Spoke Scopes

See the world from two wheels

The Mathematics of Gears — February 26, 2015

The Mathematics of Gears


Pedal Power

From the League of American Bicyclists’¬†Guide to Safe and Enjoyable Cycling, pg. 49

“How Gears Really Work: Ratios”

“Gearing uses basic math ratios. For bicycle gears, the ratio is the number of teeth in the front divided by the number of teeth in the rear cog that is engaged. The ratio would be front teeth: rear teeth.

A larger ratio indicates the pedal requires more force to turn. So a ratio of 40:8 (or 5:1) is harder to turn than 30:15 (2:1). So, in general, the “high gear” combination of the larger ring in the front and the smaller ring in the back makes it hard to pedal. The “low gear” combination of the smaller ring in the front and the larger ring in the back makes it easier to pedal.

“There may be duplicate gears. If your front chainwheel has three rings and your rear cassette has eight rings, you have 24 gears (3×8=24). Yet, you will notice that some gears feel similiar even in different combinations of front and rear. It is possible to have tooth combinations of 48:24 and 36:18, yet both create the same 2:1 ratios for pedaling resistance.”

The next time someone asks, “Is that a 10 speed?” Just think 2 cassettes on the front, five cassettes on the back.

Shifting these gears takes some calculation, too. My bike has stem shifters, intuitive levers once you practice. The left shifts the front derailleur, the right shifts the back derailleuer. Shifting up moves the chain up to create more resistance. Shifting down decreases resistance.

Looking Shifty