How Fast Should an Electric Car Travel to Maximize Distance?

[peripatein]

Hello,

(1) Is the below equation for calculating the maximum velocity for attaining the alleged maximum distance correct, i.e. at what speed should an electric car travel for it to cover the maximum distance?

E of battery - (F rolling friction + F air drag)*(alleged maximum distance) = 1/2*M*V^2

I got 83.5km/h, for M=1543kg, air density=1.2kg/m^3, battery=21kWh, rolling friction coefficient=0.01, air drag coefficient=8.5sq ft, maximum distance=115miles.

Am I right?

(2) I am also asked for the maximum time it could travel at maximum capacity (e.g. up the hill). Given that the motor's power is 95hp, I divided the battery's energy (namely, 21kWh) by that number, and got approx. 18 minutes. Is that correct? Is it reasonable?

 

[russ_watters]

For the first, no, the maximum range of an electric car has nothing to do with the kinetic energy at cruising speed. The equation should probably just have a zero on the right side.

The second one is correct.

 

[peripatein]

Following your reasoning, I now got that only for a velocity as low as 23.28km/h would that alleged maximum distance be obtained. Could it indeed be that low?

 

[russ_watters]

Typically, the most efficient cruise speed of an normal car is the lowest speed at which it can comfortably run in its highest gear. I would think it would be the same for an electric car, though I don't know how the gearing might be different.

 

[xxChrisxx]

As gears aren't really needed for full EV's as you have maximum torque at 0rpm. You'll just need a fixed reduction ratio to bring the wheels to a sensible operating range, so you can ignore it.

The motor efficiency curve vs car drag is most important. Selecting a motor that sits in the peak efficiency range @ cruise without excess power. Electric motors are most efficient at about 75% of maximum speed.


I'm fairly sure google can help out with e-motor efficiency curves.

 

[peripatein]

So if the maximum speed for that car is 135km/h, how could the speed I got (approx. 23km/h) for maximum alleged distance be correct?

 

[xxChrisxx]

What you've calculated is most likely meaningless. It's not really clear what you have done.

I can't be bothered working it out properly myself, but we can at least do a sanity check.

135 kph top speed * 0.75 = 101 kph. So about 62 mph.
This is close to the most efficient cruising speed for an IC engine when geared for best bsfc in top, so that makes sense.

 

[peripatein]

But I didn't need to calculate the top speed. It was given. I was asked for the velocity which would enable attaining that maximum distance.

 

[russ_watters]

If an electroc car has only one gear ratio, the most efficient speed would be pretty low. I'd think balancing against the power use of the accessories would play a role in limiting the minimum as well.