Bicycle Girl

Since cyclists' legs are most efficient over a narrow range of pedaling speeds (cadence), a variable gear ratio helps a cyclist to maintain an optimum pedalling speed while covering varied terrain. As a first approximation, utility bicycles often use a hub gear with a small number (3 to 8) of widely spaced gears, road bicycles and racing bicycles use derailleur gears with a moderate number (10 to 22) of closely spaced gear ratios, while mountain bicycles, hybrid bicycles, and touring bicycles use dérailleur gears with a larger number (15 to 33) of moderately spaced gear ratios, often including an extremely low gear ("granny gear") for climbing steep hills.
Different gears and ranges of gears are appropriate for different people and styles of cycling. Multi-speed bicycles allow gear selection to suit the circumstances: a cyclist could use a high gear when cycling downhill, a medium gear when cycling on a flat road, and a low gear when cycling uphill. In a lower gear every turn of the pedals leads to fewer rotations of the rear wheel. This allows the energy required to move the same distance to be distributed over more pedal turns, reducing fatigue when riding uphill, with a heavy load, or against strong winds. A higher gear allows a cyclist to make fewer pedal turns to maintain a given speed, but with more effort per turn of the pedals.
With a chain drive transmission, a chainring attached to a crank drives the chain, which in turn rotates the rear wheel via the rear sprocket(s) (cassette or freewheel). There are four gearing options: two-speed hub gear integrated with chain ring, up to 3 chain rings, up to 11 sprockets, hub gear built in to rear wheel (3-speed to 14-speed). The most common options are either a rear hub or multiple chain rings combined with multiple sprockets (other combinations of options are possible but less common).
With a shaft drive transmission, a gear set at the bottom bracket turns the shaft, which then turns the rear wheel via a gear set connected to the wheel's hub. There is some small loss of efficiency due to the two gear sets needed. The only gearing option with a shaft drive is to use a hub gear.