Why are the wheels on a penny farthing different sizes?

Answer 1

Before the introduction of bicycle chain pedals were mounted directly on to the wheel axle. Without any gears the only way to get the bike to go faster w/o pedalling like crazy was by making the front wheel(with the pedals) bigger, as one revolution of a bigger wheel will cover more ground than one revolution of a smaller wheel.

Answer 2

Penny farthings didn't have any gears, it was direct drive with the pedals mounted solidly to the front wheel. So the way to get some speed into them, when the drive wheel is locked to the same RPM as the pedals, was to make the drive wheel bigger. The rear wheel OTOH is just there to make it handle as a bicycle as opposed to an unicycle.
Before the introduction of bicycle chain pedals were mounted directly on to the wheel axle. Without any gears the only way to get the bike to go faster w/o pedalling like crazy was by making the front wheel(with the pedals) bigger, as one revolution of a bigger wheel will cover more ground than one revolution of a smaller wheel.

Answer 3

The PF had the pedals mounted directly to the drive wheel, so the drive wheel could only turn as fast as the pedals turned.

Now, to get some speed out of that at the rates of turning that's within comfortable reach for a human the only way was to make the drive wheel really big. (if a small wheel and a big wheel turn at the same rate the speed at the circumference will be greater for the bigger wheel despite the RPMS are the same)

Answer 4

In the early days, bicycles were direct drive, the drive wheel only spun as fast as the pedals did. To get any speed out of a direct drive bicycle, you have to make the drive wheel as big as possible.

Later, the invention of the chain drive allowed for an introduction of a gear ratio between the pedals and the drive wheel. This made it possible to get the bike to speed even with fairly small wheels.