## Torque, acceleration, powerrrrr

All EV’s are bloody zippy starters (that is why they have such carefully crafted it’s tail lights, those need to show off 😉 ). I did some theoretical calculations in the SpeakEV forum.

When accelerating the car maintains two limits:

- the torque that the motor and drive train can handle. For the Zoe this is 220 Nm on the motor, 2000 Nm on the wheels. This translates to a force on the car of 7400 N.
- the power the controllers and motor can handle. This is limited to 72 kW (with some peaking to 78, but we’ll stick to 72).

At first, the torque limit is maintained, giving the 1468 kg car, a linear acceleration of 5 m/s2. 7400 N acting on 1468 kg gives you that. Mind you, this is half of the earth’s gravity acceleration!

When reaching 9.8 m/s (35 km/h), so after just under 2 seconds, the car hits it’s power limit and torque (and therefore acceleration) starts to bleed off. To reach 100 km/h (27.8 m/s) under full power requires another 6.9 seconds. This can be calculated using the formula:

speed = Sqrt (2 * power * t / mass)

determining the t’s for 9.8 m/s (0.98) and 27.8 m/s (7.88), and taking the difference between those t’s.

This all totals to 8.9 seconds to get from standstill to 100 km/h, which I think is not earth shattering, but pretty impressive for a 1468 kg small family car. Most EV’s are a tad faster. These calculations ignore the weight of yours truly & friends, friction, but also said 78 kW.

A few weeks back I pulled to a traffic light, two lanes going left. Behind me was a guy, I think in an old 206, who had determined he wanted to be “that” guy, and he tried to cut immediately in the leftmost lane. As I went there (because I had to go left at the next traffic light again), he made a crazy manoeuvre to get next to me in the right lane. I was with a friend and I told him to hold tight. The 206 came pretty close to blowing his engine, we heard it screaming behind us. The youngster ended up so frustrated that he jumped next queue over the bus lane. We had a good laugh over that one.