Are we at the theoretical limit of energy density in current batteries? How much more progress can we make, in theory? Could it be that in 20 years we find drastically better materials for batteries? Materials which would make electrical flight feasible.
Assuming high energy-density batteries are coming, shouldn't you start now with developing electrical airplanes to be one step ahead of competition?
Yes and no.
Using air for the "ox" part of the redox reaction makes it possible to dramatically increase energy density (gravimetric and volumetric both).
The tricky part of that is making the battery rechargeable. Lots of research attention is focused on it.
If you want your battery totally enclosed (e.g. for use in vacuum or corrosive environments), than we are closer to the limits. Probably within a factor of 5, maybe within a factor of 2.
> Could it be that in 20 years we find drastically better materials for batteries?
No, the periodic table is fixed.[1] Maybe, if you are prepared to consider using nuclear "batteries".
Perhaps that is because there is a large number of passengers who wish to fly shorter distances than 2000 km. In most countries all internal flights are considerably shorter than that.
That doesn't make it inherently desirable.
Then there are solid state batteries. These are more difficult. But again multiple companies with lots of funding are attacking this from all sorts of angles.
The OP making this claim as if it's a law of physics is simply wrong.
The result I get is somewhere from 3 to 8 kilowatts. A quick search in the Internet shows that a typical car has engine power starting at 130 horsepowers, which is 95 kilowatts. A van the size of a Ford traffic probably uses twice as much, and the Cessna uses 132 kilowatts.
So, no, I don't think we are getting aviation as it exists today with solar panels and batteries, but one hour twenty minutes in good weather will be enough for some recreational pursuits.
I also did the math for sailplanes with solar panels. That looks better, if all you are looking for is activating the propeller for a small fraction of the total flight time, or having an aircraft that can go very slow (that, in fact, has been done). I'm just an amateur, but my opinion is that, without solving the energy density issue, about 98% of the aviation we enjoy today will be gone.