I still struggle with my understanding of how these concepts affect one another.

To lean on a concrete example, I have a Nissan Leaf motor, which is designed to run up to 10k RPM at a nominal 360V. I'm wondering what happens if I only provide it with 180V.

* * *

I don't need all the torque available from a 360V pack.

Is the motor gonna just poop out at 5k RPM with half the voltage, or will it spin to whatever it can with the (half) power available to it...?

Power is volts*amps.

746 of those gives you one horsepower.

Energy is horsepower (or power) produced over time.

Your battery is rated for its energy (kWhr).

Horsepower comes from the fuel -- in our case, the battery.

Now, the question becomes, how can you make horsepower? Because it's horsepower that gets you your coveted "safe highway speed."

A Tesla Model S needs about 50HP to run at "safe highway speed". A Nissan Leaf, for the sake of argument, might be 32HP. So the multiplication of your voltage and current, for the hypothetical Leaf has to be 32*746...off the top of my head, 24kW.

As has been said previously here, in general terms, speed is voltage, current is torque. You HAVE to make HP to get your target speed, but halving your voltage gives you half the speed (as has been noted, because of that pesky back-EMF).

Then you say, "F it, I'll just double the current with my controller", which doubles the NEEDED torque at a speed your motor no longer can get because you were a cheapskate and bought half the packs you needed.

So, you can either be happy with a car that will pull a trailer equal to its weight at 30MPH and have double the low speed acceleration OR, knowing you will not be happy because bragging about your 0-30MPH times over a beer would shrink your manhood, you have no other recourse but to throw in a 2:1 gearbox.

That halves your torque (which now becomes the torque you wanted at the safe speed), but doubles your lame speed to your target speed.

Think about it...ignoring losses, a gearbox keeps speed*torque constant, which is the same as keeping voltage*current constant -- magically horsepower into a gearbox equals horsepower out and it's horsepower that gets you your highway speed...but only if you are not limited by something (back-EMF*) in achieving the drivetrain rotational speed.

TL;DR... you need a gearbox in order to return the "voltage" to the 360V you needed in the first place. Or, go plow a field with your project.

*If you really want to give yourself a headache, you can also reconfigure the motor in terms of windings and poles. But, a gearbox is a lot easier to do and, much like owning a Corvette, the EV-hoes you attract into the passenger seat won't be able to tell the difference.