Gearing Part 1: The Basics

GearsThis is the first of several posts on gearing for road bikes.  It’s aimed at riders who are seeking a basic understanding of bicycle gearing.  All of the numbers used in this post are either approximate or chosen to make the arithmetic (which is simple) easy to follow.

There are several ways to talk about gearing, some useful, some not so much.  I once had a cycling computer that gave gearing information by assigning numbers (1, 2, 3, 4, etc.) to each of the rings and each of the sprockets on the cassette.  It would tell me I was in the 3-8 gear or the 2-2 gear, for example.  This is not a good way to think about gearing.  Rings and cassettes come in many different sizes and configurations and the 5 sprocket on one cassette may be different from the 5 sprocket on another.

Experienced riders often talk about gearing in terms of the number of teeth on the ring and on the sprocket on the rear cassette (the gear-tooth method).  They’ll talk about a 52-13 gear (a big gear) or a 42-26 gear (a smaller gear), for example.  The gear-tooth method communicates clearly to riders who are used to thinking about gearing in this way when they ride.  They know exactly what a 52-13 gear is because they have been aware of being in a gear that size while they were riding.

A third way to talk about gearing is in terms of gear-inches.  We’ll come back to this one later.

In order to make the basics of how gears work as easy to understand as possible, I think it’s most helpful to talk about gearing in terms of what is called meters of development.  This is a system that is more commonly used in Europe than in the US.  It defines gears in terms of how far the bike travels every time the pedals complete one revolution.  Someone will say they are in a 4.2 meter gear which means the bike moves forward 4.2 meters (about 13.67 feet) every time the pedals go around once.  This way of talking makes it very clear what is happening as you change gears and makes it easy to talk about gearing for riders who are not used to thinking in terms of gear-tooth pairs.

Take a look at your rear wheel.  The circumference of the rear wheel (including the tire) on an average road bike is roughly 82 inches (6 feet, 10 inches) or about 2.1 meters (rounded to 1 decimal place).  How close it is to 2.1 meters on your bike depends on things like the tire you’re using and how inflated it is.  We’ll use 2.1 meters as a rough guess to make the arithmetic clear.  A 2.1 meter circumference means that you move 2.1 meters (82 inches) forward every time your wheel completes one revolution.

casetteNow take a look at your rear cassette.  It’s fixed to the rear wheel so that every time the wheel goes around once, the cassette goes around once.  But here’s where it gets interesting.  There are different numbers of teeth on each of the sprockets on the rear cassette.  Suppose one of the smaller sprockets has 13 teeth.  If the chain was on that sprocket, it would move through 13 teeth every time the wheel went around once.  A medium to large sprocket might have 26 teeth.  If the chain was on that sprocket, it would move through 26 teeth every time the wheel went around once.

RingsNow take a look at the chainrings attached to your pedals and crank.  Each ring is fixed to the crank so that each time the pedals go around once, the ring goes around once.  A common configuration for a triple-chainring setup has rings that have 52 teeth (the big ring), 42 teeth (the middle ring) and 32 teeth (the small ring).  If you are in the big ring, the chain will move through 52 teeth every time you pedal through one complete revolution.

Combining all of this info about the circumference of the rear wheel and the number of teeth on the rings and sprockets we can see how bicycle gears work.  As you pedal, every time the chain moves through one tooth on the front ring it also moves through one tooth on the sprocket on the rear cassette.  Suppose you are in the big ring that has 52 teeth and your chain is on the sprocket with 26 teeth on the rear cassette.  One pedal revolution moves the chain through 52 teeth on the big ring.  It also moves the chain through 52 teeth on the cassette.  The big ring goes around once but the rear sprocket only has 26 teeth so it has to go around twice (26 X 2 = 52) to take up all 52 teeth.  When the sprocket goes around twice, the rear wheel also goes around twice.  The rear wheel has a circumference of 2.1 meters, it goes around twice, so the bike moves forward 4.2 meters (2.1 X 2 = 4.2).  In this example, a 52-26 gear (speaking in gear-tooth terms; 52 teeth on the ring and 26 teeth on the sprocket) is the same as a 4.2 meter gear (speaking in meters of development terms).

drive trainNow suppose that you stay in the 52 tooth big ring but instead of having the chain in the 26 tooth sprocket on the rear wheel, you change it to the 13 tooth sprocket.  One pedal revolution still goes through 52 teeth on the big ring but now it takes 4 revolutions of the rear sprocket to take up all 52 teeth (13 X 4 = 52).  The rear wheel goes around 4 times instead of two and the bike moves forward 8.4 meters (2.1 X 4 = 8.4) instead of 4.2 meters.  You’re in an 8.4 meter gear.

One way to look at this is that you go twice as far for each pedal revolution in an 8.4 meter gear as in a 4.2 meter gear.  The meters of development way of talking about gearing makes this easy to see because 8.4 is twice as much as 4.2.  Of course, you have to work harder to move the combined weight of you and your bike twice as far but that’s another story.

Notice that what changes when you shift into a harder or an easier gear is the relationship between the number of teeth on the ring and the number of teeth on the sprocket.  Suppose you stay in the big ring and shift up or down on the rear cassette.  The diameter of the rear wheel doesn’t change and neither does the number of teeth on the big ring.  What changes is the number of teeth on the sprocket.

gear ratio chart

Drive ratios (R/S) for a selection of rings (number of teeth listed in the left column) and sprockets (number of teeth listed in the top row)

It’s useful to think about this relationship as a ratio of the number of teeth in the ring to the number of teeth in the sprocket.  This is called the drive ratio.  Let R stand for the number of teeth in the ring and S stand for the number of teeth in the sprocket.  Then the drive ratio can be shown as R/S.    In the case of the 52 tooth ring paired with the 26 tooth sprocket the drive ratio R/S is 52/26 = 2.  The rear wheel goes around twice every time the pedals go around once.  For the 52 tooth ring paired with the 13 tooth sprocket the drive ratio R/S is 52/13 = 4; the rear wheel goes around four times every time the pedals go around once.   In other words, the drive ratio R/S (the number of teeth in the ring to the number of teeth in the sprocket) tells you how many times the rear wheel goes around every time the pedals go around once.

Let C stand for the circumference in meters of the rear wheel.  Remember that gears in the meters of development system are defined in terms of how for the bike goes (in meters) every time the pedals complete one revolution.  This is easily expressed mathematically as Gear = C X R/S.  In English, the gear is equal to the circumference of the rear wheel (C) multiplied by the number of times the rear wheel goes around every time the pedals go around once (R/S).

gear inch imageThe gear-inch method of talking about bike gears that was mentioned earlier is similar to the meters of development method.  They both rely on the very useful drive ratio of the number of teeth in the ring to the number of teeth in the sprocket, R/S.  Rather than use the circumference of the rear wheel measured in meters, the gear-inch method uses the diameter of the rear wheel measured in inches.  Let D represent this diameter.  In the gear-inch method Gear = D X R/S.  Gear inches are more commonly used in the US than meters of development.  As you can see, they are calculated in very similar ways and in both systems bigger numbers equal bigger gears which require more effort.  Meters of development has the advantage of telling you exactly how far you move forward every time you turn the pedals through one revolution.

Here is a table showing how the two gears we used as examples (the 52 tooth ring + 26 tooth sprocket and the 52 tooth ring + 13 tooth sprocket) would be labeled in the gear-tooth, gear-inch and meters of development methods.  The gear-inch method was calculated assuming a 27 inch diameter rear wheel.

Method Gear 1 Gear 2
Gear tooth 52 – 26 52 – 13
Gear inch 54 inch 108 inch
Meters of development 4.2 meter 8.4 meter

5 thoughts on “Gearing Part 1: The Basics

  1. Pingback: Gearing Part 2: Chainrings, Gear Ratios and the Steps from One Gear to the Next | Tuned In To Cycling

  2. Pingback: Chainring Shifting Techniques | Tuned In To Cycling

  3. I really needed to understand the gearing system. Since I’m 6’6″ and have very long, very strong legs, and can only rotate my legs so fast, I needed a way that I could ride my 10 -speed Fuji much faster, especially while riding with the wind at my back. So I’m changing the smallest sprocket gear from 14 to 11. I’m confident that it will make a huge difference, with training. As there is often a strong wind on Island Beach, usually from the south, I estimate that I’ll be able to increase my average wind aided speed from the low 20s to the upper 20s. After all, from 14 to 11 is a huge jump and I have the leverage and leg strength to take advantage of it.

    • There is a running debate about high vs low cadence cycling. Low cadence cycling generally favors those individuals with muscles and power. But generally most pro cyclists favor a high cadence of 90 rpms or so.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s