The numbers don't add up... Sorry...
Assume an average speed of 20 kph - that translates to ~5.6 meters per second. Pretty slow, overall. But we'll say it's a commuter vehicle in rush hour! And we'll negate any friction losses, too...
Now assume the vehicle weighs in at 500 kg, loaded (it'll be light!), and that it will run for 250 km (right in the middle of the range provided).
It takes about 9.8 Watts to move one kilogram one meter in one second.
So, we have 9.8 Watts per kg-m/s times 500 kg * 5.6 m/s = 27.4 kW.
Now, we have a range of 250 km, right? So at 20 kph, that is 12.5 hours:
27.4 kW * 12.5 hours = 343 kW-h.
Assuming a cost of USD$3 to run it, that would translate to around (300 cents /343 kW-h) 0.87 pennies per kW-h. Or $0.0087 per kW-h.
Here in the Pacific Northwest, we have pretty cheap electricity, thanks to all the abundant hydro we have. And we pay around 6.5 cents per kW-h. SO that would be around 7.5 times as expensive as the article's rate...
I'd expect to see refill costs in the $30 per tank range, not $3. Meaning you're paying around $1 per 10 km of range, or $3 per 30 km of range. Like a typical large vehicle if powered by gas (assuming gas at $3 per gallon, and you get 20 MPG).
And note that the small Aero, or Prius - vehicles that get 45 MPG in the same type of low speed operation - would have even more distance per dollar...
Numbers just don't add up...
I love engineers
The analysis is better than any I can give
Any idea how much air at what pressure it would take to store that much energy as compressed air? I'm not sure of the conversion factors or the efficiency, but I envision a pretty big high pressure tank.
Your calculations seem to be based on the force required for acceleration, rather than the force required to keep the vehicle moving.
This sounds like an acceleration. But a frictionless car moving at a constant velocity isn't accelerating. Such a car would in fact use no energy except in the first few seconds when it was accelerating up to speed. After that it would just coast. The total energy used would be much smaller than what you've calculated, I think.
How dare you slay such a nifty fantasy car with your brutal numbers!
. . . straight up.
Sorry, your numbers don't add up.
It takes about 9.8 Watts to move on kilogram one metre in one second? Where the heck are you getting that figure from? Sounds like you've gotten confused. It takes a force of one Newton to accelerate a mass of one kilogram at a rate of one metre per second per second. The acceleration that gravity produces is 9.8 m/s^2. A mass of one kilogram weighs 9.8 N under normal earth gravity.
Based on that (incorrect) assumption, your calculcation then moves to guestimating that the power required by this vehicle at 20 kph would be 27.4 kW, or 36.6 HP. There's no way in heck that a 500 kg car consumes 36.6 HP at 20 km/h. The average passenger car consumes no more than 15 or 20 HP at 100 km/h. I'd guess that the vehicle in question would probably consume no more than about 5 HP at 20 km/h, or 3.75 KW. That'll change your calculation of per km costs a bit, no?