Along with Jon, I’ve given a lot of thought to this specific application of space-based solar power (SBSP).
Yes, there are thousands of aircraft in the air at any one time, but I find this to be one of the strongpoints of this concept: The market is huge, and it’s not competing with grid power. Over 5 million barrels of jet fuel are burned each day, translating into an average of about 250 Gigawatts of power, about half of the US’s average electrical power. (Only a fraction of this is turned into useful thrust, of course, because jet engines are only so efficient, just like your typical piston engine… though they’re larger and are used constantly, so probably do better than your SUV… From my research, the total efficiency of a jet engine is about 20-40%. For an electric propeller with a high-efficiency motor, about 85%.)
Many of these flights are likely short-haul, and could be handled by batteries, such as advanced lithium ion and lithium sulfur batteries. (Lithium-Air batteries are also a real possibility… Some research on them is being done at NASA Langley Research Center.)
Also, there are still improvements to be made to efficiency using blended wing, larger engines, advanced alloys, higher carbon fiber usage, topological optimization of structure, etc. And many of the aircraft are older (especially in the developing world), not taking advantage of the latest improvements. Ultimately, we could probably reduce consumption to about a half, to 125GW, with almost half again being taken care of by ground-charged batteries (the ascent uses a lot of fuel, but low enough that it can be handled by advanced batteries), so let’s say 75GW average.
The market will grow substantially through the rest of this decade (a factor of 5?) as the rest of the world comes up to US standards of living. But we’ll set that aside for now.
50MW is about right, I think, for the solar power production of a SBSP satellite, each made with 1-10 launches, depending on how powerful your launcher is. A challenging figure, but possible. That gives about 1500 SBSP satellites to produce average 75GW of power, not counting eclipsing. But of course, that’s only equivalent to our average power if we can transfer that power to the aircraft and into thrust at the same efficiency that jet fuel can be transferred into thrust. Let’s say around 25% round-trip efficiency, so at least 50% efficiency transmitting and at least 50% efficiency receiving (including beam losses).
There are 2 main options for transmitting power. Microwave or laser.
But first, let’s pick an orbit. I’m going to pick a low Medium Earth Orbit altitude of about 3000km, with a total distance from transmitter to receiver of about 5000km (the receiver won’t be directly underneath very often). Geosynchronous is so far away that a mobile receiver is almost hopeless. LEO is so close that you have big slew-rate issues as well as more shadowing and a more difficult thermal environment plus atomic oxygen. (Shadowing is less of a problem than you might initially think, since there are much fewer flights at night… although for long-haul flights, this is less true.)
(BTW, if launch costs are low enough, it may actually make sense to put batteries on the satellites… but it’ll require very low launch costs… below $50/kg IMLEO.)
The drawback is higher radiation. The solar arrays will need to be self-healing (which thin-film cells are capable of, when heated).
To be economical to launch, we’d likely require 500-1000W/kg solar arrays (which is doable in a few different ways, but would require cleverness). They’ll also need to be regularly healed of radiation damage. So 50-100 tons of solar arrays. But I think the radiators will end up quite heavy as well, perhaps rivaling the solar arrays. 50 tons, because that’s a complicated problem.
The optics/antenna will be significant, too, but it’s harder just to estimate parametrically. Let’s look at the size required.
Microwaves sound great at first. High efficiency, easy conversion, just chicken wire receiver. Except none of that applies at high frequency.
With a 100m dish, 1mm wavelength, 5000km distance, you have:
5E6m/(1E2m/(1E-3m))= 50m receiver. We can just about fit that on a large aircraft.
That is 300GHz, by the way. And with 1mm wavelength, you can’t just use a mesh, you basically need a solid dish (which would need to be unfolded or pieced together on orbit).
But 300GHz sources are very hard to come by (and are often called Terahertz sources). Gyrotrons are a good option since they’re compact (200kg?) and high-power (1-2Megawatts apiece are fairly easy to come by) and fairly inexpensive (~$1/Watt), but they usually max out at around 100-200GHz for high power. In the 100GHz range, you can get around 50-55% efficiency with 1-2 Megawatt output (but usually are lower efficiency). To try to operate at higher frequency causes huge reductions in power and efficiency, and especially as you push to 300-500GHz, you may need to operate just in pulsed mode. The reason why is because they need a high magnetic field strength. About 28GHz per Tesla. So a 100GHz gyrotron needs just a relatively modest 3 Tesla. A 500GHz gyrotron needs 15Tesla, which is super difficult to come by except pulsed or using a superconductor. So realistically, we’re limited to around 100-200GHz until superconductor technology significantly improves and becomes cheaper. And I don’t think that receiver rectennas in this frequency range are much better than 50% efficiency.
So we need more like a 150m diameter antenna… even at just 3000km altitude and 25% round-trip efficiency. That’s pretty horrible.
What about lasers? Next post. Lasers are also a good option, and direct diode lasers are available at 100kW and fairly inexpensive ($1-10/Watt?) and efficient (wall-plug of about 50% or more), but they really need to wait until diffraction-limited weapon-class (>100kW) lasers are available and become more efficient since direct-diode lasers have high divergence and horrible beam quality, necessitating optics nearly as big as our microwave sources.
A good rule of thumb, by the way: The laser satellite will need to be close to the same price as the aircraft it powers, so around $150-300 million, including launch costs. That is really, really challenging, but not quite impossible.