On Electric Vehicles and Gearboxes

Electric cars generally don’t benefit electric cars. In this post, I get into why that is, and why there are some exceptions.

Why Transmissions Do Not Make Sense on Most EVs

Most EVs use a PMAC (permanent magnet alternating current) motor, sometimes called a PMDC, BLDC (brushless DC), or AC synchronous motor. It’s all the same stuff. PMAC motors expose the rotor to a magnetic field; the magnets embedded in the rotor try to align themselves with that field, which exerts torque.

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Sidenote: Modern PMACs also rely heavily on magnetic reluctance — the fact that the ferromagnetic rotor is attracted to the magnetic fields of the stator — but that is a topic for a different day.

Illustration for article titled On Electric Vehicles and Gearboxes
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Few people intuitively understand just how wide a PMAC power band really is.

In a typical internal combustion engine, peak torque is reached around 2000 RPM, and peak power between 5000 and 7000 RPM. That’s a pretty narrow power band, all things considered.

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Since Power=Force*Speed=Torque*Rotational Speed, you can get more torque (force) at lower RPM, and your torque has to drop off as speed increases. You transmission trades speed for torque or vice versa, allowing you to maximize both for a limited band of useful RPM. We’ve all experienced this with gearing on bicycles, it’s pretty intuitive stuff.

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What isn’t so intuitive is that motors just... don’t have this problem. The power band on a motor runs from about 3000 RPM to anywhere from 10,000 to 20,000 RPM, and it pulls peak torque from 3000 RPM down to zero. Power delivery is nearly flat — no matter how fast you go, you can still deliver the max torque for that speed.

A Case Example: Gen 1 Nissan Leaf

Here is a 2012 LEAF motor torque curve (annotations courtesy of MS Paint). Notice that all the way up to the governed limit of 10,000 RPM / 93 MPH, the LEAF can run up to 80kW / 107 HP. If the governor wasn’t there, it could probably continue to 13,000 RPM before hitting 90% efficiency.

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2012 Nissan Leaf Motor Efficiency Contour
2012 Nissan Leaf Motor Efficiency Contour

And here is a 2011 LEAF dyno test for at-the-wheel measurements. Once again, notice that until the speed governor kicks in, there is very little (<9%) power falloff between 30 MPH and 88 MPH.

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2011 Nissan Leaf Dyno
2011 Nissan Leaf Dyno

If you feel like an EV is losing power as it gains speed, it’s not because you’re running out of RPM or exiting the power band, it’s because you’re experiencing more and more wind / rolling resistance. If you only have 107 HP and half of it is being spent fighting the air, then of course you’re going to feel a drop in passing power.

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Based on these tests, if you add a 1:2 overdrive gear at 80 MPH, your motor speed will halve to 4300 RPM, motor torque will double to 180 Nm, and the torque and speed at the wheels will remain almost constant. You’d gain a grand total of 5 horsepower and <2% efficiency.

In short, if you want more high end performance out of a cheap EV, you don’t need more gears, you need more horsepower.

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Why Transmissions Could Make Sense in Some Edge Cases

1. Induction Motors and Exotic Architectures

All right. Remember the PMAC motor with its beautiful, flat power delivery, and its swoopy torque curve? Well, enter the induction motor.

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The induction motor generates a rotating magnetic field to create eddy currents in the conductive rotor, thus inducing magnetic fields. Despite being Very Cool, this is an inherently lossy way to run a motor, and it has some gaps in performance.

The Tesla Model S P85 below uses an induction motor. Notice how much the power drops off towards the high end compared to the Leaf, and how there’s a “hump” in torque around 3500 RPM. With a transmission, you could mitigate these. Tesla’s answer was to stop using so many induction motors, but you do you.

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2014 Tesla S P85 Dyno
2014 Tesla S P85 Dyno

2. Extreme Speed

As a motor speeds up, the back EMF in the coils increases until it matches the input voltage, at which point, the current stops flowing and torque tapers to zero. The motor’s top speed is typically limited by the voltage of your driver/inverter, as well as its ability to withstand centrifugal forces without exploding.

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It’s not easy to exceed a motor’s RPM limits, especially with modern high-voltage batteries and high-strength materials, but you can do it if you really believe in yourself. So some hypercars have a high gear for the top end.

3. Extreme Stall Torque

As the rotor in a motor spins slower, the back EMF reduces to zero, increasing the current driven through the motor, which increases the torque. Just like an automatic transmission, an electric motor swaps speed for torque as you load it down. At 0 RPM, the motor is “stalled,” and can provide maximum current. Stall torque is generally limited by the amount of current the motor can handle without melting (and the batteries without blowing up).

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If you have a hard limit on current, and adjusting your final drive ratio or number of stator coil turns isn’t an option, then a low gear could prove useful. This could turn your vehicle into a winch at walking speed, but once you hit ≈25mph, you’ll be out from under the current ceiling, and the limit on how much you can tow will be determined once again by total motor power.

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