Hi mech,

Cool

, some technical questions.

I want to be able to do 50 mph. The EMC-R is rated at 3700 rpm @ 48V no load. Obviously I don't want to gear it for 3700 rpm @ 50 mph.

You're correct about that. The only time that would happen is downhill or like a 70 mph wind on your back

What RPM should I gear it for my desired top speed? AKA...how much RPM sag/droop in RPM will it need before there is sufficient torque to achieve my 50 mph?

What you need is a motor speed torque curve and need to know the voltage sag in the battery at load. If you knew the power required at 50 mph and had the motor curve (which included battery sag), it would be simple to find.

I assume both these motors are brushed PM motors??? Then the speed torque and current torque and therefore speed current relationships are all linear. And also a good approximation of battery sag is linear. But we don't know the slopes

Sometimes for PM motors they will supply you a factor for this call Kv. Which is the RPM per volt (at no-load). This would be helpful.

O.K. That didn't answer your question. So let's try this. Say at 50 mph the actual voltage from the battery is 46 volts. And at that torque, the actual 48V motor speed would have dropped to 3500 RPM. Multiply 3500 times 46/48 to get 3350 RPM. Give that a shot and test it on the bike. Leave yourself some room with those sprockets so you can change a couple of teeth to adjust it if needed.

Torque questions: In a typical DC motor, what does the torque curve look like? Is max torque at 100% throttle, zero rpm? Does the torque stay the same all the way up the rev range, or does it decrease in a linear fashion until 3700 rpm (in the ETEK-R's case), where the available torque is basically zero?

Torque is proportional to armature current and linear with a PM motor. You are going to have a PWM controller. So the throttle is going to set the PWM duty cycle, which is the percentage of voltage applied to the motor. However there is another factor governing this PWM duty cycle called current limit. So, at a standstill, without a current limit, if you apply full voltage to the motor it would draw stall current (like 2000A) and produce maximum torque, probably breaking something. But with the current limit, at standstill, when you give it full throttle, the controller will set the PWM to limit the current, say to 400A.

Now the torque the motor will produce at 400A is independent of RPM. And if 400A is the maximum current, that will be the maximum torque. At standstill (0 RPM) the 400A and maximum torque will only require a low voltage to the motor, so a low duty cycle PWM on the controller. As the motor accelerates and the RPM increase, the motor voltage needs to increase, so the controller will increase the PWM, all the while the motor will produce maximum torque. This continues as a constant torque acceleration until the PWM hits 100% duty cycle. This will be at the maximum power point. Beyond that, the vehicle and motor will continue to accelerate (increase RPM), however the current will start to decrease. As the current decreases, the torque will decrease and the acceleration will decrease, although you will continue to increase speed, just at a lower rate. Until the RPM increase and current decrease reach an equilibrium point with the motor natural characteristic, namely 3350 RPM, if my guess was correct.

Power draw questions: I imagine that at full throttle, full batt pack voltage is applied to the motor.

Not when in current limit. See above.

Is the highest amp draw at zero rpm, full throttle?

This will be the highest motor current, but not the highest battery current.

Does the amp draw stay the same all the way up the rev range, or does it decrease in a linear fashion until 3700 rpm?

On an acceleration from zero, full throttle, the motor current stays constant at current limit until you reach 100% PWM (full voltage to the motor) and then the current decreases until equilibrium.

On acceleration from zero, full throttle, the battery current starts low and increases until you hit 100% and then is equal to motor current and decreases in the same fashion as motor current.

I remember learning the basics about DC motors in my apprenticeship (starter motors): as the rpm increases, electromotive force (induced voltage opposing the flow of current) increases, which basically self governs the motor at a certain rpm and limits current flow as the revs get higher.

Yes, and this plays out once you come out of current limit (100%) and is why the current drops as you approach top speed.

I hope that didn't totally confuse you

major