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 ...