For a stationary bicycle, there is a maximum force that the cyclist can apply to the pedals. This will be the cyclists weight at zero pedal velocity, unless the bike is of recumbent design and the seat can be used to push against. As the pedal speed increases, more work is done in moving the legs and the force that can be applied to the pedals decreases. The limit is reached when the legs can only just keep up with the pedals, but the cyclist is unable to apply any force to them. Since the power output to the bike is the product of pedal velocity and pedal force, the power output curve is peaked over some optimal velocity range as shown. Matching this rider power output curve to the needs of the bicycle in covering different terrain requires a gear system.

From: Abbott & Wilson, "Human-Powered Vehicles,"
Human Kinetics (1995)