The voltage will depend on the flux and amount of coils if you want to look at it from a mathematical perspective. If you want to look at it on the quantitative side, in an ideal situation, a 24V motor can produce 24V while being turned at the RPM it would normally spin at when attached to a 24V power source. This is for DC motors of course, you could also look into Stepper motors.
It would be a bit more complicated than your simplification. You would need to maintain over 13.8V to charge a lead acid battery. 12V would essential be its peak voltage. If it were up to me I'd use a 24V motor with a 12V lead acid battery, and would gear the motor to ouput ~14.5-15V.
alternatively, the generator is also connected to a series of LED and 7-segment to show the amount of voltage produce by the user. it is programmed by virtual instrument, some sort of interactive games to show students who is able to produce more voltage
If you think the generator might produce 8A, then the charge controller should be this much, plus a safety margin. 8A would charge a 28AH battery in around 3 hours.
24V, 8A is about 1/3 horsepower. Your charge controller would need to be designed to manage the burden (demanding less power). Some athletes can generate that much power, but you can ask them not to.
If your "bicycle" rider is achieving a virtual 10mph, that's around 50 to 100 rpm. A "1800rpm" generator would need to have some gearing (some of this can be done in electronics). Beware of losses in gears and chains.
Does anyone have a schemetic of a charge controller which does not use PV but a voltage regulator ... i m not really sure how it goes, but definelty not using charge contoller with a solar source