The Math Behind A Wide Range 2×11 Drivetrain

I recently modified a mountain bike that came with a 2×11 drivetrain. It was nice, but I wanted a wider gear range. The result was a 10/42T 11 speed cassette paired with a 40/24T 2x crankset. I can hear the cries already: “A 24×42 granny gear? That’s madness!” “You will never get shifting to work with that!” “You will create a discontinuity in the space-time continuum!” “What do you need gearing like that for?” Well it is not as crazy as it may sound.

The crankset was originally 36/24T. Now is it is 40/24T.

All I want to deal with in this blog is gear ratios. I am going to look at two things: the ratio of the front to rear gear teeth. i.e. for every rotation of the crank, how many times does the rear wheel rotate? By looking at those numbers we can compare 1x, 2x and 3x drivetrains on level ground. I also want to take one other thing into account, and that is the difference in diameter of the wheels. 29er wheels increase gearing vs 26″ wheels. How much? This is where gear inches come into play. Gear inches are how far the bike moves forward with a single revolution of the crank. Sound familiar? So we can use these two numbers together. More on this later.

Let’s start with a baseline: the classic drivetrain that was the standard of mountain biking for years until 2x, 1x and 29er’s entered the scene. And that is the following: a 3×9 drivetrain with a 11/34T cassette and a 22/32/44T crankset on a 26″ wheels. Here is the total gear range:

Range: 44/22 * 34/11 = 6.18 or 618%

i.e, the high gear is 6.18x higher than the low gear. Keep this in mind when look at 1x and 2x drivetrains. The latest 1x 12 speed groups have a range of 500% (50/10) or 511% (46/9). To put it another way, to get about 618% range in a 1x drivetrain, you would need a 10/62T or 9/56 cassette. Rohloff internally geared hubs have a range of 526%. Shimano Alfine 11 have a range of 409%.

The rear was originally 11/32T. Now it is 10/42T.

As for the 2×11 combo that I put together:

Range: 40/24 * 42/10 = 700%

To replicate that in 1x you would need a 10/70T or a 9/63T cassette, which don’t exist yet. If you want a range like this you need to go 2x, at least for now.

Here are some other parameters I keep in mind. The max spread I go for on the crankset is 16T. That is, the big ring is 16T bigger then the small ring. That is a wide but common range with road bikes and a compact 50/34T crankset. Road and mountain bike front derailleurs seem to handle that kind of range. The standard 10/42T 11 speed cassette has a drop of 32T. So together the crank and cassette have a total drop of 48T, which is about the max a mountain bike long cage rear derailleur can take up. Note that the 9/46T cassette has a drop of  37T, so pairing that with a double crankset would mean reducing the drop of the crankset, since 37+16=53T is just to much for even the longest of rear derailleur cages to deal with.

Let’s have another look at wheels. Gear inches are a function of the circumference of the tire, which in turn depends on the diameter. Circumference is pi times diameter, if you remember your geometry. But since we are going to divide the numbers, we can use just the diameter. The new ISO diameters are the best numbers to use. For 29ers, the diameter is 622mm, for 26″ it is 559mm. So 29ers increase gear inches compared to 26″:

622/559 = 1.11

29er rims are 622mm at the bead. Not to be confused with the ERD of 605mm.

In other words, if the gearing is the same on a 29er and a 26″ bike, the wheel diameter would give the 29er 11% higher gearing. If we want to compare the 3×9 above to the 2×11, we should increase the gearing on the 2×11 by 11% giving us:

High gear: 40/10 = 4.0 x 1.11 = 4.44
Low Gear: 24/42 = .571 x 1.11 = .634

The range is unaffected. So while it may not seem like it, a 24/42 granny on a 29er is actually only slightly lower than 22/34 gear than on a 26″ bike (.634 vs .647). This 2×11 29er drivetrain provides a wider range of gears than our 3×9 26″ benchmark, and mostly on the higher ratios.

Of course the advantages for 1x are numerous. A drivetrain like this wide range 2X11 is not needed for most bikes. In this case it is for an adventure bike that is meant for off road use with a touring load. At the same time the bike is well suited for the road where it is a shame to be without the taller gears. You could use similar gearing on a road touring bike but with larger chainrings (say compact 34/50) and get gearing comparable to traditional 3×9 road touring triple group but with the simplicity of 2x shifting.

This is not the end of the comparison by any means. Some 3×9 groups have wider ranges with a 46T big ring or a 36T big cog. I think we will see wider gear ranges and more gears going forward for 1x drivetrains. i.e. the trend of 10/42T 11 speed to 10/50T 12 speed will continue. Shimano has patents on a 14 speed drivetrain. And what about 27.5 / 650b wheels? Now you know how to compare these drivetrain options.