarily replace fossil burning as it might boost the economy and keep demand rising. On the other hand, if we plant the same area with trees, it will not fuel demand for energy so much. I think the issue is more one of our human software as the driver of climate change, and is not a simple engineering question.

#### anorlunda

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Gold Member
I like @fresh_42 's approach with solar flux counting all the land and water surface of the planet. Doing the math on that, (hopefully correctly) I get about 8 million GW.

But if we capture all that energy and don't re-radiate any energy to space, the temperature of Earth will increase until we're all dead.

#### fresh_42

Mentor
2018 Award
But if we capture all that energy and don't re-radiate any energy to space, the temperature of Earth will increase until we're all dead.
But what else do we have?
• fossil fuels: makes no sense, as it is a living on the savings of former solar energy
• earth's mantle energy: good idea, but someone has to calculate whether we can do this long enough before earth's natural end and without damaging our magnetic field
• uranium and transes: that's spending the savings of a former supernova and should be o.k. if there only wasn't that garbage problem
• fusion: I guess we will be able to harvest some extraterrestrial resources before we will run out of own; unfortunately it cannot be done as of yet
Seems like Iceland is the currently only working model which can be called reasonable, i.e. without nasty side effects.
Btw., did you look up our current use worldwide? 8 PW doesn't sound very much if I take all resources we use into account, i.e. including the transportation sector.

#### anorlunda

Mentor
Gold Member
But what else do we have?
We have the mandate to reduce demand; not just energy but all resource demands.

World population can not increase perpetually. GDP (gross domestic product) can not increase perpetually. Every additional person has an environmental footprint. The person's footprint might be smaller if the person is "green" than if not "green" but nonzero in every case.

The "hockey stick" curve began to bend up when the global population was about one billion. So that is my first approximation for the sustainable population of Earth. IMO, population reduction is the one and only strategy that could succeed.

#### lavinia

Gold Member
I found this 2016 Forbes Magazine article which says that at that time world power use was about 17.4 terawatts and this could be supplied with 43000 square miles of Sahara desert at least for half the day.

https://www.forbes.com/sites/quora/2016/09/22/we-could-power-the-entire-world-by-harnessing-solar-energy-from-1-of-the-sahara/#5b0e294dd440

The article says that the entire Sahara is about 3.6 million square miles in area. So if the entire Sahara were a big solar array that would supply around 84 times the current power use of the world.

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#### fresh_42

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2018 Award
I think this will happen sooner or later, esp. if the gulf (and less populated sunny) states will run out of oil. There had been a project already planned for the Sahara, but it was cancelled. I think due to the costs of the necessary infrastructure or simply for the lack of investors. Also maintenance could be a problem. All this will naturally change some day.

I have my problems with those data for power usage, as I suspect they simply add the supplies of power plants and thus only measure electrical power. The transportation sector, however, is by no means negligible, nor is the heating sector. I'm not sure whether this suspicion is justified, but it's strange that they never mention it. For real data we had to add those major factors as well.

A quick internet search gave me $60 \,kWh\,m^{-2}$ from a supplier company for field installations and more than $100$ for roofs. Now if I subtract the advertising aspect and add that the efficiency is much higher in the Sahara, but also the amount of broken panels, then let's say $100$ may serve for an estimation. Wikipedia says, the worldwide energy consumption (total, i.e. all sectors) had been more than $140 \,PWh$ in $2008$ at a growth rate of $40%$ within eighteen years. Now we are ten years later, so let's assume $140 \cdot (1,2)\, PWh \approx 170\,PWh$ per anno. This is an area of three times the size of Texas or $20\%$ the size of the US, resp. the Sahara. I have no idea how accurate this is, but it gives at least an idea of the magnitudes. However, I'm not sure about the time span data of the panel company: $60 \,kWh\,m^{-2}$ per day or year, or hour? Do they measure power or energy?

#### lavinia

Gold Member
I think this will happen sooner or later, esp. if the gulf (and less populated sunny) states will run out of oil. There had been a project already planned for the Sahara, but it was cancelled. I think due to the costs of the necessary infrastructure or simply for the lack of investors. Also maintenance could be a problem. All this will naturally change some day.

I have my problems with those data for power usage, as I suspect they simply add the supplies of power plants and thus only measure electrical power. The transportation sector, however, is by no means negligible, nor is the heating sector. I'm not sure whether this suspicion is justified, but it's strange that they never mention it. For real data we had to add those major factors as well.

A quick internet search gave me $60 \,kWh\,m^{-2}$ from a supplier company for field installations and more than $100$ for roofs. Now if I subtract the advertising aspect and add that the efficiency is much higher in the Sahara, but also the amount of broken panels, then let's say $100$ may serve for an estimation. Wikipedia says, the worldwide energy consumption (total, i.e. all sectors) had been more than $140 \,PWh$ in $2008$ at a growth rate of $40%$ within eighteen years. Now we are ten years later, so let's assume $140 \cdot (1,2)\, PWh \approx 170\,PWh$ per anno. This is an area of three times the size of Texas or $20\%$ the size of the US, resp. the Sahara. I have no idea how accurate this is, but it gives at least an idea of the magnitudes. However, I'm not sure about the time span data of the panel company: $60 \,kWh\,m^{-2}$ per day or year, or hour? Do they measure power or energy?
I think in the equatorial deserts power can be used virtually uninhibited by weather and clouds year round for about half of each day. So energy and power are simply related. In other environments this is not true and with climate change may be currently unpredictable.

I wonder what the numbers are if one includes transportation.

#### fresh_42

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2018 Award
I wonder what the numbers are if one includes transportation.
The wikipedia number (142 PWh in 2008) included oil and all other sources. They also have it per country or per capita.
https://en.wikipedia.org/wiki/World_energy_consumption
although I took it from the German version, which was a bit better presented.

I'm a bit confused: They say we needed 505 EJ/a in 2010. @anorlunda calculated 8EW from the sun.

#### phyzguy

Is there an upper bound on the amount of sustainable energy/unit time that could ever be made useful to mankind?

For instance, if we imagine that the entire surface area of the earth were covered with deserts and no cloud ever appeared in the sky and then computed the rate of sunlight energy hitting the planet that would seem to be way above any realistic bound on the amount of usable solar energy per unit time. There must be some reasonable calculations that allow for a relatively small usable surface area and for normal weather conditions and for an upper bound on the efficiency of possible solar collectors.
You might be interested in the Kardashev scale, which explores these limits on a very long time scale.

#### Andy Resnick

Is there an upper bound on the amount of sustainable energy/unit time that could ever be made useful to mankind?

For instance, if we imagine that the entire surface area of the earth were covered with deserts and no cloud ever appeared in the sky and then computed the rate of sunlight energy hitting the planet that would seem to be way above any realistic bound on the amount of usable solar energy per unit time. There must be some reasonable calculations that allow for a relatively small usable surface area and for normal weather conditions and for an upper bound on the efficiency of possible solar collectors.
I don't think that's a good 'upper bound'- for example, sunlight also provides energy for the entire food chain, omitting that consideration would seem to have dire consequences.

Perhaps a better starting point is to begin with the current level of human energy consumption (approximately 160000 TWh per year) and work backwards to determine, for example, what the required area of solar panels would be.

#### SongDog

"Is there an upper bound on the amount of sustainable energy/unit time that could ever be made useful to mankind?"

That depends. Are you assuming it must be used on Earth?

If so, we can start by considering how much sunlight intersects our disc.

Earth has a polar circumference of about 4E7 metres (using the original definition of the metre), for a radius of 6.4E9 metres. This then means 1.3E14 square metres intersect about 1.4 kW of sunlight each. That's 1.8E17 W, always hitting dayside. To be sustainable we must reflect or reradiate it all. The practicable upper bound will of course be lower, as Earth will never be perfectly black.

On the other hand, there`s no good reason to assume humanity will remain indefinitely an Earth-bound economy. If we survive long enough to start talking Dyson spheres or Ringworlds, there are much higher power budgets.

#### Klystron

Gold Member
We have the mandate to reduce demand; not just energy but all resource demands.

World population can not increase perpetually. GDP (gross domestic product) can not increase perpetually. Every additional person has an environmental footprint. The person's footprint might be smaller if the person is "green" than if not "green" but nonzero in every case.

The "hockey stick" curve began to bend up when the global population was about one billion. So that is my first approximation for the sustainable population of Earth. IMO, population reduction is the one and only strategy that could succeed.
Is there an upper bound on the amount of sustainable energy/unit time that could ever be made useful to mankind? [snip + bold]
After re-reading this excellent thread defining an upper bound to useful energy and after reading several books on related subjects including examining various Drake equation forms, a reasonable answer must include an upper bound on species population. Human population on earth and eventually in space must maintain numbers within upper (sustainability) and lower bounds (species viability).

#### hutchphd

Let me add this TED talk to the mix.......I love a good comprehensive graph:

#### OmCheeto

Gold Member
Let me add this TED talk to the mix.......I love a good comprehensive graph:

Any opinion if he has any contemporaries?
I was somewhat devastated to find out he passed away, without leaving me someone else to worship.

#### lavinia

Gold Member
After re-reading this excellent thread defining an upper bound to useful energy and after reading several books on related subjects including examining various Drake equation forms, a reasonable answer must include an upper bound on species population. Human population on earth and eventually in space must maintain numbers within upper (sustainability) and lower bounds (species viability).
While I sympathize with the footprint idea I don't know scientific proof that it categorically limits population potential. Maybe population potential is a function of energy and other technologies yet to be discovered. I would love to know the proof or the compelling scientific research that this is not a possibility.

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#### russ_watters

Mentor
Let me add this TED talk to the mix.......I love a good comprehensive graph:
That's a great Ted talk, thanks. It's sober, factual, non-judgemental*, and yes, graphical.

*One caveat where he only implies a problem, but doesn't say it: "I like renewables, but I also like math."

"Long term sustainable energy bounds"

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