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For exercycles with the tire in direct contact with an alternator, one could build up the shaft of the alternator by epoxying or bolting (with the nut that held the pulley) a pipe to the shaft to make it bigger until the optimum diameter is reached. What you are doing is balancing power output capability of the individual to maximize charging rate and charging time, while minimizing wear on the tire. My best educated guess at a possible end point optimum pulley size for this approach is a diameter between 1" and 1.5". The above approach should work well with alternators that have internal voltage regulation.

If an older type alternator is used with a external voltage regulator, fine tuning would then be done with a resistor in series with the field circuit and the battery. The lower the resistance the stronger the field will be and the harder to turn the alternator and the more current it will produce at low speeds. Note that once the alternator is not turning the battery will drain back through the field coil unless disconnected. You can get around this by putting a diode between the battery and output of the alternator. This diode would allow flow from the alternator to the battery, but not back from the battery through the field coil. The output of the alternator is also connected through a variable resistor to the field coil. Note, the field coil is in reality the rotating armature.

Now if one uses a 10 speed 26" tire bike what can be expected: Assume we are going to use a belt to drive it and the rear tire will be removed. Rim diameter is about 23.5". Assuming a multi-ribbed pulley (5,6,8 ribs) diameter of about 2.2" is used on the alternator. Assume the bike is running in 3.75:1 gear ratio (in high gear). Assume we will be pedaling at 60 RPM. Then, the rotational speed of the generator will be about
(23.5"/2.2")*3.75*60RPM = 2,403 RPM
If the pulley is 2.8", then the rotational speed of the generator will be about
(23.5"/2.8")*3.75*60RPM = 1,888 RPM

Smaller pulley sizes are desirable. This arrangement should work fairly well, especially since you have the other gears of the bike to adjust the speed for the strength of the peddler. This arrangement should work well with internal and external voltage regulated alternators.

Now what if all you have is a 20" kids bicycle: Using the belt over the rim, the rotational speed of the generator will be about
(16"/2.2")*2.5*60RPM = 1,091 RPM
Putting the tire in contact with a 2.2" diameter pulley would give about
(20"/2.2")*2.5*60RPM = 1,363 RPM
Taking off the pulley and using a 5/8" bare shaft against a 20" tire then
(20"/.625")*2.5*60RPM = 4,800 RPM
Highly likely to ware out the tire quickly. None of the above options are optimum but any may work in a pinch. Especially if the peddler is the size of the bike.

Summary: If you plan to use the pulley, get it as small as you can. A small change in pulley size can make a significant difference in final speed of the alternator. An old 10 speed 26" bicycle and a small diameter multi-ribbed V-belt over the back wheel rim, looks like the best approach. Next most workable solution, the exercise cycle with a small pulley put in direct contact with the hard rubber tire.

Offered by Mike.