Tech: Deep dive on 1×10 narrow/wide conversion gearing
Editors Note: ‘Science Behind the Magic’ delves into the inner workings of your two-wheeled steed. Art’s Cyclery web content editor Brett Murphy uses his mechanical engineering background to explain the latest industry advances and breakdown the inner workings of common components. The original article can be found here.
I recently wrote reviews of the e*thirteen Extended Cog and GuideRing M after converting my own bike to a 1×10. I had great things to say, and have received some requests to further discuss 1×10 gear ratios, including extended cog range setups. I thought it would be useful to compare some stock setups with the 1×10 extended range possibilities. Comparing the gear ratios and the cost differences should help you make an informed decision about where to spend your money.
The growing popularity of extended cogs is a result of 11-speed 1x drivetrains by SRAM and Shimano. There are mechanical and weight advantages to ditching the front derailleur in favor of a wider range cassette that can do the job of a double or triple chainring system. The manufacturers have decided however that these wide range cassettes should come with a hefty price tag and the requirement for a new shifter, derailleur, and potentially a new freehub body or hub. E*thirteen, Hope, and others all have extended cogs that increase the range of your current 10-speed system by adding a 40 or 42-tooth cog to the freehub body; making room by removing the 15T or 17T cog on the existing cassette.
The following graphical representation shows a comparison of gearing between four setups. The X-Axis is arbitrary and represents the number of gears available. A 3x system has 30 gears to choose from, however most of them overlap and are redundant. The Y-Axis shows the number of centimeters of forward movement per crank revolution. Rolling centimeters are calculated by multiplying the circumference of a 29-inch tire by the gain ratios of the gearing.
The jumps in rolling distance observed in the 3x (blue plot) and 2x (red plot) show the change from one chainring to the next. While 3x does offer a slightly better range of gearing, the amount of redundancy in gear ratios is extreme. Comparing the 24T ring of the triple to the 32T ring, you can see that the first 8 high gears overlap in rolling distance to gearing in the 24T ring. Only the last two shifts offer a new ratio. The same is true of the 42T ring. Of the 30 gearing choices on a triple 10-speed setup, only 14 combinations offer unique gearing, the rest are redundant. The same is true of a double but to a lesser degree. Of the 20 gearing combinations on a double, 14 are unique ratios. Doubles offer an almost identical range of a triple with one less ring.
The major concern for most people when moving to a 1x system is that they will be losing gears, making it harder to climb. I set up the gearing in the chart so that all combinations would have approximately the same gearing for climbing. All setups have roughly 150 centimeters of forward movement per pedal stroke in the lowest gear. So let’s set that concern aside, it will be just as easy to climb with your new extended range (42t) 1×10 as any other factory setup. Now on the high end of the gear range there is a bit of a different story to be told. The 3×10 setup wins the highest gear award with the ability to move 878cm per pedal stroke and the 1×10 comes in last at 627cm. This explains some of the reasoning behind SRAM’s XD freehub body that allows for a 10-tooth cog, which increases high-end ratios.
Now before dismissing the 1x setup on account of a lack of high gearing, ask yourself if you really think you’ve ever used this range before. Looking again at the chart, we can see that the same ratio of a 1×10 extended setup (30T ring in the 11T cog) is available with a 3×10 setup using the 42T ring with the 15T cog. So take your current 3×10 bike out for a ride, and when you are descending the trails or riding back to the car on the flats, see if those last two gears (the 13 and 11-tooth cogs) make a difference to you. From personal experience, I find I don’t have an issue spinning out on my bicycle. At 90RPM this last gear would have you traveling at 30mph. While I do have loads of fun ripping trails at 30mph, I don’t find myself pedaling in these situations and also don’t spend time on the road spinning at this speed.
Depending on your bicycle and riding style, perhaps higher RPMs and speeds are more important to you. Check out some of the pro XC setups around today. For the most part they are running an XX1 10-42 cassette with either a 36T or even a 38T chainring. So perhaps if you are building a XC rig, you look at a bigger front ring paired with that 10-speed extended cassette. Below we can see the results of the new 1×10 11-42T cassette with a 36T chainring stacked against the original triple and 30T 1×10 setups. Shifting the line upwards in favor of higher speeds and less climbing.
Continue to page 2 for calculations and the bottom line »
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