It seems to me, that thinking about an electric motor transmission needs to be different that thinking about a gas motor transmission. Here’s what I mean:
Using a transmission spreads out the load for the electric motor, giving you good acceleration at the low end, and your top speed at the high end. Maybe.
This is just trying to show the load (thus, the heat) on the motor. With a transmission, you’re getting a more dramatic drop in load at low speeds (the motor is working less, so it stays cooler) then it averages out to be more even- you’re putting more load at the top speeds than without the tranny (so you can keep pulling) yet you’re putting less on it at low speeds (so you can accelerate faster).
What becomes totally clear when I was working on this graph is that the more gears you add, the more you spread out the power. You can literally distribute it to wherever you want it to be. If you gear it really low, the load drops really fast, and by adding more gears you can keep it low.
Obviously there are other factors, and I’m sure the engineers and physicists are gonna go nutzo on the details… for instance, when you add more gears you add more weight… yeah, fine. I like pictures. (…and strawberry ice cream.)
edit: I think it just dawned on me why this is so hard to get my head around. With a gas motor you’re looking at the output, because that’s basically fixed over the RPM range. You’re looking to take an available resource and put it where you need to. With an electric motor you’re dealing with a powerplant that will draw as much as it needs to do the work, and the issue isn’t as much delivering a resource, but keeping the thing from drawing more than it can handle before it goes all melty… Like I said, we gots to tink different.
Here’s another way to look at it.
Two gearings, low and high. The low tops out at 60 mph. The high tops out at 75, but takes longer to get there.
So, with a transmission, the first gear gets you up to 60 fast, then the second gets you to 75. Total ET is less time to 75 mph.
…and here’s the idea with a 5-speed: