Fun topic and I'm still in lockdown here so I'll join in.
Check my logic but I reckon you can get an "at least" figure for the torque a rider of a given weight can exert at the bottom bracket just by considering his applying his weight fully to one pedal with the crank horizontal.
If we take AndrewJ's stated weight, just over 100kg, then if the crank were a metre long that would produce a little more than 100kg-m of torque, which conveniently is 1000Nm.
If in fact the crank is 0.17m long, then we have torque of 1000 x 0.17 which is 170Nm.
Various informed sounding discussions around the net claim that in practice most riders can exert a force greater than their body weight on the crank arms at this point, in part because they can hold their body down through gripping the handlebars, and in part because their opposite leg if clipped in can do the same and add torque.
A third additional factor is the inertia of the rider. Even without being clipped in and with no pressure on the handlebars, the rider can exert more than 100kg downforce on the pedal by attempting to accelerate his body more than gravity does. To see this, imagine that someone holds your bike upright on a steep hill in a gear tall enough that when you stand on one pedal with that crank horizontal the bike rolls neither backward nor forward. Are you stuck like that or can you move your bike up the hill? Well, you could move it a little if you bent your leg and then straightened it sharply. You're accelerating your body upwards, and the force generating that acceleration would add to the force at the pedal. The bike would move forward briefly.
Maintain that mental image, hold on the the handlebar, clip in your other leg, and now see what you can do. It's pretty clear that you'd be capable of advancing the bicycle.
So when you look at the maximum instantaneous torque a 103kg rider could exert on the crank spindle, we can be confident it is greater than 170Nm. What's less clear is how much greater. Still, the 247Nm at a gear ratio of 1.9:1 that would meet Rohloff's specified 130Nm maximum at the hub for light riders (thanks buffet) is not a huge leap away.
What about with electric assist? From what I can see the rated peak torque output of the strongest bicycle motors is about 80Nm. So if a 103kg rider balancing at a standstill on one pedal were to add maximum specified torque from a pedelec motor that applied it all at the spindle, total torque at the spindle would be 170 + 80 = 250Nm.
Note that even with the light-rider 1.9 input ratio this barely exceeds Rohloff's specified maximum at the hub of 130Nm.
As I think we've seen, the rider if clipped in could increase that figure. By how much is not clear. From would I could find in a quickish scan of the webs, researchers haven't paid a lot of attention to the peak torque a fit rider can exert through a crank system.
If that's so it might be because it's not that important. In practice it would never be delivered, because in practice there is no other good reason to conduct the exercise I've just described. The bike will always be moving forward at least fast enough to stay upright, and the possibility that the rider can time his peak output to match precisely the horizontal crank position with each revolution is slim. What matters much more is the maximum average torque he can exert as he pedals a circle. That multiplied by his cadence and a factor appropriate to the power unit chosen (thanks Andre) will give his power output at his maximum torque, and that will determine the tallest gear he can hold briefly for a stated rate of climb - road speed at slope steepness. As the slope steepens, the gear he needs falls, and with it his road speed at cadence. Given infinitely variable gearing, at a certain slope he'll be too slow to balance the bike. It is not likely that at this point he'll attempt to generate peak torque (as distinguished from max average torque). It's not likely either that if he tried he could manage it, and even if he did manage it he could not sustain it for more than a moment.
What's the implication for hub life?Glad you asked. I think that without knowing how much peak torque a rider might add to the torque he generates when standing on a pedal with the bike stationary, we can draw some conclusions about risks to a hub.
Lets observe at first that Rohloff's stated maximum input torque of 130Nm is not likely to be the torque at which the hub goes crunch and stops. Rohloff doesn't say this, but to my eye that's common sense. There would be no point in Rohloff specifying that figure, because it's of no help to anyone. What we need is the maximum torque it can accept reliably and sustainably. It's quite likely that's 130Nm. Which is what a 103kg rider exerts momentarily through a 1.9:1 input ratio if he stands on a horizontal pedal while assisted by an 80Nm motor that's operating at maximum torque.
Obviously using the 2.5:1 ratio adds a margin of more than 25 per cent.
Now let's look at the rider - we've theorised about the peak load he might impose momentarily, but what might we expect him to reach even briefly in practice?
I've rambled on for long enough, so I'll leave you all to speculate about that. My guess is it's under what he might exert when standing on a horizontal pedal. Yes he
could exert more when climbing or sprinting out of the saddle, but I reckon he exerts less because he's much more interested in exerting a high average torque - i.e. in sacrificing some peak torque in order to carry that sub-peak output output further through the pedal circle.
Finally, what of the DC electric motor? Well, they tend to make peak torque at zero rpm. At typical cadences they'll be doing less than that. But I've assumed above that the advertised torque is what reaches the crank spindle - if what's specified is the torque at motor output shaft and it multiplies that through a gear train to the cranks then my theorising is out by the factor of the gear ratio.
Assuming I haven't made some silly error with the weight-torque conversion.
