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Assume a world in a distant (2100+) future. Assume an exponential construction rate (1, 2, 4, 8 etc.) in skyhooks/time. Assume significant solar system exploration and industrialization. Assume shykooks and full space elevators are possible, strong enough and stable. Assume several orders of energy availability (SBPS), Assume sophisticated transhumans, including significantly higher intelligence. Assume no distinctive singularity. Assume nonstop economic growth since 2018.

Can an equatorial "forest" of thousands of space elevators be used to gather industrial (mostly computational) waste heat off world, up the gravity well and funnel it out with 'thousands kilometers long' radiator fins? Would this make sense or would this be a self-defeating proposal in one or more steps? Is this still hard science or "way too much handwavium"?

Context - writing a series of "far out" lateral short stories about 'the earth a century from now' and taking basic premises, fairly hard science to the most absurd conclusions I can do.

Suggestions for this thesis/premise highly appreciated.

Love you all

1. Space elevators do not have to sit above the equator. See, for example, Blaise Gassend, “Non-Equatorial Uniform-Stress Space Elevator”, 3rd Annual International Space Elevator Conference, Washington DC, June 20, 2004 (or his web page); or consider the "forked" design popularized in Kim Stanley Robinson Mars trilogy.




2. You don't say what a "forest" means. Let's say we want to use 10,000 space elevators.



3. 
   

   You don't say how much waste heat you want to radiate into outer space. Assuming energy consumption grows at the same rate as from 2010 to 2015, that will be 1,420,000 TWh/year, or 162 TW.

   
   
   

   Justification: the Wikipedia article on world energy consumption gives the total amount of primary energy supply in 2010 as 150,000 TWh, and in 2015 as 170,000 TWh; thus the increase from 2010 to 2015 was 2.53% per year; keeping the same rate of increase, in 2100 mankind will use a primary energy supply of 1,420,000 TWh.

   
   



4. Since we said we'll use 10,000 radiators, this means that each radiator needs to radiate about 16 GW. That's a big radiator.




5. Now the problem bifurcates. On one hand, we need to gather those 16 GW to the radiator; on the other hand, we need to radiate them into outer space.



6. 
   

   How do we gather 16 GW, presumably from the ocean or from the air? I don't have the foggiest idea.

   
   
   

   (a) We need to suck this amount of heat as uniformly as possible from the entire area serviced by the radiator. Since we said that we use 10,000 radiators, each of them needs to service about 50,000 square kilometers (20,000 square miles). A dystopian landscape filled with finned heat exchangers comes to mind.

   
   
   

   (b) Once gathered, this heat must be moved to the radiator.

   
   
   

   (c) Presumably, the heat will be gathered in the form of some hot fluid. Since the coefficient of performance decreases as the temperature differential increases, it would be rather impractical to heat the fluid to more than 300 °C (572 °F) or so. (Assuming that the heat is gathered from room temperature, at 300 °C the maximum theoretical coefficient of performance is 2, meaning that we need to spend at least one watt for every watt of heat extracted.)

   
   
   

   (d) Assuming that the working fluid is water, how much water is that? The heat capacity of water is 4186 J per kilogram kelvin (higher than any other common substance); to move 16 GW of heat in the form of water at 300 °C we will need a flow of about 13 cubic meters / second; that's a sizeable river. (For comparison, the Thames discharges about 65 cubic meters per second, and is navigable by ocean-going ships.) The total flow of water for all 10,000 radiators will be 130,000 cubic meters/second, about 50 times the discharge of the Nile or two thirds of the discharge of the Amazon.

   
   
   

   For fun, the water will be at a pressure of about 90 atmospheres. Size the pipes accordingly.

   
   



7. Black body radiation power is about 5.67E-8 W⋅m⁻²⋅K⁻⁴; to radiate 16 GW at 600 K, each radiator will need about 2 million square meters (about 0.85 square miles) of radiating surface; the radiation will be in the form of infrared light with a peak at a wavelength of 4830 nm.




8. In the grand scheme of things, how much power is 162 TW? The Earth receives about 174 PW of energy from the Sun; 162 TW is about 0.1% of that, which is about the same as the difference between the maximum and the minimum of solar energy hitting Earth during each solar cycle.

Sure, though it's an amazingly inefficient way to do it!

To make it work you need technology to transfer heat up the beanstalk, and then you need to dump that heat into radiators pointed out into space.

As far as transferring heat goes, convection is probably the most efficient. Think of it as basically a giant air conditioner with the Earth side containing coils filled with fluid to be heated (this is the cool fluid which came down from space). The heated fluid is then pumped up the beanstalk to the heat dumping side where the hot fluid transfers its heat to some external environment.

You'd effectively have an up pipe and a down pipe and the cost of circulating the working fluid would be only to replace friction losses, since the energy to lift the hot fluid up to space is balanced by the gravitational energy released as the cooled fluid descends.

It's hard to say what the right fluid would be -- that's a very technical engineering tradeoff -- but it's likely to be a liquid rather than a gas because a gas would require much, much larger pipes which is very costly in terms of beanstalk infrastructure.

The radiators would probably be a lot like the standard radiators we use today to cool spacecraft. One side is black (which radiates most efficiently) and points to empty space, while the other side (which would face the Earth or Sun) would be silver so as not to absorb radiation.

Could radiators actually remove enough heat to matter? If you look at the Earth's energy budget, the Earth absorbs around 240 W/m² of sunlight and thus must radiate slightly more than that back into space. (There's some heat leakage from the Earth's interior.) Earth's current total electricity production is about 25,000 TW. Divided up by the surface of the Earth, that's .005 W/m². So human electricity production is .00002 of the Earth's radiating capacity. So space radiators of area .00002 of the Earth's area will handle it all. That's about 4000 square miles. That's not particularly large given the space elevator technology postulated.

Other than the space elevators, there's no new technology needed. (Though the scale is daunting.)

But it's still a magnificently inefficient and hugely costly way to cool the Earth!

No need for elevators: Pump it out on beams of light

You can pump heat off the planet simply by beaming it into space via light emitters. Infrared light is the most obvious, but spectral light will suffice. The emitters can be on the ground as long as there isn't cloud cover. By "as long as" I mean you may be able to simply wait until clouds are gone.

You can also run this day and night, but by day there's a "problem". In another question I propose using pumped storage to use hydro dams to store wind-generated electricity. And I realized that it would be fundamentally stupid to back-pump at the same time the dam's turbines are generating electricity. Just send the wind power to the customer and generate less at the dam; it's all a wash transaction. The very same physics apply to light-pumping by daylight. It is stupid to send light energy up whilst the Sun is sending light energy down.

Simply reflect solar energy

It's cheaper. Here you use whatever technology is easiest: orbital solar shades, paint roofs white (my paint supplier reports several white-ish paints with over 90% albedo), help deserts radiate, etc. For instance, in Star Wars: The Last Jedi, the planet with red soil just millimeters under its white surface was a natural (or artificial?) case of this.

This doesn't do anything to reduce your industrial heat, but it sheds natural heat, which is a wash.

Solar energy can help too. Solar panels make two kinds of heat, first their albedo is much worse than the natural earth they replace, so almost all the solar energy that isn't turned into electricity becomes heat at the panel. Second they prevent the underlying earth from radiating heat in its normal way. However they prevent electricity from being made in ways that could create a lot more heat and things like CO2 which then have knock-on effects to warming. The math is a little complicated, but turning the unwanted natural radiation into electricity may be a win.