Building E-Bike Help

Considering that your question is based almost entirely on the use of an alternator, this answer should provide a global "solution."

You should have NO alternator (or generator).

An alternator will remove additional capacity from your battery, because the energy necessary to drive the alternator will be removed from the battery. That energy will not propel the bicycle forward. The alternator cannot provide to the battery more energy than it uses, becoming a net drain on the entire system.

It will not make the battery last longer, it will reduce it. Efficiency losses are accepted by the engineering community, because it's a law of physics, and designs are built around those losses.

I own a number of different electrically propelled vehicles and have been asked many times why I don't, for example, have a wheel off the back driving an alternator to charge the battery. This is mechanically similar to your question.

Ignoring for a moment the alternator aspect, having an additional wheel adds weight and rolling resistance. The energy necessary to move that wheel must come from the battery. This increases the depletion of the battery over the un-wheeled design. Loss point one.

Add an alternator and wiring, add weight. Loss point two.

Alternators have bearings and magnetic field interaction, which absorb energy. Loss point three.

The circuitry for energy management in an alternator has a conversion factor less than unity. Loss point four.

Adding up these losses means that the additional system(s) on this electric vehicle shortens the range, not increases it.

A bicycle without additional equipment and well maintained is considered the most energy efficient mode of transport. When you add weight consisting of a battery and motor, that level of efficiency is reduced, but compensated for by having the motor "take up the slack."

If you are intent to add a motor to a bicycle, consider that the motor has a specific range of rpm in which it is most efficient (miles per kilowatt hour) and a different range in which it is most powerful. Some manufacturers can provide graphs of this information, although I have found it to be rare.

Perform research regarding what is called mid-drives or crank-drive motor assist and you will find that you'll get the best result by using the motor to drive the pedals (with or without a freewheel) and use the bicycle gearing to keep the motor rpm in the desired range.

Hub motors are notoriously inefficient in that they must operate from zero rpm to maximum. This inefficiency is compensated by having large powerful batteries (or reduced range). Mid-drive systems are known for improved performance if desired as well as improved efficiency.

My e-assist bicycle used a mid-drive configuration as well as nearly perfect matching of rpm and operator preferred cadence. I had electrical consumption figures of one-fourth to one-fifth that of hub motor users.

Some trade-off is made due to the additional mechanical complexity, slightly increased noise and weight of having a mid-drive, but the increase in efficiency and range more than made up for it.

I would provide links to references for the above statements, but for the fact that it is primarily direct experience.