There is no god add there is no free lunch. As was pointed out you can
generate a little power but it is very difficult to sustain. An
automotive generator runs best around 4500 RPM. I Figure the surface
speed of a 4 inch pulley at 4500 RPM and figure what a maintainable
cadence is on the bike. Use that to work out the gear ratio and how big
a wheel is needed to get that surface speed.
Start with an alternator for a GM car from the 60s to 90s. These are
one wire units and have V-belt pulleys. You may be able to use the
wheel wothout a tire mounted to get the surface speed but you will have
to use lower gears.
Just some back of the envelope calculations when I am a bit tired from
spending the afternoon climbing under the dash of my daughters car
fixing the brake lights and turn signals.
A 4" pulley has a circumference of about 12.56 inches. At 4500 RPM that
works out at about 4710 Feet per minute or about 53 Miles per hour. I
know that alternators produce current at much lower speeds but that is
just an example. How long can you pedal at 50 mph?
Now take another tack. A common GM one wire alternator size is 60 Amps,
they are available up to 120 Amps. Newer Nippon Denso alternators like
the one on my pickup are good for 170 Amps but I have a 60 GM somewhere
around here. 60 Amps at 13.8 Volts is a bit over one hp ignoring
inefficiencies. I do not have the figures handy but a male in average
shape is only good for a sustained .2 hp or about 150 Watts. At 13.8
Volts that is something like 11 Amps. I have a bunch of those small
gell cell 12V 7 Ah batteries used in UPS. It would sustained pedaling
about an hour to charge one of those batteries. A 7 Ah battery is
speced to output .35 amps per hour over a 20 hour discharge.
But don't let reality get in the way of a fun project.