Let's say that you're ordering a new Thorn bike with an electric motor for any of the usual reasons of age, health, handicap, etc. It doesn't matter whether it is a front or a rear or a centre motor, though with the front and centre motors you get a free choice of hub gears, which are desirable for many reasons.
The question is, how many gears do you need, whether inside a hub or operated by derailleur?
I live in hilly West Cork, in the far south of Ireland. My daily bike is a Utopia Kranich with 60x622 Big Apples and a Rohloff 14 speed gearbox, and 38x16 gears. This setup was chosen for a manually operated bike to allow me just to get up a particularly steep part of the hill on which I live. It was also arranged so that the 1:1 gear 11 was my normal gear, the higher ones used as overdrives as intended by the designer, the lowest ones used only on hills.
Then I fitted a motor, Bafang 8FUN's QSWXK, the most torquey of the street legal pedelec motors. This I use to fill in when my heart rate goes over a defined limit. In short, I regulate both my effort and the motor's effort by my heart rate monitor reading. It works well.
However, I've found a tendency to ride in gear 14 and use the motor to fill in, and to gear down from there for hills. In short I ride faster and use the battery to fill in so that the level of my effort doesn't disturb my cardiac team.
The motor, with a thumb control, is effectively a continuously variable transmission (CVT), like the NuVinci hub gearbox.
This leads me to heresy: With an electric motor of sufficient torque rating for your and the bike's weight, taking into consideration your normal hills, you don't really need a Rohloff gearbox. In fact, it seems to me that you don't even need any of the Shimano or SRAM 7/8/11 speed boxex either.
All you need is a 3 speed box, with a decent range, say 300%. Because the motor itself is a CVT, you can fill in the holes in the ranges by judicious use of the motor. Essentially, unless I pay attention and deliberately use my Rohloff to the width of its awesome capabilities, that's how I use my current bike when just tootling socially up and down the hills of West Cork.
Note though that this notional 3 speed box, with its big range by huge steps of 150% would have to be pretty sturdy. I haven't done the math to discover whether current 3 speed boxes can handle the torque.
I've made some tests on really steep but short hills, and one really long steep hill said by my doctor to be the steepest hill in West Cork, the sort of hill that motor or no motor, one would normally push up, and 300% will generously cover any hill you can find on any public road.
Why not a fixie or a single-speed, if the motor is that flexible? Two reasons. One is the obvious one. The gearbox will get you home if the motor or the battery clocks out. If you fitted the motor for health reasons/hills, you don't want to pedal home the dead weight of the motor and battery without any mechanical advantage.
The second reason is that batteries weigh a lot, so you should choose the smallest that will do the job you want it to do. I've chosen a "lightweight" bottle battery of 8.8Ah from its Panasonic cells. The way I use it I reckon it may be good for 40-60m of part-time use on my very hilly terrain. But, without the gearbox, on hilly terrain with the motor in constant use at high or even full current draw, 1-2m per A/h is the upper limit of what you can expect. So the gearbox would help maximize the range from a given battery. Even an 8.8Ah battery is already well beyond commuting needs, and almost there for relaxed guest house touring even without a gearbox. The gearbox makes touring possible.
Okay, so that's the logic and my answer. Share your answer with us.
My electric motor installation is illustrated in the photo essay at
http://coolmainpress.com/BICYCLINGbuildingpedelec1.html Andre Jute
