IMO, Due to cost savings electric aircraft would likely become common at around 4x the current Specific Energy and fully take over at about 10-20x.
PS: Energy density is fine for lithium ion, the issue is energy per weight (Specific Energy) not energy per volume (Energy Density).
Talking about 5.000 km is hard: While it won't get you from London to New York without some post-crash landing swimming, the current largest electric plane can fly ~100 miles at around 114mph, with 9 passagers.
I see that you take the laws of physics into account, but allow me to state this for the sake of the conversation: In order to replace jet fuel, we must match what we could call it's useful energy density (energy/kg * efficiency). While electric engines are probably more efficient, we're still up to 2 orders of magnitude away – that's requires a 50-100x improvement of energy density, while maintaining the needed high discharge characteristics, developing a sufficiently efficient electric jet engine and taking into account the increased weight. All at a price where people won't need to save up for years, in order to visit their families.
While I hope to see a zero emission future in my lifetime (actually a negative-emissions might be needed for at time), I feel like putting batteries into airplanes is a bit too much "Silicon Valley Sophism" – shoving the same solution at each and every problem, rather than figuring out what the core of the problem is.
I do love electric cars, but they are not for everyone('s budget). Perhaps the solution is synthetic fuels, combined with carbon capture and a cheap, clean and reliable energy source, such as nuclear power. I know this isn't exactly cheap or readily available either, but it seems like one would bypass a lot of the issues above, by focusing on the source of the problem: Non-neutral use of carbon fuels.
They also experimented with nuclear powered drones. https://www.popularmechanics.com/military/research/a33565112...
And Russia now claims to have a nuclear engine that can make a cruise missile fly for days. https://en.wikipedia.org/wiki/9M730_Burevestnik
edit: Sigh.. disregard, cf. https://web.archive.org/web/20080109011832/http://www.nuclea...
Right now, we have relatively large, relatively fast, jet planes. Do we need that size and that speed to be commercially viable? Could we also run a larger fleet of smaller, more automated planes or helicopters? If there was no kerosene left by tomorrow morning, would there really be no alternative?
I suspect the medium term solution would be to make some, either from other hydrocarbons or plant cellulose, or even by the US Navy seawater CO2 to liquid fuel process.
Only if you value overseas travel... It currently takes ~16 hours to fly from SF to Singapore depending on weather. Any longer, and you're going to see a lot of that travel disappear.
It takes that long because it's more efficient to do it in a single flight. Taking off and landing are a massive waste of time and fuel. If we only had short range planes people would change their destinations in some cases or they'd plan layovers as part of the trip. I don't think you'd see that many people just stop travelling abroad.
[1] https://tripsintohistory.com/wp-content/uploads/2012/10/Clip...
the efficiency gain by not taking off and landing is eaten away by the efficiency loss of having to carry so much fuel (which also comes at the expense of useful load..)
What happens if the KC-135 misses the rendezvous? What if the charging port fails to work for some reason? What about the carbon footprint of these airborne generators?
Plus, now you have the weight of the capacitors to carry around all the time, further reducing the effective payload.
The same thing that happens today with combustion aircraft: the crew makes an emergency landing if they can, or bails out and waits for a Seahawk to pick them up.
This actually happens with fuel-driven aircraft regularly today.
Actually significantly worse than that. A plane gets lighter the longer it flies, especially at takeoff when everything is at max thrust. A battery becomes more and more dead weight the longer you fly.
Fire up google earth and start drawing 500 mile radius circles around metro areas.
I'd expect this kind of tech to debut in premium phones and laptops, and work its way down.
However, i think any successful real world demo starting with niche applications will help. We need all the battery tech to succeed.