Bicycle Generator mathematics? Confused with project

[Rana13]

Homework Statement

Hello everyone. I am doing a project where I have built a bicycle generator. We have everything set up and the alternator is putting out approx 45 amps and we also have a 12V car battery.

My issue is that we need to write a short paper on the mathematics behind this device.
Data I have:
Crank arm=170mm
Radius of sprocket= need to be measured, but its a 46 tooth track chainring
Alternator=1999 Honda Civic used, is putting out about 45 amps
Battery=12V car battery used

Homework Equations

torque=r*F*sin(theta)
force=m*a

The Attempt at a Solution

All I need is relevant equations that are involved in such a project.
My initial thought was to say, well if I ride an average of 5 mph for 10 minutes, I can sort out from there how much power out I generate.

Does the above sound like it's possible? Is there a connect from the bicycle to the power out of the alternator? Do i need to know how many rotations of the alternator wheel generates how much current, etc?

Very confused, would love some help. It doesn't need to be overly complicated, just a page or two worth of equations and information explaining we understand using math how this works.

 

[lippyka]

The equations you provided should be enough to get started. The torque equation will be useful in understanding the rotational force generated by the crank arm. This can then be related to the speed of the bicycle, as well as the radius of the sprocket. The force equation can be used to calculate the acceleration of the bicycle, which can then be related to the power output of the alternator. Finally, you must consider the efficiency of the alternator and the battery. This will dictate how much power is available from the system.