I want to calculate if it is possible to get 0-60 mph in 3.5 sec with a 5,000 lb Karma.
What is the horse power required to go 0 - 60 mph in 3.5 sec for a 5,000 lb car, assuming constant acceleration and 100% efficiency.
To work with metric, converts 60 mph to 26.82 m/s.
Acceleration = delta V/delta t = 26.82 m/s / 3.5 s = 7.6628 m/s^2
Force = mass x acceleration = 2,272 kg x 7.6628 m/s^2 = 17.4 KN
What is the distance travelled in 3.5 s?
delta d = a x (delta t)^2 / 2 = 7.6628 m/s^2 x (3.5 s)^2 / 2 = 46.935 m
Power = Force x distance / time = 17.4 KN x 46.935 m /3.5 s = 234 KW
What is the available power from the electric motor and from the battery.
From the electric motor, we know it has 400 hp which is 298 KW. This is 27% greater than the 234 KW, so the motor is capable.
What about the battery?
For 20.1 KWh energy storage on a Karma, there are 310 cells, each stores 65 Wh. Each cell is 496 g. 310 cells is 153.76 Kg. The specification says 2,400 W/kg.
Therefore total KW = 153.76 kg x 2,400 W/kg = 369 KW.
The battery is oversized to the motor by 23%. So the battery is quite capable to drive the motor to its full capacity of 298 KW. And the motor has 27% more power to drive the Karma to accelerate from 0 - 60 mph in 3.5 s. The battery would have been working in 63% of its output capability.
Doing similar calculation for 0 - 60 mph in 6.1 s. The battery is working at 36.3% of its output capability.
So for you speed demon out there, you know your Karma has more stuff inside, just not showing it
Also the Buckeye Bullet 2.5 using the A123 battery has broken the 300 mph land speed record. The Buckeye Bullet 3 will try to break 400 mph this year! You definitely have a fast car inside