"If a load is applied that slows the motor, the back-EMF is reduced and more current flows, increasing the torque to better handle the load. "

so the website says by going to a higher gear (load) back emf is reduced, so my top speed can only be limited by the amount of current i can apply to the motor and the number of gears in my transmission, right?

Sort of.

The fundamental principle is that back EMF is proportional to the product of field strength and motor speed.

Top speed in a vehicle with a series DC motor is set by two things. First of all, you need enough speed from the motor. With a series DC motor, it turns out that they are capable of almost infinite speed, if the field current is low enough; they can be seriously damaged by overspeeding at low loads (e.g. in neutral). But when determining the top vehicle speed, air resistance will provide a considerable load (say 20 kW), so you will need a considerable field strength to get that sort of power. If you look at the performance graph for a DC series motor, you will see that high power comes at low motor RPM (the opposite is true for most other motor types), so to get the maximum speed, you need to carefully choose the gear to get enough load on the motor, yet enough speed to the wheels. [Edit: this is wrong; see my next post.]

So motor current shouldn't have any effect on back emf, i think so anyway

I don't see how that follows from what was said before. Back EMF is set by two things; speed and field strength. These two quantities are multiplied together, then multiplied by a constant, to determine back EMF. So field strength is just as important as speed in determining the back EMF of the motor.

Field strength is closely related to field current, and in a series DC motor, field current is equal to motor current. For most purposes, we can say that field strength is proportional to motor current. So motor current directly influences back EMF.

So load has a double effect on back EMF. Load affects RPM: increasing the load reduces the RPM, which

*reduces* the back EMF. This increases the current, which increases the field strength, which

*increases* the back EMF. So there is a sort of balance that gets struck as load is increased. The controller and pack may interact with this; the increased current load may cause the controller to limit its current, and the batteries may sag more which could decrease the current to the motor.

Overall, I think that increased load will always result in decreased back EMF, though people more familiar with series DC motors might have more to say on that.

Finally, the increased torque from the increased field strength will eventually increase the motor's RPM. But that's not an instantaneous effect; the other effects all happen more or less instantaneously.