Bicycle Gears, Cogs and Gear Inches

What are gear inches and why do we care?

Ordinary bicycle

Gear inches give you a way to calculate and compare gear ratios. The larger the gear inch number, the farther you will go with each rotation of the pedals with greater effort. Gear Inches are based on the old high-wheel bicycles. Imagine you are perched on a saddle over a 50 inch wheel. The pedal cranks are connected directly to the wheel. Each rotation of the crank is one rotation of the wheel. This means with a "gear" of 1 to 1 ratio (direct drive) the high-wheeler will have 1 x 50 or 50 gear inches. Pedaling one full rotation of the crank moves you forward fifty inches.

Now imagine pedaling on your modern bicycle. A standard 39 tooth inside chainring and a 21 tooth cog at the rear gives you 50 gear inches. That is 39/21 x 27 = 50. You will go the same distance with one complete rotation of the crank as the old penny-farthing bicyle. The nominal diameter used is 27 inches.

Gear inches give you a way to compare the distance you travel with one revolution of the crank. Smaller gear inches mean more gear reduction. You can pedal more easily, and you travel less distance with one revolution of the crank set. In contrast, larger gear inches mean less reduction and greater travel for one rotation of the crank.

Rear Cassette

Now to the modern bicycle. While road bikes today typically use 700c wheels, the charts using gear inches usually show a diameter of 27 inches. For the purpose of comparing gears it does not matter. First let's look at the gear inches.

Front chain rings often have 52 teeth. Mate this with the smallest cog in the rear cassette, e.g. 13 teeth. We calculate the gear inches by dividing the chain ring (52) by the cog (12) multiplied by the tire diameter in inches (27). This is 52/13 x 27 = 108 gear inches. Compare this to the small chain ring (39) and a rear cog of 17. This is 39/17 x 27 = 62 gear inches.

You can use a chart to find the gear inches for you bicycles gear combinations. Many people find that a selection around 70 gear inches works well for riding on level smooth roads. If you are a traveling cyclist, the rations become more important. Riding up a mountain pass or along a hilly road riding with your panniers fully loaded is a different proposition. You need enough low ratios to climb, middle ratios to ride on the level and higher ratios, if you pedal down hill.

Now that you understand the formula you can calculate the gear inches for each combination of chain rings and cogs. You can easily discover if you have any overlap in your gearing and what shifting order is required, if you were to work your way through the gears.

If you do not have a cyclometer, you can estimate you speed using gear inches and crank revolutions per minute. How fast are you going? You could work out the math multiplying your gear inches times you cadence(revolutions per minute)then converting to hours and feet, arriving at miles per hour. For our example with the 52 chain ring and 13 cog the speed at cadence of 100rpm is just over 32mph. Here is a neat trick. If you spin at 100 using the 52/13, just multiply 4 x 8 = 32mph! This will work for any gear ratio. What if you don't spin at 100rpm? Work out the ratio. At a cadence of 80rpm your multiplier becomes .8 x 8 = 6.4.

Now that you understand what is behind the gear ratios, there is an even easier way to get the information. Use Sheldon Brown's Bicycle Gear Calculator Gear Calculator . Sheldon Brown passed away a few years back, still, his technical articles are a great source of information for bicycle repair.

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