It's not really about the amount of traction available relative to speed... it's all about the ability to apply your motor power towards acceleration - relative to speed.

Several ways to approach this... but the ability to effectively apply torque is relative to your current momentum (vehicle speed).

Take the 184 lb-ft of the i3 electric motor torque, multiply by 9.70 (final drive ratio) you have 1784.8 lb-ft of torque at the drive axles. My i3 has 175/55R20 rear tires, that's a radius of 1.15 feet. 1784.8 divided by 1.15 = 1552 lb-ft of torque **applied at the road **at full rated motor torque.

If you apply that full torque at zero forward speed, you have to be able to have that much tire grip to resist spinning the tires.

Close... accepting your calculations without checking them, you would have 1552 pounds of force (not lb-ft of torque) applied to the road.

That's less than half the weight of the car - not a huge traction challenge for a rear-heavy rear-wheel-drive vehicle, but I do realize that this one has skinny tires, and so the traction control needs to act, especially if the surface is less than perfect.

The real issue with very low-speed acceleration of the i3 appears - from a

chart on a

a BMW web page - to be that BMW has chosen to limit torque, presumably to help people drive smoothly: torque ramps up linearly until it reaches the peak. It isn't even really trying until 1500 rpm at the motor, which is 155 rpm at the wheels or 20 km/h (13 mph); this is way short of the 20-30 mph where a change is felt. Of course, this same chart also claims constant torque output to 7000 rpm, while we know it is only sustained at that level until 4800 rpm, so it's presumably distorted by some marketing idiot.

The transition from nearly constant acceleration in the constant-torque region of the motor and controller (within the limits of traction, and reduced a bit by aero drag as speed increases) to smoothly decreasing acceleration in the constant-power region of the motor and controller should be at 4800 rpm, or 65 km/h (40 mph).

Remember, as electric motor speed increases from zero (maximum torque), its torque begins to drop off and horsepower begins to climb [HP = torque x RPM / 5252 (radians/sec)]... and horsepower is easier to effectually apply as acceleration.

SO... once you have *any* forward speed, the resistance to accelerate is reduced by your forward momentum... your tires are now applying less torque to the road, but more horsepower.

Then there's this little matter of Newton's first law... An object (car) at rest wants to stay at rest (has the greatest resistance to being accelerated)... because you have to overcome the inertia of the car. This resistance decreases as speed/momentum increases.

Oh, you were so close. All you had to do was stop after you realized that acceleration is proportional to torque. After that, you go completely off track.

Inertia does not change with speed (or momentum). "F=ma" does not contain a velocity term; a=F/m (that's the acceleration of an object equals the net applied force divided by the object's mass), at any speed. As the car speeds up in the constant-power regime of the motor and controller, the force decreases and acceleration decreases. It's even worse than that, since drag increases so the force decreases even more.

These are

BMW's specs for acceleration:

- 0-60 km/h: 3.7 s
- 0-100 km/h: 7.2 s
- 80-120 km/h: 4.9 s

so

- 0-60 km/h: 3.7 s -> 16.2 km/h per second, or 4.5 m/s2
- 60-100 km/h: 7.2-3.7 = 3.5 s -> 11.4 km/h per second, or 3.2 m/s2
- 80-120 km/h: 4.9 s -> 8.2 km/h per second, or 2.3 m/s2

The faster you go, with constant power, the lower the rate of acceleration. That's expected, and it's okay.