Average plane cannot fly with batteries; the weight is still too high compared to jet fuel and the range is too short. Only short flights of up to 1000 km and 90 minutes will be in reach initially, jet fuel minus efficiency loses is still over 3000 Wh/kg, 6 times more than these new batteries.
Furthermore, the energy needed for takeoff is significantly higher than the energy for cruising. For an hour's flight, it's close to 50/50. The impact is disproportionately skewed towards shorter fkights
No. It is not the takeoff as in "raising the wheels from the tarmac" part that is consuming most energy, but reaching the flight altitude. Real case, with smaller plane, I take off in 300 meters in less than 30 seconds at max power, than raise to 3000m in more than 10 minutes of 90% power. That makes the assisted takeoff less than 10% of the energy to get to cruise altitude.
I don't have the numbers for a jet fighter on a carrier, but I think it is in the same range. The takeoff assist is not for saving fuel, but to allow takeoff at the loadout of the plane that would require otherwise a longer runway or lighter loadout (less fuel and weapons).
We could, but it would require new aircraft. Passenger aircraft are not designed for that kind of stress. I'm not sure that passengers would like that much acceleration either.
I don't know that it would actually save anything though. Aircraft of carriers are held back while they throttle the engine to full throttle. Only after the pilot is convinced the engine will run long enough to take off do they release the brakes - probably using more fuel than a regular takeoff. (the other option is to get in the air and then discover the engine isn't running and so you crash land a few meters later). I'd want a real aircraft engineer to speak to this.
You could save some energy by catapulting a plane at a reasonable acceleration, like a glider is launched with a ground tractor wire. I flied gliders this way and I think the acceleration was not worse than a regular airliner. Problem is, the saving is not worth the cost and complexity.
The carrier example is wrong, the planes stay on the catapult only a few seconds while they go full throttle (this takes time), even with the burn rate it is not a significant quantity of fuel. Regular planes can do the same on the runway, I did it myself several times for fun, but it rarely bring benefits - the only place where it helps is with very short runways. In any case, the fuel consumption is not significant.
How about you elevator passengers up to a runway that is a thousand feet up in the air. Then use electric lines on the runway to power the takeoff to avoid using any onboard batteries until airborne. Just daydreaming here a bit!
It is easy, you put small BLDCs in the wheels. No need to push on air while you are on the ground. You could also have basically a super car drone or a maglev rail under the plane, launch it into the sky.