Note from author: I've been working on this idea of a presentation/workshop/blog post on gearing for some time. I have attempted to minimize the "geekiness" and math as much as possible. Feel free to send us comments on whether you found this useful or confusing. Steve Andruski, RBH President
Some History
The “ordinary” or “penny-farthing” bicycle had pedals connected directly to the wheel. There was no freewheeling – when the pedals move, the wheel moves. The speed, or distance travelled for each pedal rotation was determined by wheel size – the bigger the wheel, the faster you could go.
Darren Wilkinson from Chester-le-Street, England, CC BY-SA 2.0 <https://creativecommons.org/licenses/by-sa/2.0>, via Wikimedia Commons
Then came the “safety bicycle”. Both wheels were the same size, with the rider seated between them. The pedals and rear wheel were connected by a chainring, cog and chain.
Jonathan Cardy, CC BY-SA 3.0 <https://creativecommons.org/licenses/by-sa/3.0>, via Wikimedia Commons
The number of teeth on the chainring and cogs determines the number of wheel revolutions per pedal revolution.
How does this work?
Here’s an example:
A 52-tooth chainring will move 52 chain links per pedal revolution. If the chain is on a 26-tooth cog in the back, that cog, and therefore the wheel, would need to turn two revolutions for each one revolution of the chainring and pedal. This is called the gear ratio. Expressing this as an equation you get:
52/26 = 2 ⇒ the gear ratio
This works for any number of teeth on the chainrings or cogs. We chose the 52/26 example to make the math simple. The gear ratio, then is just a way of expressing how many wheel revolutions you get per pedal revolution for any combination of chainrings and cogs.
Shifting Your Gears
When riding your bike and shifting, you may have noticed that shifting to a larger chainring requires you to shift “down” in the rear to a larger cog to get to a gear that feels about the same or a little harder than the one you were just in. On most bikes, the ranges of gears you have for each chainring will overlap. There may even be gears that feel identical, or nearly identical on different chainrings. Let’s explore the ways can you figure out how your gears are related to each other and find out if there is duplication.
Comparing Gears
Remember this guy?
Darren Wilkinson from Chester-le-Street, England, CC BY-SA 2.0 <https://creativecommons.org/licenses/by-sa/2.0>, via Wikimedia Commons
On this type of bike, your speed was determined by the size of your wheel. It was common to use that as a way to compare bikes and potential rider speed. “What size wheel do you ride?” was a common question. When the safety bicycle came on the scene, people had this “feeling” for what size wheel gave a certain speed and effort. The old “ordinary” had a gear ratio of 1:1; or one pedal revolution to one wheel revolution. By taking the gear ratio of a safety bicycle (which is just the number of wheel revolutions per pedal revolution) and multiplying it by the wheel diameter on their safety bike, they would get the equivalent wheel diameter that an ordinary would need to give the same “gear”. This was called “gear inches”. This is still a commonly used way to compare gears. A less commonly used term is “development” which is the distance travelled in meters per pedal revolution and is more commonly used in Europe.
•Gear Ratio = (# Teeth on Chainring)/(# Teeth on Rear Cog)
•Gear Inches = (# Teeth on Chainring)/(# Teeth on Rear Cog) × Your Wheel Diameter
•Development = Gear Ratio × Wheel Circumference (in meters)
Because the wheel size is included in the calculation, using Gear Inches or Development allows us compare different gears on one bike AND between bikes with different wheel sizes (e.g., road bike vs. mountain bike or road bike vs. folding bike).
Enough Math – What Does it Mean?
All else being equal, the bigger the gear inch number, the harder/higher the gear & the higher your speed. To find out what gears your bike has and how they are related to each other find the number of teeth on each chainring and each rear cog. You can physically count them, but sometimes the number of teeth is printed on the chainring or cog, making this job easier and less messy. Then go to an online gear calculator like these:
· https://mike-sherman.github.io/shift/
· https://ritzelrechner.de/
Print the results or write the numbers down. We’ll use a gear chart template to show some examples and discuss the meaning. But first…
Why Do This? - Some Perspective
Back in “the old days” when bikes had 2x5 drivetrains (two chainrings and 5 cogs on a freewheel) you had to make a choice. You could either have a narrower range of gears and get small steps between gears, or you could get a wide range of gears, but you would have to put up with large jumps between gears. Choosing cogs and chainrings was more important. You wanted to minimize duplication of gears and have a convenient shift pattern to change to the next harder or easier gear. One of the first bicycling books I purchased in the late 1970’s dedicated 17 pages to a discussion on gearing. Here’s a chart for a typical 10-speed bike. Using a graph like this makes it easier to visualize the relationship between the different gears.
As a result, most bike shops had freewheel cog boards like this. It was not uncommon for riders to build up their own freewheels with specific cogs.
While modern drivetrains are less limited than in the past, understanding your gears can still help you ride more efficiently. Let’s go to some examples.
Some Example Gear Charts
A note on why some gear inch numbers are colored grey in the charts:
Road Bike (2×7-speed)
The “large/large” and “small/small” combinations should be avoided, and therefore are grey in the charts. The large chain angle causes more wear on the chain and the cogs and chainring. Also, the large/large combination will put the rear derailleur into a very stretched out position, stressing the springs. Also, if the proper length of chain was not used, shifting into that position could damage the rear derailleur. Of course if RBH teaches you how to install a new chain, we will show you how to get the correct length.
Road Bike (2×10-speed)
A Graphic Comparison
Road Bike (2×7-speed)
Road Bike (2×10-speed)
Other Examples
Mountain Bike (3×9-speed)
Touring Bike (3×7-speed)
Your Next Steps
Once you’ve got your gear chart –
• Figure out what gear(s) you ride in most often.
• See where they fall in your range of gears on your gear chart.
• Decide if you need to modify your drivetrain.
• Use the range of gears you currently have more effectively.
• Ride farther, faster, or more efficiently – and have more fun!
Using your gears
Let's go back to the 2x7 speed road bike example and see how to think about where to shift:
As you can see from the chart, the 39/17 gear (60.2 gear inches) is nearly identical to the 53/23 gear (60.4 gear inches). Also the 39/14 and 53/19 gears are nearly the same. In addition, you can tell that the useable 39/19 gear covers your 53/26 gear which is unfavored because of cross-chaining. This duplication seems wasteful. Your 14 speeds not only drop to 12 to avoid cross-chaining, but duplication means that you only have 10 unique gears. How is this useful? Well, let's say you're rolling along comfortably in the 39/19 gear on flat ground. You come to an area that starts a bit downhill, so you what to go into a "higher" gear. You could just shift to the 39/17 using the rear derailleur, or you could shift to the 53/23 requiring both a rear derailleur shift and a front derailleur shift. Looking ahead, if you see that the road is going to level out again, or even start to go a bit uphill, you can stay in the small chainring and just shift up on the rear one or even two gears. Then when you need to shift back down into easier gears, a simple shift of the rear derailleur is again all that is needed. Alternatively, if you see that you've got a downhill stretch that will continue or even get steeper and you want to maintain or build speed, making the "double shift" into the 53/23 might make sense.
Why change? - Example of a Modification
Since the early ‘90’s, a traditional 2-speed crankset on a road bike would have 53-tooth and 39-tooth chainrings. Most people who wanted lower gears to make hills easier to climb would need to go to a triple chainring setup. This adds weight and makes setting up the shifting on the front derailleur a bit more complicated, but it was the best option for a long time. Then, along came semi-compact and compact cranksets. These had chainring combinations of 52/36 or 50/34 for semi-compact and compact cranksets, respectively. Wider range cassettes in the back were also becoming available. With more cogs in the back becoming available on 9, 10, and 11-speed cassettes, larger cogs for lower gears could be added while keeping the jumps between gears smaller. The 34-tooth chainring in front, combined with wider range cassettes in the back meant that a 2-speed compact crankset could give you the range of a triple crankset (especially on the low end), without the complications and with less weight.
Road 2×10 – standard versus compact cranksets
Standard crankset (53/39):
Semi-compact Crankset (52/36):
Compact Crankset (50/34):
So, converting a standard road crankset to a compact crankset could increase the type of terrain you could access on your road bike. Keep in mind though that the crankset is just one part of the equation in this kind of conversion. You might need a different rear derailleur to accommodate the wider gear range. In this article, we’re just covering the impact on gearing.
Another possible conversion would be to take a bike with a triple crankset and replace the crankset with a 2-speed compact crankset. This would simplify the shifting in the front and save some weight. This conversion, however, would involve a new front shifter.
A Possible Simplification for Some
With the introduction of wide-range rear cassettes and derailleurs built to handle larger and larger cogs, some people consider a gearing system with only one front chainring. This make sense for some uses. For example, cyclocross bikes typically use a relatively narrow gear range compared to a road bike. In cyclocross races, you can usually dismount the bike, put it on your shoulder and run up a hill faster. In fact most cyclocross courses have uphill sections designed to force riders to dismount. On the other side of the gear range, since cyclocross races are off road, riders do not find big gears to be very useful. Again, the courses tend to have technical downhill sections where bike handling rather than speed are key. So using a "1x" system on a cyclocross bike would make sense. On road bikes, there would be a trade-off on either the high end or low end of the gear range, making it less beneficial. Again, as technology improves, the disadvantages start to get smaller, and in fact, you will see 1x drivetrains on many gravel bikes and some mountain bikes where really high gears are less needed.
A downside for converting a current 2x drivetrain to 1x is the need for a narrow/wide chainring and a rear derailleur with a clutch. These are needed because there would be no front derailleur to keep the chain from coming off the chainring, especially over bumpy terrain where a regular rear derailleur moves and causes the chain to loose tension momentarily. A clutch on the derailleur keeps it from moving as much and the narrow/wide teeth on the chainring provide a bit of "grip" on the chain. Also, since your new single chainring would probably be larger than your current small chainring, a new cassette with a wider range may also be needed.
Internal Geared Hubs
Another type of gearing you might see on older utility or commuting bikes is the internal geared hub. While there were a few earlier attempts at multi-gear hubs, the first to work well enough to gain popularity was the Sturmey-Archer 3-speed hub. Conceived by Alfred Pellant and Henry Sturmey, it was perfected by James Archer, a machinist in the Raleigh factory. Raleigh’s investment in perfecting this hub was well spent. Many Sturmey-Archer hubs are still in service even after decades of use. The standard 3-speed internal geared hub has one gear in the middle of the range which gives the exact gear inches reflected by the chainring and cog. Other gears are usually listed as a percentage of that gear. Since the Sturmey-Archer was first made commercially available in 1903 (you read that right, over 120 years ago!) other configurations have been designed to give a larger number of gears. The percentages can be obtained from the hub manufacturers and other online resources. They cannot be readily determined without disassembling the hub. Here are some examples:
• Sturmey-Archer AW 3-speed: 75%, 100%, 133%
• Brompton Wide Range 3-speed: 64%, 100%, 157%
• Shimano Nexus 7-speed: 63%, 74%, 84%, 100%, 115%, 134%, 155%
• Shimano Alfine 11-speed: 53%, 68%, 77%, 88%, 100%, 113%, 129%, 146%, 167%, 189%, 215%
• Rohloff Speedhub 14-speed: 28% to 147%
Note that while it might seem really attractive to have 14 speeds all without any derailleurs, it comes at a cost. The Rohloff hub is pretty heavy (~1.8kg – almost 4 pounds) and costs around $1,500.
Other Alternative Gearing
Another recent entry into the bicycle market is the Pinion gear box. Here, the gearing is placed at the bottom bracket, but otherwise uses a similar set of internal gears like the Sturmey-Archer hub, or an automobile transmission. These gear boxes are expensive, and require a bike frame built to accommodate them.
Other Useful Concepts
Here are some other useful terms:
Cadence
i.e., pedaling speed. Usually given in revolutions per minute (rpm). This, along with the gear measurement can be used to find out how fast you will go in a certain gear.
Derailleur Capacity
The number of chain links a rear derailleur can accommodate (or “wrap up”) and still maintain chain tension. Along with the rear derailleur’s maximum cassette cog limit, this will tell you what derailleur will work with your gearing.
In Conclusion
I hope you have found this article informative and useful. I've tried to keep the level of technical detail modest. Many older books on bicycling will have discussions about gearing. However, for those who really want to "geek out" on gearing, the most complete discussion I've seen is in the 1989 book, "Bicycle Gearing: A Practical Guide" by Dick Marr.