This has nothing to do with the cost of fuel, an aircraft can't afford to be sitting for hours because the aircraft is very expensive (so you need to pretty much fly all the time) and the space at an airport is at a premium.
Airports don't have unlimited apron space and the costs are pretty high the apron costs for LGA for examples are:
For the first 15 minutes or fraction thereof $ 50.00
For each additional 15 minutes or fraction thereof $100.00
And even with these charges apron space is still a "premium" and it's not designed to be constantly used (this is why airlines usually have a home airport where they can actually reserve space).
How could parking "only the wings" for charging be significantly cheaper than parking the whole plane? In the unlikely case of superbattery airliners, infrastructure and logistics would change as much as the planes.
A Concorde-load of fuel costs around $40k (100000 liters * $0.40/liter). From your numbers, a 90-minute recharge costs $550. So apron costs don't seem like the deciding factor.
That works out to approximately 1GWh. At $0.10/KWh divided by two because of worse efficiency, that's $50,000 worth of electricity.
So the electricity at $50k costs more than the $40k for gasoline. (Or about the same depending on the exact price.)
The bigger issue is a 90 minute recharge of .5GWh would require 333MW of power, which about half the total output of a typical power plant. i.e. not a chance in the world of that happening.
Can you imagine just grabbing the power lines on a typical power plant and plugging them in here and there?
An electric plane wouldn't need as much energy as a fuel burning jet because you only need to be turning the fan blades. Where a jet loses a lot of energy compressing the air, a electric jet would probably be more like a propfan or a ducted fan. The best jets are about ~35% efficient at turning energy in to forward speed. Assuming an electric motor is 80% efficient and the propulsion is 80% efficient, you'd be looking at 64% efficiency.
It's possible there are other factors reducing the efficiency of an electric motor, but I doubt they are worse than parity with the existing jets. Using your numbers, that means an electric plane would use $25,000 worth of electricity.
The typical plant outputs much more than 333 MW as well. As we move toward less fossil fuel use, infrastructure will better support our increased energy usage. When internal combustion engines were first introduced, someone easily could have said "Do you realize how many billions of gallons of fuel it will take to power all of that? Not a chance in the world of that happening!"
The state I live in has well over 100,000 MW of generating capacity. Given that scale, supplying energy to planes doesn't seem so ridiculous.
I'm willing to bet that we won't just be slapping electric motors in place of fuel turbines anyways. Plane designs will probably progressively move towards better suitability for alternative energy. Maybe electronic motors for extra energy during take-off, with enough reserve power for emergencies?
> Where a jet loses a lot of energy compressing the air
It does not loose energy from this. The compressed air expands afterward, returning almost all the energy.
> The best jets are about ~35% efficient at turning energy in to forward speed.
Where are you getting these numbers? I'm seeing much much higher numbers than that then I google it.
> Assuming an electric motor is 80% efficient and the propulsion is 80% efficient, you'd be looking at 64% efficiency.
Again, those numbers don't sound in the slightest bit correct.
> Using your numbers, that means an electric plane would use $25,000 worth of electricity.
What? Run your numbers again. I assumed 50% efficiency for Jets and 100% for electrical.
> The state I live in has well over 100,000 MW of generating capacity. Given that scale, supplying energy to planes doesn't seem so ridiculous.
It's not about the energy usage, it's about how do you connect the thing to an airplane. Do you plan to move cables the size of telephone poles? 100,000 volts?
Have you seen electrical substations? Does that look like the kind of thing you would put on an airplane?
On electric you have transmission losses, charge losses, discharge losses, losses in the motor controller and losses in the motors. Most batteries aren't better than about 80% charging and about the same discharging. So 0.8 to the fourth, or about 40%
There's also some consideration needed here of jet plane vs electric plane efficiency. From what I've read about Rolls Royce jet engines - it's a very serious contender. Anything that runs fast, hot and a lot of power needs very careful design.
My prediction is that you would need cooling for such large motors travelling at such high speeds and that too would drop your efficiency. The airframes get pretty got at those speeds and every electrical component with high power will generate it's fair share of heat too. You won't be able to keep the thing cool enough to fly for any period of time. I have MX Dynamixels sitting beside me that sometimes weld themselves shut because of the immense heat they generate. The bigger they are, the bigger the problem.
For now, the only viable method I see is low-speed, short journeys as somebody else suggested. Maybe these sorts of flights would be more viable where solar panels can be utilized to also work off some of that money and make recharging quicker and adding less weight.
Well, he's kind of right, if fuel cost was suddenly zero, the profit margin would explode, and planes wouldn't need to fly as many flights to recoup the capital investment.
Profit margins exploding is shortly followed by profit margins declining as everyone gets busy competing on cost. By any measure an airplane is a high cost asset, and increasing (or maintaining) utilization will be important.
Airports don't have unlimited apron space and the costs are pretty high the apron costs for LGA for examples are:
For the first 15 minutes or fraction thereof $ 50.00 For each additional 15 minutes or fraction thereof $100.00
source: http://www.panynj.gov/airports/pdf/scheduleofcharges-lga.pdf
And even with these charges apron space is still a "premium" and it's not designed to be constantly used (this is why airlines usually have a home airport where they can actually reserve space).