SpaceX’s Falcon 9 now advertises a cost of $62 million to launch 22,800 kg to LEO, $2,720/kg. https://ttu-ir.tdl.org/bitstream/handle/2346/74082/ICES_2018_81.pdf
Given an average solar silicon price of around $9 US per kilogram in 2020 https://www.solarquotes.com.au/blog/solar-silicon-price-hike/#:~:text=Compared%20to%20the%20average%20solar,%2434%20Australian%20dollars%20per%20panel.
This would increase costs 2720 / 9 = 302 times.
The cost of a solar electric system is measured in dollars per watt. The average cost for a residential system is currently $3-5 per watt. That means the average 5-kW residential system will cost $15,000-$25,000, prior to tax credits or incentives. https://sites.energycenter.org/solar/homeowners/cost#:~:text=The%20cost%20of%20a%20solar,to%20tax%20credits%20or%20incentives.
So this system would cost about 4*302 = 1208$ per watt.
This calculation is extremely approximate, but no, it will never work, even if the cost of sending a kg to orbit plummets.
Sorry, I might be missing something here but
Isn’t price of energy typically measured in kW hours. Energy = Power x Time.
If a space solar system can output more energy since it stays on for longer, wouldn’t this mean that the cost per watt hour would naturally decrease? This would be because the price of a watt hour I imagine would be Energy / price. So, if our launch cost is a fixed cost, then we would find that E / price decreases.
Very good point: I think the website I linked to refers to peak power, so the Kilowatthours would be lower. (not sure on this, sorry)
If the panels on orbit last double the time and produce double the energy that is only a factor of 4, while the system is about 300 times more expensive. (but again you have transmission losses that I did not consider)
This is probably the worst-case comparison for space solar, since it assumes you’re just going to pack a bunch of terrestrial systems onto a rocket and shoot them into space, where they will (just like terrestrial systems) only work at a fraction of capacity due to clouds, bad sun angles, getting dirty, and night-time.
In practice they would provide a lot more power per unit mass by at least one order of magnitude and possibly two. Mirrors in space can be relatively flimsy thin things and still work since they don’t need to withstand winds and other loads, giving relatively lightweight concentrated solar power options at much lower masses than terrestrial systems.
The conclusion is the same though: space launched solar is still not worth it for us now. It could be in the future or with some alternative history.
I am not really sure about that. There is not only a huge money cost but also a huge energy cost when sending something into orbit, would the panels even make back the fuel spent to send them? Even if the rocket hardware is reused 100% with no serious maintenance costs (reusing costs more fuel) would the panel even make back that fuel energy alone? I did not do the math but maybe not even that. If we could put them in orbit with a space elevator almost for free the tune would be way different though.
Oh yes, there is no question at all that they would make back the fuel energy cost. In money terms the fuel is a tiny fraction of launch costs (less than 1%). In fuel energy terms it costs about 400 MJ/kg to get payload into orbit via Falcon-9.
With fairly standard terrestrial designs you can get about 5 W/kg rated power (mass including support electronics), which in space would be available nearly continuously. That gives a energy payback time of about 2.5 years. With solar power designs more suited to space use, I would be very surprised if that couldn’t be reduced to weeks.
In practice they would provide a lot more power per unit mass by at least one order of magnitude and possibly two.
Can you elaborate more on that? It was clear to me that in space PV in space can give much more energy/mass than in Earth, but close to 2 orders of magnitudes is huge! Is this “only” due to temperatures losses + constantly running at full capacity + concentration?
Almost all of the mass of solar panels on Earth is structural strength to deal with various types of weather (mostly wind). That alone would increase power per unit mass by a factor of 5-10, though some of that would be eaten by beamed power equipment that isn’t necessary on Earth.
Permanent cloudless daylight with the light coming from an essentially fixed direction increases average power by a factor of about 4-6, while not affecting mass.
Using thin-film mirrors for concentration could enable even more power for given mass.
Ahhh! What I was missing is the structure part. I was thinking in E/surface not on E/mass. Thanks.
no, it will never work, even if the cost of sending a kg to orbit plummets.
A solar electric system on earth doesn’t make 1 watt all the time. Obviously there is night, and there is geographic differences.
A quick and dirty approximation is here: https://unboundsolar.com/solar-information/sun-hours-us-map . The idea of “sun hours”. Let’s take the median “sun hours” of 4.
this means just 1⁄6 of the time do you get a rated solar panel’s full output.
Negating the microwave transmission system’s cost and other costs, if the cost of sending a kg to orbit is less than 5⁄6 the cost of a panel on earth plus storage, it could work. Not “never”.
I concede it’s unlikely, sending a kilogram to orbit has immense energy costs and so even advanced technology will hit a limit on how cheap it can be. Space based solar probably would only make sense if you had a society so in need of energy that you had exhausted your options on earth already, with entire continents covered in panels, and you still needed more energy.
You also have an issue that at that point you are importing more heat to earth than it can radiate to space under normal climate conditions, so it probably wouldn’t be a good idea to do this..
Yes, I meant plummeting “within reason” (like x10) not plummeting to extremely low values that, as you correctly said, are not possible given the energy cost.