Like i originally posted, but i cant seem to grasp with so many conflicting ideas, is that if the rear sprocket (19T) and the motor sprocket (9T) remain the same then the assisted speed is not altered?
If the chain ring size is altered then this only alters the cadence speed? This was what i wanted to obtain i.e. at 15mph cut off, my legs not flying round, but extra unassisted speed available downhill or on the flat if i was capable?
If i am still wrong, please explain it so an idiot can understand it.
The only way i can see any difference is if the speed is picked up from pedal rotation instead of motor speed
It can be a little difficult to understand with a three way relationship that isn't intuitive. so you are not in any way an idiot.
The first bit you said is correct for the motor drive, the same motor sprocket and rear sprocket will always have the same assisted speed for a given gear and wheel size.
However, since the assist limit is set by the motor and therefore the rotation of the motor sprocket, different size chainwheels will rotate at different speeds. For example, choosing a fictitious number for convenience, if 40 turns of the 9 tooth motor sprocket is the point of 15 mph cutout, that 40 turns onto the chain will turn a 35 tooth chainwheel 10.3 times. (40 x 9 = 360 teeth, which divided by the 35 = 10.3 turns)
For a 41 tooth chainwheel, 40 turns of the 9 tooth motor sprocket will turn the chainwheel 8.8 times. (40 x 9 = 360 teeth, which divided by the 41 = 8.8 chainwheel turns.
Therefore, to get slower pedalling for a given assist speed, you need either a larger chainwheel or a smaller motor sprocket. Many like to do the opposite, get higher pedalling speeds so that the assist phase down does not start at 40 pedal rpm but allows faster pedalling for greater efficiency. To do that they use the 11 tooth motor sprocket which increases pedalling speed by 22%. For those like yourself who like slower pedalling, an 8 tooth motor sprocket with the standard 41 tooth chainwheel helps a bit, slowing the pedalling at any given speed by 11%.
However, the 8 tooth motor sprocket will also slow the assist limit road speed by 11% on your Agattu, so you'd need to reduce the rear sprocket by the same 11%. That 19 tooth would need to be changed to a 17 tooth.
N.B. Crossed with Tillson's post.
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