Right. Theoretically.
Project feasibility based on potential future tech that doesn't exist isn't a great strategy. That's my only point. Otherwise, I'm designing an airliner powered by rubber bands. Sure, the rubber band tech we have now doesn't store that kind of energy, but hey, it might in the future.
Literally read what I wrote - if batteries aren't going to work, fuel cell tech may pick up the pace. hell, we may end up using some sort of weird hybrid tech in the interim - who knows. What I'm saying is that eventually, we almost certainly will move away from using fossil fuels to power our aircraft. If (and this is a big "if") literally nothing in technology changes, no breakthroughs are made, and we only have 3% growth, a lithium battery presently at 9.0 MJ/kg will be just as good as a Jet-A at 42.8 MJ/kg when you can extract the same amount of work out of in "not that long."
Think about it like this, the thermal efficiency of a gas turbine engine is less than a piston engine - the mechanical efficiency is higher, but the the thermal efficiency is lower.
Gas turbine engines are at most around 40% efficient. In the same link you'll see that lithium batteries are around 80% to 90% efficient. Let's say that they're 80% efficient. Note now, that the larger the electric motor, the greater efficiency, so it's totally plausible that an electric motor could be somewhere around 95% efficient (they're actually between 90 and 99.9% efficient depending on design), for the sake of argument let's say that we have a crappy motor and it's
only 90% efficient.
We lose 20% on the batteries, and we again lose 10% at the motor, that means that of the lithium 9.0 MJ/kg, we're only really getting access to 6.48 MJ / kg. Similarly, with the gas turbine engine, we're getting at most 40% efficiency (realistically, probably much less in actual aircraft) - so we're only getting access to 17.12 MJ /kg. So, if literally nothing changes and there's no new battery technology (which is unlikely, because the technology is the same as what's used in your phone, so there's insane financial motivation to throw money at battery tech), and the current rates of improvement continue on, we match it in just over 32 years*. This is basically the worst case scenario.
The reality is probably much quicker. We have Tesla and many others pushing the edge of battery tech, we have a wide array of institutions pushing for this. On the other side of the equation are "blue sky" tech like super-capacitors, or graphene, or whatever crazy materials science of the day is pushing the boundaries stands to jump us forward. If we average 7% growth we reach parity in 13 years. Regardless this is coming - and quicker than you'd think.
The changeover point may actually happen sooner for other reasons - it might be more cost effective (efficiency aside) to use electric motors much sooner because of the sheer lack of maintenance costs associated with electric motors - they basically don't break, don't have hardly any moving parts, and cost next to nothing to build - this is especially true for smaller airplanes with less range. If you could take 6 people 200 miles with an electrical motor you'd start to see adoption in the GA world almost immediately if the acquisition costs weren't too high.
*dM/dt = (0.03)M
This is a separable diffy q
dM/M = (0.03)dt
Integrate both sides
ln M = (0.03)t + C
let c = e^C
so M = ce^(0.03t)
M(0) = 6.48 , so M = (6.48)e^(0.03t)
So, let's find where the efficiencies match up.
17.12 = 6.48 e^(0.03t)
ln (17.12/6.48) = (0.03)t
t ~= 32.38 years.
17.12 = 6.48 e^(0.03t)