A chain drive without gears, is effective on flat surfaces and going downhill. But, when it comes to headwinds, hill climbing, and even starting on a bicycle without gears the cyclist has to strain while pedaling at a very low rate. Gears allow the cyclist to pedal at a comfortable and efficient rate while traveling either uphill or downhill or with a headwind or a tailwind.
On old high-wheelers, where the pedals were attached directly to the wheel. One turn of the pedals equaled one turn of the wheel. A selection of gears allows the cyclist to change that. For steep hills, we choose a gear that lets us turn the pedals many times to turn the wheel once. For flats or downhills, we choose a gear that turns the wheel many times for each turn of the pedals.
Your bike comes with several gear choices, or "gear inches." To create a gear chart, you need to count the number of teeth on each freewheel cog and each chainwheel. Record this information in a chart such as the one above.
The next step is to calculate gear inches for each gear set (freewheel cog and chainwheel). The formula for gear inches is to the right.
After this one can make a graph such as the one to the right, which shows how ones gears intermesh. To determine how far one travels per pedal revelution, multiply gear inches by pi or 3.14.