Motor Torque and Power.

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I started this thread to answer Selrahc 1992 from another thread. It necer does any harm to talk about how motors work. All the statements below are generalisations and should be considered at maximum throttle/PAS or whatever.

Basic principles:
Torque is proportional to current. The more current, the more torque. Torque is what pushes you along. We feel torque as power.
As soon as a motor starts to turn, it becomes a generator. The faster it turns, the more volts it generates. Unfortunately, the power generated is in the opposite direction of what you give it, so as the motor speeds up, the net power becomes less and less until it becomes zero at a certain speed. It actually generates volts, so when the voltage reaches the same as your battery, you can't go any faster. That is why getting a higher voltage battery increases your speed.
Current depends on speed. When the motor starts from stationary, it doesn't generate anything, so all the battery voltage can push the power through the motor, which would mean a lot of current. As the motor speeds up, the net voltage would go down, so the current goes down in proportion until it becoes zero at the maximum speed of the motor. The current at low speed would be too high for the motor, so we have to have a controller that limits it. This means that up to a certain speed the current will be constant and equal to the maximum allowed by the controller, then it will ramp down to zero at maximum speed. Therefore, the torque from the motor does the same. You get maximum torque up to the speed where the net voltage is not enough to push the maximum current through the motor anymore. The cross-over point depends on the controller setting. The higher the allowed current, the sooner you reach the cross-over point.

Efficiency also has a bearing on power. Maximum efficiency happens somewhere about 3/4 maximum rpm. It drops down a lot once you are below 50% of maximum rpm, so that maybe 50% of the power that comes from your battery is wasted, and you get reducing power and torque as you slow down until the motor stalls out.The wasted power is converted to heat, so your motor can burn if you overdo things.

Maximum power happens at about 2/3 maximum rpm. It drops off after that because net voltage and current are reducing. The cross-over point mentioned above has a bearing on the speed at which maximum power occurs. When we talk about maximum speed, we normally mean the maximum speed the motor will spin. You don't get this speed on the road because the power reducest before you get there.

The same rules apply to crank motors as hub-motors, but speed means crank speed for them, so ideally, you want to get peak efficiency at your own personal natural cadence, but at that point, power is already reducing. If you had peak power at your natural cadence, you'd suffer a slight efficiency loss. You can get more torque by slowing down your cadence, but then also less efficiency. If the motor speed doesn't match your pedal speed, efficiency will suffer too, either for you or the bike or both.
 
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trex

Esteemed Pedelecer
May 15, 2011
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for Chinese crank drives like the Woosh Krieger, the maximum efficiency is at about 60 RPM, maximum power is at around 52 RPM (at the chain ring), roughly coinciding with the natural cadence for leisure cycling. For the legal BPMs like the woosh Big Bear (motor winding code 13), maximum efficiency is around 275 RPM, maximum power is around 245 RPM (at the wheels). With a typical reduction of 14T at the rear, 44T at the front, the BPM's sweet zone (245/77 RPM-275/87 RPM) is too high for most leisure cyclists. If you are a distance cyclist, the CD is more efficient.
 

awol

Esteemed Pedelecer
Sep 4, 2013
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Thanks for taking the time to explain it.
Something I have been thinking about recently I may as well ask here.

Is there such a CST motor with as much torque as a 36v 250w bafang CST @16a but smaller/lighter maybe sacrificing speed to get the lighter motor?
I like the torque I have into headwinds/hills but I don't bother with the high speeds anymore and would like a lighter bike, I could increase to 44v 20+amps too if necessary.
 

1boris

Esteemed Pedelecer
Sep 10, 2013
344
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for Chinese crank drives like the Woosh Krieger, the maximum efficiency is at about 60 RPM, maximum power is at around 52 RPM (at the chain ring), roughly coinciding with the natural cadence for leisure cycling. For the legal BPMs like the woosh Big Bear (motor winding code 13), maximum efficiency is around 275 RPM, maximum power is around 245 RPM (at the wheels). With a typical reduction of 14T at the rear, 44T at the front, the BPM's sweet zone (245/77 RPM-275/87 RPM) is too high for most leisure cyclists. If you are a distance cyclist, the CD is more efficient.

Code 13 is 235 rpm
 
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Deleted member 4366

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There's a small MXUS CST motor. The one that I had didn't have fantastic torque, but I think it had Chinese spec magnets, which are not as strong as the export version- apparently! They have a new smoother one now, but it seemed to lack torque too.

Then, there's the small Bafang CST - as used in the smaller Oxydrive kit. I've never tried that one.

The Q100C - maybe a bit less torque thgan the MXUS, but responds to over-volting better.

The Keyde has quite a bit of poke for its size, but there's questions over its fragility.

I have seen other ones but I don't know who makes them. I think that the small Bafang is your best bet:

http://www.szbaf.com/en/components/component/motor/rm-g01285v.html
http://www.szbaf.com/en/components/component/motor/rm-g01250dv.html
 

1boris

Esteemed Pedelecer
Sep 10, 2013
344
58
Thanks for taking the time to explain it.
Something I have been thinking about recently I may as well ask here.

Is there such a CST motor with as much torque as a 36v 250w bafang CST @16a but smaller/lighter maybe sacrificing speed to get the lighter motor?
I like the torque I have into headwinds/hills but I don't bother with the high speeds anymore and would like a lighter bike, I could increase to 44v 20+amps too if necessary.
Xiongda (not cst) and Dapu.Dapu motor are smaller in diameter 155mm.vs 177mm Bafang Cst and a little lighter,very strong and takes a lot to get it hot.My favourite motor.The torque feels diffrent.I belive the Dapu motor is buildt like a mac/Ezee motor.Smaller,but wider.But I dont know if it is sold as a kit anywhere
http://dapumotor.manufacturer.globalsources.com/si/6008848498179/pdtl/DC-motor/1118229213/Motor.htm
 
D

Deleted member 4366

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The Xiongda at 48v is fantastic. It's a bit wider than normal, so a bit of jiggery pokery to fit, but well worth the hassle. It's the best hub-motor by far for commuting and touring. It's so quiet and has adjustable power from hardly notice it's there (50w output) to about 600w output power. At only 15A, you can use a downtube battery and still get a reasonable range. Plus, those batteries aren't too heavy, so you can carry a spare for 80 - 100 miles in a day.
 

selrahc1992

Esteemed Pedelecer
Dec 10, 2014
559
218
I started this thread to answer Selrahc 1992 from another thread. It necer does any harm to talk about how motors work. All the statements below are generalisations and should be considered at maximum throttle/PAS or whatever.

Basic principles:
Torque is proportional to current. The more current, the more torque. Torque is what pushes you along. We feel torque as power.
As soon as a motor starts to turn, it becomes a generator. The faster it turns, the more volts it generates. Unfortunately, the power generated is in the opposite direction of what you give it, so as the motor speeds up, the net power becomes less and less until it becomes zero at a certain speed. It actually generates volts, so when the voltage reaches the same as your battery, you can't go any faster. That is why getting a higher voltage battery increases your speed.
Current depends on speed. When the motor starts from stationary, it doesn't generate anything, so all the battery voltage can push the power through the motor, which would mean a lot of current. As the motor speeds up, the net voltage would go down, so the current goes down in proportion until it becoes zero at the maximum speed of the motor. The current at low speed would be too high for the motor, so we have to have a controller that limits it. This means that up to a certain speed the current will be constant and equal to the maximum allowed by the controller, then it will ramp down to zero at maximum speed. Therefore, the torque from the motor does the same. You get maximum torque up to the speed where the net voltage is not enough to push the maximum current through the motor anymore. The cross-over point depends on the controller setting. The higher the allowed current, the sooner you reach the cross-over point.

Efficiency also has a bearing on power. Maximum efficiency happens somewhere about 3/4 maximum rpm. It drops down a lot once you are below 50% of maximum rpm, so that maybe 50% of the power that comes from your battery is wasted, and you get reducing power and torque as you slow down until the motor stalls out.The wasted power is converted to heat, so your motor can burn if you overdo things.

Maximum power happens at about 2/3 maximum rpm. It drops off after that because net voltage and current are reducing. The cross-over point mentioned above has a bearing on the speed at which maximum power occurs. When we talk about maximum speed, we normally mean the maximum speed the motor will spin. You don't get this speed on the road because the power reducest before you get there.

The same rules apply to crank motors as hub-motors, but speed means crank speed for them, so ideally, you want to get peak efficiency at your own personal natural cadence, but at that point, power is already reducing. If you had peak power at your natural cadence, you'd suffer a slight efficiency loss. You can get more torque by slowing down your cadence, but then also less efficiency. If the motor speed doesn't match your pedal speed, efficiency will suffer too, either for you or the bike or both.
Many thanks,it explains much,weird to think motor works against itself beyond certain speed
 

cwah

Esteemed Pedelecer
Jun 3, 2011
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www.whatonlondon.co.uk
80 miles a day??? never happened to me. You must pedal hard
 

awol

Esteemed Pedelecer
Sep 4, 2013
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374
There's a small MXUS CST motor. The one that I had didn't have fantastic torque, but I think it had Chinese spec magnets, which are not as strong as the export version- apparently! They have a new smoother one now, but it seemed to lack torque too.

Then, there's the small Bafang CST - as used in the smaller Oxydrive kit. I've never tried that one.

The Q100C - maybe a bit less torque thgan the MXUS, but responds to over-volting better.

The Keyde has quite a bit of poke for its size, but there's questions over its fragility.

I have seen other ones but I don't know who makes them. I think that the small Bafang is your best bet:

http://www.szbaf.com/en/components/component/motor/rm-g01285v.html
http://www.szbaf.com/en/components/component/motor/rm-g01250dv.html
Thanks for that, the small bafang looks nice I may see if oxydrive could sell me one on it's own instead of a kit.
I would be tempted to try the Xiongda but I don't want to go up to 48v as that will mean more battery weight.
 

VictoryV

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Feb 15, 2012
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Many thanks,it explains much,weird to think motor works against itself beyond certain speed
In technical terms its called "back electromagnetic force (back emf)", and it happens the instant the motor starts running, without it an electric motor running unloaded would spin itself to destruction, . Much like full throttle on car or motorbike whilst in neutral.
 
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jonathan75

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Apr 24, 2013
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The Xiongda at 48v is fantastic. It's a bit wider than normal, so a bit of jiggery pokery to fit, but well worth the hassle. It's the best hub-motor by far for commuting and touring. It's so quiet and has adjustable power from hardly notice it's there (50w output) to about 600w output power. At only 15A, you can use a downtube battery and still get a reasonable range. Plus, those batteries aren't too heavy, so you can carry a spare for 80 - 100 miles in a day.
What sort of wh/mile were you getting out of yours on a moderate ride? Just asking as curious about the whole hypermiling thing, i.e. which motors get a person the furthest, and how much further than others, all other things being equal.
 
D

Deleted member 4366

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All motors go the same distance for the same pedal effort unless you've got one that's poorly matched to the way you ride. How far you go depends primarily on the battery size, then on hills, the wind, your weight, etc - assuming that you go at the same speed on each one.

To answer your question, if it's meaningful. My rides are moderately hilly with 100kg on board. Moderate steady pedalling. Level one I get 7wh/mile. level three 12 wh/mile and level five 22wh/mile. That's unrestricted speed. Restricted to 15 mph, level 5 is about 15wh/mile. When you engage the winch, power goes up to about 550w at 8 mph, so that's 68wh/ mile, but only used on the steepest hills (25% +)
 
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awol

Esteemed Pedelecer
Sep 4, 2013
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This got me thinking during my cryogenic deep freeze commute today.
Lets say I use PAS level 3 (of 5) with a 16a controller and battery is at 44v and I am at max of PAS level 3=60% of max amps=10a powering the motor. So that works out to 440w right?
Now lets assume same controller but I drop to 36v but I want the same torque. Do I now want to keep the 440watts? 440w/36v=12.2a or max of PAS level 4 will give the same torque as before?
So in a nut shell with my booster battery on I use PAS level 2 and 3 and without it I using level 3 and 4 will feel the same power?
Time to defrost the brain.
 
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Your controller uses speed control (unless its a BMSB S-series), so current depends on speed. If you increase the voltage, the speed/power algorithms don't change, so we can assume that under the same conditions,the PWM will be the same, except the amplitudes of the pulses are higher with the higher voltage, so more energy per pulse, so proportionally more speed.

I would guess that the speed limit on each level will also increase with the higher voltage. I've never tested that to confirm.