You have probably seen a picture of the funny-looking "penny-farthing" or "high-wheeler" bicycles -- the ones with a huge front wheel and a tiny rear wheel. You might even have seen someone riding one in a parade or in a movie. These bicycles became popular starting in 1870, but by the turn of the century were replaced by the "safety bicycle." A bicycle from 1900 or 1910 looks almost exactly like any bicycle you see today. Today's bicycles have two wheels of the same reasonable size, a pair of pedals in the middle of the bike and then a chain that connects the pedals to the rear wheel.
So why did penny-farthing bicycles ever exist? In a penny-farthing bicycle, the pedals and the front wheel are directly connected just like they are on a kid's tricycle. That means that when you turn the pedals one time, the wheel goes around one time. That's an inexpensive way to build a bicycle, but it has a problem. Think about a kid's tricycle. The front wheel might be 16 inches (40 cm) in diameter, or 16 * 3.14 = 50 inches (127 cm) in circumference. That means that each time a kid on a tricycle pedals through one revolution of the front wheel, the tricycle moves forward 50 inches (127 cm). Let's say that the kid is turning the front wheel at 60 rpm, or one revolution per second. That means that the tricycle is moving forward 50 inches per second. That is only 2.8 miles per hour (4.5 kph). If the kid pedals twice as fast, at 120 rpm, the trike is moving at just over 5 miles per hour (9 kph), and the kid looks like his legs are about to spin off because 120 rpm is a lot of pedaling!
If an adult wants to ride a tricycle at a reasonable speed, maybe 15 mph (24 kph), and if the adult does not want his or her legs to fly off, then the tricycle's front wheel has to be pretty big. If the adult wants to pedal at 60 rpm, the front wheel needs to be 84 inches in diameter -- that's 7 feet (more than 2 meters) in diameter!
The first thing that causes bicycles to have gears is the fact that gears can reduce the wheel size from 7 feet in diameter to something reasonable. As described in the article How Gears Work, gears and gear ratios are a good solution to this problem. For example, if you put a gear with 42 teeth on the front chain wheel and a smaller gear with 14 teeth on the rear wheel, you have a 3-to-1 gear ratio. Now the back wheel can be 84 inches / 3 = 28 inches (71 cm) in diameter -- about the size of a normal bicycle wheel. This is a much safer approach.
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