I've wondered about this before, but I'm doing a Brompton Rohloff conversion for someone and the moment has finally arrived where it's not just a theoretical issue:

Shimano and Rohloff both recommend gearing selection based on minimum chainring to rear cog ratios. In Rohloff's case, they explicitly state this is to prevent "overstraining the hub" at the low end, and there is no maximum ratio. If the goal is to limit the torque going through the hub internals, how does it make any sense to specify a wheel-size-independent tooth count ratio?

For example, the recommended ratio 40:21 on Rohloff on a 700x35 (35-622, i.e. a Euro trekking bike, a stereotypical use case for Rohloff) gives 14.4 gear inches. On Brompton (35-349 tire) it's 8.5. Their own chart on the applicable page in the manual shows how the meters development plays different on a 406 versus a 622 wheel.

It would seem like wheel radius is a simple factor on all the loads that all the internal parts will experience. Is there some subtlety going on with the design considerations of an IGH that makes that not true? Other than some people having a hard time knowing what to do with them, what bad thing would happen if they issued these limitations in terms of a gear inch or meters development number?

rohloff min

shimano min

  • 8.5 gear-inches is utterly useless on any bike - my lowest is 15 and I only ever use that for heavy trailer towing. Are you able to fit a smaller chainring and a larger drive sprocket to this bike ? Even larger tyres might help.
    – Criggie
    Aug 17 at 7:37
  • 2
    The load on the hub from pedaling is not dependant on wheel size. Torque loading at 0mph doesn't care how big the wheel is but could still damage hub internals if the ''lever'' of gear ratio is ''long enough''
    – JoeK
    Aug 17 at 8:08
  • (The bike itself is being set up 54-13, presuming we can source the 13. 54-13 is the "mainstream" choice for these conversions. I'm here asking the question because I'm curious if there's a reason for the manufacturers presenting it in terms of a tooth count ratio other than being an attempt to simplify things.) Aug 17 at 8:49

What propels you forward is force not torque. A small wheel requires little torque to generate a given force, whereas a large wheel requires more torque to generate a given force.

Thus, on a small wheel like a Brompton you would use a big chainring and a little sprocket in the rear to create a low torque at high speed. On a 27.5" fatbike you would use a small chainring and a big sprocket in the rear to create a high torque at low speed. The most problematic for the gear hub is the small chainring and big sprocket on the large wheeled bicycle.

What you as a cyclist see is force. What the hub sees is torque. The hub can only withstand a certain amount of torque. For example, for Rohloff they assume the torque at hub never exceeds 130 Nm. However, with 1:2 sprocket to chainring ratio a 110kg cyclist using clipless pedals (thus pulling up from the rear pedal at 25 kg) and pulling up on the handlebars at 20 kg when sprinting would easily create 300 Nm at the 170mm cranks and thus 150 Nm at the hub.

The most hard time a hub is having is on a large wheel bicycle. A small wheel bicycle typically puts smaller torque on the hub due to the different sprocket to chainring size ratio. Bicycle wheel sizes go up to about 27.5" fatbike, you won't see larger wheels anywhere else except perhaps penny farthings that don't use geared hubs. 27.5" fatbike is not that much different from for example 28" (622mm bead seat) city bike or road bike. However, children's bikes and specialty folding bikes use very small wheels.

Also note that the torque at the hub is only dependent on rider weight, rider strength, riding style, crank length and sprocket to chainring ratio. Wheel size does not matter. So for example with the same 1:2 sprocket to chainring ratio the strong sprinter could sprint on a Brompton for example. It would then create too 150 Nm at the hub if the sprinter can use the Brompton handlebars as efficiently as drop bars. The gearing would be very low so to provide any "resistance" to pedaling the 150 Nm could most reasonably be achieved when sprinting on a steep uphill. On a flatland, achieving the 150 Nm at the hub might not be possible because the bicycle would accelerate so hard below the cyclist that the cyclist can't maintain the maximum force on the pedals.

Oh, and also after reading the question a second time more carefully: yes, you can use 8.5 gear inches on Brompton. You can use anything larger than that. You cannot use anything below 8.5 gear inches. I think it's self-evident that you won't be gearing it to lower than 8.5 gear inches.

The lower the gear, the more torque the hub sees. Thus, it's not high gears that the rule is trying to prevent you from using. It's low gears.

  • Your edit is leading you to the same question that made me post this. On a 700x35 the number you can't go lower than is 14.4. The question is what if anything would be the difference in terms of the force going through the internals between cheating the gear lower than 14.4 on a 700x35 and simply running the recommended 40:21 with the resultant 8.5 on the Brompton. Aug 17 at 8:45
  • The 14.4 gear inches on a 700x35 is the same sprocket size ratio than 8.5 gear inches on Brompton. Because the sprocket size ratio is the same, the torque at the hub is the same for identical rider and cranks.
    – juhist
    Aug 17 at 8:58

The bicycle is being propelled from the drivetrain, not from the rim.

Assume the worst case scenario: the wheel is frozen in place and the rider is pushing on the pedals. The chain tension force here is independent of wheel size. The torque the hub internals see is a function only of chain tension force and sprocket radius.

If it was instead the wheel applying torque to the hub, then yes, the wheel size would be important; the same force at the rim generates different torques depending on the wheel’s radius.

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