Bicycle Gears Basics
Bicycles have two sets of gears driven by a chain drive. The gears in the front are attached to the pedal axle, and the gears in the back are connected to the rear wheel. Most bikes have several gears of different sizes in both the front and back, and a derailleur, which can move the chain from one gear to another. When a cyclist pedals, the front gear pulls the chain, which in turn pulls the corresponding rear gear, turning the wheel.
Ratios
Every gear has a certain number of teeth proportional to its size. The ratio of the number of teeth on the front gear the cyclist uses to the number of teeth in the rear determines how fast the cyclist needs to pedal. If the front gear and the back gear both have 20 teeth, for example, the ratio is 1 to 1. The rear wheel will turn one time for every time the cyclist turns the pedals. If the front gear has 30 teeth and the rear has 10 teeth, the ratio is 3 to 1. The wheel turns three times for every turn of the pedal.
Effective Gearing
Low gears make it easy to pedal the bike, but hard to go fast. Higher gears allow you to go much faster, but require a lot of leg strength. Many bikers will shift down when climbing up a hill, then shift to a higher gear on a downhill or straightaway. Each biker has an optimum cadence at which his legs produce power most efficiently. Bicycle racers try to find this speed and adjust their gears so they are always moving their legs at the same rate.
(adapted from http://www.ehow.com/how-does_4701553_bicycles-gears-work.html )
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