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A major ranking criterion for electric bikes is the torque rating of the motor. Generally speaking, bikes/motors with higher torques are sold at a higher price than bikes/motors with lower torques.

As a follow-up of this thread, I get that having a bigger torque helps in torque intensive situations, like hill climbing.

However torque can easily be multiplied/demultiplied using gears between the wheel axis and the motor axis. For example, these gears can be dedicated (embedded in the motor itself) or in the transmission system of the bike.
So the torque that matters is the final torque on the wheel axis, not the torque output on the motor axis.

So, this implies two questions:

  1. Use of dedicated gears to change output torque: Why is torque rating sold as a discriminatory constant of the bike (especially for the price), where it's easy to just add a gear on the motor itself to increase the torque, at the cost of increased RPMs of the motor axis (as it's done on electric cars)?
  2. Effect of the transmission system on the motor torque: Since motors can be hub motors or mid-drive motors, the motor is not at the same transmission step: meaning the same motor output torque will not have the same impact on the wheel torque.
    For example, a hub motor with a torque of 50 Nm will provide a final torque of 50 Nm to the wheel. However, a mid-drive motor with a torque of 50 Nm, with a gear ratio of 0.5, will provide a final torque of 25 Nm to the wheels.
    With this in mind, how to interpret the advertised torque for a bike with a mid-drive hub, since it's heavily dependant on the transmission?
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    Because Torque rating is a single number that can be easily compared. Like speakers with "PMPO" wattage ratings, and computer CPUs in Megahertz or Gigahertz, the easiest comparison is that "more is better" Why buy a bike with 25 torkies when that one has 50.
    – Criggie
    Apr 22, 2021 at 11:13
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    1. "it's easy to just add a gear on the motor itself to increase the torque, at the cost of increased RPMs of the motor axis " from the engineering point of view / costs-profit-benefit it may be that it is easier to increase the torue rather than having additional cooling/wearing out due to increased RPM. And efficency (energy used over torque provided) varies with RPM of the motor, so increasing RPM may not be ideal in an absolute sense, too. 2. mid-drive torque are provided at the crank, transmission will not affect that measure, transmissions are the "standard" bicycle gears.
    – EarlGrey
    Apr 22, 2021 at 12:37
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    For electric motors, torque at the output shaft is constant over all rpm for which it is designed, so it sets the base for motor performance. Power varies with rpm but torque stays the same -- you reach max power at max rpm. More importantly in a bicycle application where speed and power are often constrained by legal rather than engineering limitations, torque will determine the acceleration possible.
    – R. Chung
    Apr 22, 2021 at 15:19
  • They make bicycles with dynamic field induction drives now? :)
    – Affe
    Apr 22, 2021 at 18:30
  • With a hub motor, the wheel axis and motor axis are the same, so the answer is self-evident there. With a mid-drive, the torque has to go through the same transmission as the rider’s pedaling. I believe current mid-drive motors are indeed geared.
    – MaplePanda
    Apr 23, 2021 at 4:38

2 Answers 2

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Addressing just the actual question as stated to avoid a 3,000 word essay:

With this in mind, how to interpret the advertised torque for a bike with a mid-drive hub, since it's heavily dependant on the transmission?

The advertised torque on a mid-drive bike will tell you over how large a band of cadences and how steep a hill the bike can actually provide the advertised assist level in watts. (generally 250W equivalent mechanical rider input at the crank.)

A low torque bosch active line motor might only provide 250W of equivalent mechanical input assistance at exactly 70rpm on flat ground, whereas a Performance CX can provide that assist level at much lower cadences and on much steeper inclines. The manufacturers try to reduce this to a simple number because it's consumer marketing. (and also the drive system manufacturers don't sell you a final assembled bike, so they don't know what final numbers will be at the drive wheel in the installed system.)

The marketing is targeted to consumers buying finished bicycles made out of mass market bicycle parts. In reality the transmission is always going to go from a bit over 1:1 to around 36:11 to 38:11 and the drive wheel will always be about 26" to 29" outer diameter, these things aren't just infinitely variable to get whatever outcome you want.

Certainly if it were all made out of infinitely ideal "high school physics" components you could use any combination of motors and gearings to get any torque number you like, but these things have to be made out of real materials that don't strip teeth or snap in half or overheat when spinning at the speeds that people's legs actually turn, so there are a lot of engineering compromises to be made.

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  • My interpersonal skills are twisted and withered from too many long days fixing utterly broken Yuba Spicy Curries, so I'm compelled to point out that there are a number of popular 20" mid-drive cargo and folding bikes, such as the Yuba Spicy Curry. Also Bosch chainrings can be teenier than one might assume. Apr 23, 2021 at 5:08
  • Haha, fair enough re: 20" wheels :) Those old "teenie" Bosch chain rings have a 2.5x gear between the cranks and the chain ring so from the 'human' perspective it's a 37.5 or 40, but you're right the drive system's output shaft sees a different ratio. I still did my best to address what the number means to the buyer without writing a book to cover every possible case!
    – Affe
    Apr 23, 2021 at 19:29
  • (Also with those Bosch systems you literally only have the options 15 or 16 teeth unless you machine your own replacements, so it does in a way reinforce the point of the paragraph that the circumstances of the overall drive system that the "torque number" is being considered in the context of are actually pretty constrained ;) )
    – Affe
    Apr 23, 2021 at 19:45
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So the torque that matters is the final torque on the wheel axis, not the torque output on the motor axis.

Indeed. The torque output on the motor axis doesn't matter.

But a 50 Nm mid-drive e-bike does NOT have 50 Nm on the motor axis.

A mid-drive has a fast-spinning motor that's connected to the slow-spinning bottom bracket axle via gears and an electrically controlled clutch. For example, the motor could have 5 Nm that with 1:10 reduction gearing gives 50 Nm.

Now the important question is, why are mid-drive e-bikes sold by torque on the bottom bracket axle? The reason is certain stupid laws.

There is a very stupid law that restricts e-bikes to 250 watts in many European countries. For example, at 85 rpm cadence, 250 watts is 250/(2*pi*85/60) = 28 Nm.

Everyone who knows e-bikes is very well aware that 28 Newton meters doesn't do much to help hill climbing. Also every cyclist who knows about the power cyclists produce (for example having used a power output meter) is aware that a cyclist climbing up a hill can very easily produce 400 watts momentarily. Add 250 watts to that and you'll see the the e-bike power assist isn't very much.

However, the European law has a loophole: it restricts e-bikes to 250 watts continuous. This means that e-bike manufacturers sell 750 watt e-bikes with 85 Nm torque output, and add a limiting software that limits them to 250 watts average over a very long period.

A cyclist who doesn't ride in mountainous regions requires power assist way less than half of the time. When riding down hills, power assist is always zero. When riding on flat terrain, a typical rider will anyway reach 25 km/h (unless there's a headwind), the limit at which power assist needs to stop, so the cyclist needs power assist only uphills. If we claim that 1/3 of riding is uphills, 1/3 on flat and 1/3 downhills, then we can say that 750 watts assist uphills means 250 watts average assist. And usually flat terrain dominates and uphills (and downhills) are quite rare.

The only situation where this breaks is that someone may want to ride up a mountain and ascent on steep gradient for many hours continuously. In this case, the full torque output is not available for the entire climb.

So because of this law you can find:

  • An e-bike that produces 40 Nm and 250 watts (a big lie, it's actually 356 watts at 85 rpm)
  • An e-bike that products 50 Nm and 250 watts (a big lie, it's actually 445 watts at 85 rpm)
  • An e-bike that produces 70 Nm and 250 watts (a big lie, it's actually 623 watts at 85 rpm)
  • An e-bike that produces 85 Nm and 250 watts (a big lie, it's actually 757 watts at 85 rpm)

But you won't find an e-bike that produces 40 Nm and 251 watts! That would be illegal.

The reason manufacturers can get away with this is that the law doesn't limit power output: it only limits continuous power output and quite rarely you need the maximum instantaneous output for many hours.

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