# Volts, Amps, Speed & Torque as they relate the DD Hub

#### teslanv

##### 1 MW
SO I have spent a bit of time here and on the ebikes.ca simulator (http://www.ebikes.ca/tools/simulator.html) and I think I understand the basics of how all of these concepts relate.

Here is how I might try explain this to a "NOOB" :

Concept 1: A Direct Drive Hub is configured with copper wires in a variety of options. Depending on the size (diameter) of the copper wire, how many strands of that wire, and how many "Turns" those wires are wound around the armature, you will get a certain kV of motor. - 1kV = 1 RPM per Volt of applied electricity.
A Common ebike direct drive hub might have a kV of 9, so that when a battery of 48V is used, that motor will have an unloaded RPM of (48X9) = 432 RPM

Concept 2: A Hub Motor may be rated "1000W", but can usually accept much higher wattage, as long as the temperature is controlled. - Various methods of cooling are possible, the most simple being to drill holes in the side covers to allow air ventilation.

Concept 3: Size Matters - at least with respect to Wheel Diameter- wheel diameter makes a BIG difference in the speed of your bike.
Given the Hub Motor example above at 432RPM (48V) the standard 26" Mountain Bike Wheel diameter would provide an unloaded speed of 33.4 mph and a 20" Diameter Wheel would provide an unloaded speed of 25.7 mph, but would have more torque than the 26" Diam wheel. 700C or 29" Wheel would have even higher speed than the 26" Wheels, but less torque.

Concept 4: Voltage = Speed - If you want to go faster, get a higher voltage battery. If the 26" MTB Wheel and 9KV motor can go 33.4 mph on 48V (unloaded), then the same motor and wheel can go twice as fast (unloaded) on twice the voltage, so 96V = 66.8 mph (unloaded)

Concept 5: Voltage alone won't get you the real world speed you desire, because factors like mechanical and electrical inefficiencies, rider & bike weight, slope of incline, and most importantly wind resistance will all work to slow you down from your unloaded speed. - to compensate for the non-efficiency-related factors, you need more torque or current (More AMPS) to overcome these factors. So a high voltage (and high Unloaded RPM) system will struggle to overcome the factors listed above, unless you have the torque (and thus thrust) required to offset them. However, higher current also comes with the cost of higher temperatures, and at some point all motors, when provided with too much current will overheat, and bad things start to happen. Usually the insulation melts off of the phase wires and cause an electrical short, which will pretty much kill the motor.

Concept 6: - Thicker (heavier gauge) wires will help to keep the system heat down. If your Motor's phase wires are small (16ga or 18ga - higher number = smaller diameter) it will help to replace the phase wires with a thicker (12ga or even 10ga if you can fit them) to keep the phase wires cooler, longer.

Concept 7: Hub motors like to spin at their nominal kV rating. When they are spinning slower (like starting off or climbing a hill, loaded down with weight) they are not very efficient, and the power (Watts) being supplied to the Motor is turning into heat, rather than motion (speed). The goal is to operate the motor at it's peak efficiency (usually around 80%) which is typically between 1/2 to 2/3 of it's unloaded RPM.

How might you explain these concepts differently? Anything you would want to add?

teslanv said:
Concept 7: Hub motors like to spin at their nominal kV rating. When they are spinning slower (like starting off or climbing a hill, loaded down with weight) they are not very efficient, and the power (Watts) being supplied to the Motor is turning into heat, rather than motion (speed). The goal is to operate the motor at it's peak efficiency (usually around 80%) which is typically between 1/2 to 2/3 of it's unloaded RPM.

This might be the most common misunderstanding on the E-S forums.

Efficiency is not related to speed as much as it is to amperage. Amperage is more of the limiting factor for motors and most specifically, the amperage at which the coils saturate the permanent magnets. Because the motors often receive the most amperage at lower speeds, its often conflated with heat and saturation issues. If the amperage is controlled sufficiently, lower speed operation can be reasonably efficient. Low speed and amperage means low power, however, and most people whack the throttle until the efficiency suffers from increased amps.

gogo said:
teslanv said:
Concept 7: Hub motors like to spin at their nominal kV rating. When they are spinning slower (like starting off or climbing a hill, loaded down with weight) they are not very efficient, and the power (Watts) being supplied to the Motor is turning into heat, rather than motion (speed). The goal is to operate the motor at it's peak efficiency (usually around 80%) which is typically between 1/2 to 2/3 of it's unloaded RPM.

This might be the most common misunderstanding on the E-S forums.

Efficiency is not related to speed as much as it is to amperage. Amperage is more of the limiting factor for motors and most specifically, the amperage at which the coils saturate the permanent magnets. Because the motors often receive the most amperage at lower speeds, its often conflated with heat and saturation issues. If the amperage is controlled sufficiently, lower speed operation can be reasonably efficient. Low speed and amperage means low power, however, and most people whack the throttle until the efficiency suffers from increased amps.

So perhaps a better way to explain this is that often when starting out from a stop or climbing a hill, the user is feeding the motor a high amount of current, which equates to higher temperatures, but if current (amps) is limited by a controller or prudent use of the throttle, heat and thus efficiency can be kept to reasonable levels.

Also adding pedal power while in a climb shows a great deal of difference for lower powered setups.

For instance if you know your hub has an absolute maximum torque output of say 20 N-m then you can see if a given grade is even doable with your motor (edit: and wheel size), if the necessary torque with your tire size and your weight is 25 N-m then you aren't going anywhere unless you pedal. Interestingly even a few watts of pedaling will get you up the hill when lots of amps of battery current result in zero.

Jonathan in Hiram said:
Also adding pedal power while in a climb shows a great deal of difference for lower powered setups.

For instance if you know your hub has an absolute maximum torque output of say 20 N-m then you can see if a given grade is even doable with your motor, if the necessary torque with your tire size and your weight is 25 N-m then you aren't going anywhere unless you pedal. Interestingly even a few watts of pedaling will get you up the hill when lots of amps of battery current result in zero.
True, because although human power does not provide a lot of total watts, it CAN provide a lot of torque, when a sufficiently low gear ratio is selected. - a DD Hub motor cannot benefit from the bicycle's gears like a human (or mid-drive motor) can.

teslanv said:
gogo said:
teslanv said:
Concept 7: Hub motors like to spin at their nominal kV rating. When they are spinning slower (like starting off or climbing a hill, loaded down with weight) they are not very efficient, and the power (Watts) being supplied to the Motor is turning into heat, rather than motion (speed). The goal is to operate the motor at it's peak efficiency (usually around 80%) which is typically between 1/2 to 2/3 of it's unloaded RPM.

This might be the most common misunderstanding on the E-S forums.

Efficiency is not related to speed as much as it is to amperage. Amperage is more of the limiting factor for motors and most specifically, the amperage at which the coils saturate the permanent magnets. Because the motors often receive the most amperage at lower speeds, its often conflated with heat and saturation issues. If the amperage is controlled sufficiently, lower speed operation can be reasonably efficient. Low speed and amperage means low power, however, and most people whack the throttle until the efficiency suffers from increased amps.

So perhaps a better way to explain this is that often when starting out from a stop or climbing a hill, the user is feeding the motor a high amount of current, which equates to higher temperatures, but if current (amps) is limited by a controller or prudent use of the throttle, heat and thus efficiency can be kept to reasonable levels.

Yes. Let's take the common example of a 9C type 9X7 motor. It starts to saturate the permanent magnets at 50 phase(motor) amps. Because most controllers supplied with those motors have a 2.5X max amp multiplier-limit and 20 amp battery limit, they can supply the motor with enough amps to stop just shy of saturation. The motor will heat up quickly at 50A phase current and when the coils get hot their resistance increases which causes even less efficiency.

So (oversimplification), anytime the (20 battery amp) controller is in current limiting mode and your forward speed is less than 40% max. no-load speed, the motor can receive more current (50A) than it can continuously sustain. At 50% of max. no-load speed, the motor can see 40A, and at 66% it can see up to 33A. How many amps a 9C 9X7 can tolerate depends on the rate and temperature of the air flowing over it, or in other words its ability to shed heat.

If the motor is truly a 750W@48V, that would give us roughly 15A continuous. So this common set-up can potentially be forced to overheat unless judicially throttled on steep hills, or into high headwinds. Most use is momentarily high amp during take-off from a stop, and as long as that doesn't overheat the motor we get to enjoy brisk acceleration from a motor stressed to almost saturation and then up to 750W of continuous power at top speed.

Jonathan in Hiram said:
Also adding pedal power while in a climb shows a great deal of difference for lower powered setups.

For instance if you know your hub has an absolute maximum torque output of say 20 N-m then you can see if a given grade is even doable with your motor, if the necessary torque with your tire size and your weight is 25 N-m then you aren't going anywhere unless you pedal. Interestingly even a few watts of pedaling will get you up the hill when lots of amps of battery current result in zero.

Re number 7.

It's low rpm combined with heavy load that makes heat in the motor. So starting up, hills, headwinds, or worst of all starting up on a hill all combine max load with whatever rpm you are turning.

But with a low load, such as flat terrain, you can operate at low rpm and be very efficient. Even with very heavy weight, you can get surprising good wh/mi at low speeds. I thought this would not be possible when I went to a heavy cargo bike, but it still is.

But back to that hill, on an 8% grade, you'd better be turning that motor faster or it will pull huge watts and not go anywhere. You can see this on a wattmeter, if you ride up as many hills as I have. My current cargo bike climbing an 8% grade will pull 1000w at 15 mph, but at 10 mph the watts go to 1750, the controllers max. Backing off the speed actually increases the wattage on that grade. That extra 750w is going straight into heat.

So I learned what I had already known, keep your speed up going up hills. But if you can maintain 15 mph on less than full throttle, then you can back off and ride up hills relatively slow. Just don't ride up it at 8 mph. My cargo has a high load when climbing hills, so I can't back off the throttle unless the grade is less than 8%. Above 8% grade, I must throttle wot, and stomp on those pedals. But lighter bikes I have ridden up 10% grades at 3/4 throttle, at you guessed it, 15 mph.

This is all very hard to transfer into a riding style out on the road that is efficient. I learned by riding with both a wattmeter on the battery and a thermometer inside the motor. Particularly the thermometer, if the temp didn't go up, I know I'm not running exess heat. I can't be if the motor stays cool. But if you enter that inefficient combination of load and RPM, man you see it on that thermometer in the motor immediately.

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