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by Matt Wikstrom
November 16, 2017
Photography by Matt Wikstrom
TECH NEWS BROUGHT TO YOU BY BIKEEXCHANGE
There is more to the gearing on a bike than simply the size of the big ring. In short, size does not matter because it’s the ratios that are generated by each combination of the chainrings with the sprockets that are most important. In this post — an updated version of an article first published in 2014 — Australian tech editor Matt Wikstrom looks at how to make sense of gear ratios and discusses all of the nuances they can provide.
Over the past 30 years, the number of gears on road bikes has steadily increased. Current groupsets now provide 22 gears through the combination of two chainrings and 11 sprockets. The range of sizes for the chainrings and sprockets has also grown in that time, too, providing riders plenty of scope to fine-tune the gearing on their bikes.
With such a generous number of gears on offer, it is tempting to think that there wouldn’t be much point to tinkering with them, but the human engine demands it. After all, there is a finite amount of power on offer and the efficiency of the system depends upon maintaining a consistent cadence (~80rpm), regardless of any change in the terrain or riding conditions.
Every road cyclist understands that size of the chainrings and sprockets dictate the gearing of the bike, however there is more to the concept than simply the number of teeth involved. What is most important is the ratio and the way that the sprockets multiply the effort made with the chainring.
Before the advent of the chain-drive, early cyclists determined that the size of the drive-wheel had a profound impact on the speeds that could be achieved. Penny-farthings were not designed with a huge front wheel for aesthetic reasons — the massive circumference allowed higher speeds provided the rider was strong enough to turn the wheel.
The introduction of the chain-drive improved the efficiency of the bike because gears could be used. By combining a large cog on the cranks with a small one on the wheel, a single turn of the cranks produced multiple revolutions of the rear wheel, so it could operate just like the massive drive-wheel of a Penny-farthing.
Calculating the number of wheel revolutions produced by a bike’s gearing is simply a matter of determining the ratio of the chainring to the rear sprocket. For example, when a 53T chainring is paired with a 12T cog, it has a ratio of 53:12, or 4.42, so one complete rotation of the crank will cause the rear wheel to rotate 4.42 times. In contrast, 39 x 25T produces a gear ratio of 1.56.
With all of the options available to today’s road cyclists, it is possible to produce gear ratios that are as small as 1.0 and as large as 5.0 with increments of 0.15-0.40. On their own, those numbers aren’t particularly descriptive, but they can be transformed into more meaningful values in one of two ways.
The first method is to relate the gear ratio to wheel size by multiplying the gear ratio by the diameter of the wheel (Figure 1A). In the case of a road wheel, 27 inches can be used for simplicity (although the true diameter of a 700c rim fitted with a 23mm tyre is more like 26.3 inches). The resulting value, gear inches, represents the diameter for an equivalent direct-drive wheel (like the front wheel of a Penny-farthing).
For example, using a high gear ratio such as 53 x 12T is equivalent to riding a penny-farthing with a front wheel that is nearly 10 feet (or 3m) tall. In contrast, a low gear ratio like 39 x 25T is equivalent to a 42-inch wheel.
Figure 1: converting gear ratios into (A) gear inches and (B) roll-out.
The second method, roll-out (a.k.a. meters of development), is calculated by multiplying the gear ratio by the circumference of the wheel (measured in meters, Figure 1B). This value represents the distance the bike will travel with one crank revolution. Thus, 53 x 12T yields 9.28 meters of roll-out for a road bike fitted with 25C tyres compared to 3.28 meters for 39 x 25T.
Of the two, roll-out is a little more informative, if only because it is more tangible than a theoretical wheel diameter. Nevertheless, either value can be used to easily calculate the expected speed for any given cadence:
Speed (km/h) = Roll-out/1000 x cadence (rpm) x 60
Speed (miles/h) = Gear inches/63, 360 x Pi (3.14159) x cadence (rpm) x 60
Such considerations are critical for those riders using a fixed gear (e.g. track and BMX racers). In this setting, a minor difference in gear ratios (0.1m/1 gear inch) can affect how easily the rider can accelerate and the maximum speed they can attain. Out on the road, though, such differences won’t be felt, and in general, larger increments (0.5m/5 gear inches) are more meaningful.
Figure 2 shows the range of roll-outs provided by each of the major chainring combinations — standard (53/39T), semi-compact (52/36T), and compact (50/34T) — with a variety of sprocket sizes. At face value, it is easy to see that a standard crankset generates higher roll-outs than the other chainring combinations, however there is a lot of overlap, too. Indeed, there is far more similarity between the three cranksets than there are actual differences.
Figure 2: Comparison of the roll-outs generated by standard (53/39T), semi-compact (52/36T) and compact (50/34T) cranks and a variety of common sprockets.
For example, there are are six chainring and sprocket combinations that will provide 5m of roll-out: 39 x 16T, 36 x 15T, 34 x 14T, 53 x 23T, 52 x 21T, and 50 x 21T. At a cadence of 80rpm, a cyclist will always end up cruising at 24km/h, regardless of the specific combination they happen to be using.
The same applies for almost any given roll-out: the gear ratio is far more important than the number of teeth involved. It is only when a rider is hoping to maximise, or minimise, the roll-out of the bike that it becomes important to pay attention to the size of the chainrings and/or sprockets.
At face value, the combination of two chainrings and 11 sprockets promises an impressive range of gear ratios, however it also gives rise to a significant amount of redundancy, regardless of the crankset and sprockets in use (Figure 3A).
This redundancy always occurs around the middle of the range of gear ratios, where the roll-outs generated by the small chainring and the smallest sprockets essentially match those produced the big ring and the largest sprockets. When this overlap is removed, the number of discrete gear ratios offered by a 2 x 11 transmission can be as small as 14 and as large as 17, depending on the range of sprockets (Figure 3B; see also Figure 7).
Figure 3: There is significant overlap in the rollout-outs generated by standard (53/39T), semi-compact (52/36T) and compact (50/34T) cranks when combined with an 11-speed 11-28T cassette. (A) A look at the roll-outs for every chainring-sprocket combination. (B) After removing the redundant gear combinations, 14 discrete roll-outs remain.
For those riders that diligently refrain from cross-chaining, much of this redundancy will go unnoticed. It is simply the product of the relatively modest difference between the big and small chainrings, so there is no way to reduce or eliminate it without opting for a very different combination of chainrings.
For example, a 53/28T crankset combined with a 7-speed 11-19T cassette will provide the same number of discrete ratios as a standard crankset paired with an 11-speed 11-27T cassette, as shown in Figure 4.
Figure 4: The combination of a 53/28T crankset and a 7-speed 11-19 cassette yields the same series of discrete rollouts as a standard crankset (53/39T) combined with an 11-speed 11-27T cassette.
While the idea of a drive-train without any redundant ratios might be quite appealing, those “wasted” combinations make the transmission more convenient to use. That’s because there’s no strict need to shift from one chainring to the other in order to find the next gear ratio. That every groupset manufacturer has created front derailleurs better able to accommodate cross-chaining only adds to this convenience.
It is important to note that if a rider cross-chains for long periods of time, it will accelerate wear on the chain, cassette and chainrings. It may also indicate that the rider will benefit from a subtle change in gear ratios.
I’ve already discussed the fact that standard, semi-compact, and compact cranksets all generate many of the same gear ratios. However, for any given sprocket set, a standard crankset will always generate more roll-out than semi-compact and compact cranksets (Figure 2). Thus, the choice of chainrings does a lot to determine the overall feel of the bike’s gearing.
For those riders that like to spin and can maintain a high cadence for long periods, compact chainrings are likely to suit them better than a standard combination. In contrast, riders that can push bigger gears at a lower cadence are more likely to prefer bigger chainrings.
However, there is more to the effect of chainring size on the gearing of the bike than simply maximising or minimising roll-out. It also has an effect on the size of the steps between each gear ratio. Some sense of this can be gained from Figure 2, but it’s easier to visualise by using a line graph to plot the same values, as shown in Figure 5A.
Figure 5: Reducing the size of the chainrings decreases roll-out but the steps between each gear ratio are more gentle. (A) Comparison of the roll-outs generated by standard (53/39T), semi-compact (52/36T) and compact (50/34T) cranks and an 11-speed 11-28T cassette. (B) Comparison of the discrete roll-outs generated by a standard (53/39T) crankset and an 11-speed 11-32T cassette with a 1×11 transmission (50T/10-42T cassette).
It is the slope of each line in this figure that is important: it gets steeper as the steps between the gear ratios get larger. In this example for an 11-speed 11-28T cassette, the slope of the line for a standard crankset is steeper than compact cranks, especially for the small chainring, so there are relatively bigger steps between each gear ratio. The same applies for semi-compact cranks, though the differences aren’t quite as marked.
Will they be felt on the road? For some riders, the answer is a definite yes, while for others, it may amount to nothing more than a nuance. Ultimately, it will depend on how readily a rider is able to vary their cadence and whether or not they have the freedom to dictate their own pace. For those riders that need to fine-tune their cadence for any given speed (e.g. when racing or time-trialling), such nuances will be important and the benefits can be measured in terms of comfort and efficiency.
There comes a point, though, when the steps between gears can be too big for road cycling. Figure 5B compares the rollouts for a 1×11 transmission (50T chainring/10-42T cassette) with a standard crankset paired with a 11-32T cassette. At the low end, both combinations offer the same gear ratios with relatively gentle steps, but as the roll-out increases, the steps become progressively larger for the 1x transmission.
While these larger steps promise bigger increases in speed with each gear change, riders may find it much harder to maintain an even cadeence without making abrupt changes to their speed (or vice versa). Nevertheless, at least one professional team will be using 1x transmissions in the peloton next year, albeit with a change to a 12-speed cassette and perhaps the introduction of a 9T sprocket.
The size of the sprockets also affects the progression of the gear ratios. When there are small differences between each sprocket (ie. 1-2T), the gear ratios will exhibit relatively small steps compared to a cassette where there are bigger differences between the sprockets (ie. 3-4T).
For example, an 11-speed 11-23T cassette offers a very smooth progression of roll-outs due to the fact that there is a one-tooth difference between all but the largest two sprockets (Figure 6A). In contrast, the majority of sprockets (9/11) that make up an 11-32T cassette are separated by two teeth or more, so while it provides three lower ratios, the steps are generally steeper and the progression much bumpier.
Figure 6: A smaller range of sprocket sizes provides a smoother progression of gear ratios. (A) Comparison of the discrete roll-outs generated by a compact (50/34T) cranks and 11-speed 11-32T and 11-21T cassettes. (B) Comparison of the discrete roll-outs generated by a standard (53/39T) crankset and 11-speed 11-28T and 14-28T cassettes.
The same effect can also be seen when comparing an 11-speed 11-28T cassette with a 14-28T cassette (Figure 6B). In both cases, a smaller range of sprocket sizes not only smoothes out the progression of roll-outs, it also adds to the number of discrete gear ratios. However, it will limit the overall range of ratios, so riders must be prepared to sacrifice at least a couple of gears at one end of the spectrum in order to enjoy small steps between each gear ratio.
At this point, it is worth noting that 3x transmissions can overcome much of this kind of compromise, extending the range of low gear ratios while preserving a modest rate of progression (though this will ultimately depend on the choice of rear sprockets). However, 3x transmissions have largely disappeared from the market, and for those products that still persist, they may not always be compatible with a contemporary road frame.
Over the last few years there has been a change in thinking and road riders have started celebrating the extra comfort and grip provided by wider tyres. As a tyre gets wider, it also gets taller, increasing both the diameter and circumference of the wheel. This will, in turn, increase the roll-out for every gear combination on the bike.
This effect can largely be dismissed when the difference in tyre sizes is small. For example, the circumference of a 28C tyre is only 1.4% larger than a 23C tyre, so it only has a mild effect on the roll-out (Figure 7A). In contrast, the diameter of a 40C tyre is almost 4% larger than a 23C tyre, and the effect on the roll-out of the bike is equivalent to adding an extra two teeth to each chainring (Figure 7B).
Figure 7: Larger tyres increase the roll-out of every gear combination. (A) Comparison of the roll-outs generated by the indication chainring and sprocket combinations for 23C and 25C tyres. (B) Comparison of the roll-outs generated by the indication chainring and sprocket combinations for 23C and 40C tyres.
Thus, for those looking at a gravel/all-road bike, it is worth considering a compact or even a sub-compact crankset to compensate for the change in gearing.
The only way to decide how any of these effects on the gearing of a bike translate to the road is to put them to the test. This can be a costly exercise, especially when considering a change of chainrings, so the best time to explore the issue is when one or all of the parts of the transmission are due to be replaced. In general, changing the sprockets will have a smaller effect on the gearing of the bike than replacing the size of the chainrings.
For those riders that are planning a trip to tackle more challenging terrain (e.g. visiting the French Alps), then it is possible to make some guesses based on the range of low ratios that are currently in use. Nobody ever wants to be stuck wishing for a lower gear, so it is prudent to add at least one extra low ratio to contend with the worst-case scenario.
In this context, there is typically much less need for high gear ratios, especially when plummeting down unfamiliar roads, so a couple of high ratios can be sacrificed without affecting the utility of the bike. Indeed, there is generally far too much emphasis on preserving high gear ratios on road bikes since the majority of riders simply don’t have the horsepower to push these gears at any time except on a descent, at which point gravity can perform much of the work.
For those that are in the process of selecting the parts for a custom road bike build, the gearing on an existing bike will serve as a pretty good starting point. If the wheel and tyre sizes are identical, then minor changes to the sprocket sizes may be all that is needed, but it is worth going through a comparison of the ratios offered by specific chainring combinations (as detailed above) before making a final decision on the cranks.
There was a time (over 20 years ago) when sprockets were sold individually and riders could pick and choose the sizes they wanted for the rear wheel. Nowadays, buyers are constrained by what cassette manufacturers choose to assemble, so there is a lot less freedom when it comes to choosing the gearing for a bike.
For example, when looking at the 11-speed cassettes currently on offer from Shimano and SRAM, almost all favour an 11T sprocket, even when sprockets that are as large as 32T or 36T are included. There are just three exceptions — 12-25T, 12-28T, and 14-28T — all of which are offered by Shimano.
The same kind of constraints also apply to the selection of chainrings — where once it was possible to obtain road chainrings in one-tooth increments, now it is limited to just a few choices. The range of options for any given cranks are further limited by the bolt-pattern (e.g. four-bolt versus five-bolt) and bolt-circle diameter (e.g. 110mm versus 130mm). As a result, there is much less interchangeability amongst chainrings than what might be expected.
A variety of incompatibilities affect the derailleurs, too. In the case of the front derailleur, while it is possible to use many current models with a range of big rings (46-54T), there is a limit (due to the dimensions of the cage) on how much smaller the second chainring can be. This is typically no more than 16T, which is why a 34T can never be paired with a 53T.
As for the rear derailleur, the geometry of this component dictates what size sprockets can be used. Those derailleurs with a short cage are limited to 28T (or 29T in the case of Campagnolo); medium-length cages can accommodate sprockets up to 32T; while a long-cage derailleur is required for a 36T sprocket. In some cases, it is possible to use a slightly larger sprocket for any given derailleur, but this must be assessed on a case-by-case basis. preferably by an experienced mechanic.
Today’s road cyclists are equipped with more gear ratios than ever, and thanks to the growing size of sprockets and shrinking chainrings, those ratios have been getting smaller, too. It is the latter that has served the sport well, lowering the barrier to entry and making it possible for occasional cyclists to spend more time on the bike.
While the industry has provided a reasonably generous range of chairing and sprocket sizes, there is no easy way for a cyclist to decide the utility of any given combination without putting it to use. Ultimately, gearing is a personal choice and every rider should have the freedom to decide the matter for him or herself rather than obeying conventional wisdom.
In this regard, the appearance of new technologies surrounding electronic groupsets show a lot of promise. It is now possible to view and collect data on how much time is spent using each gear ratio on the bike and this kind of information will prove invaluable for assessing the utility of specific chainring and sprocket combinations. When combined with heart-rate and/or power measurements, there is the potential for identifying those ratios that are most efficient for a rider while highlighting any bad habits they may have developed (such as cross-chaining for extended periods).
In time, road transmissions may progress to the point where intelligent shifting becomes a reality, stepping in to preserve the efficiency of the human engine rather than leaving the choice of gearing in the hands of an inexperienced rider. While this notion may offend the purists, there is the promise that it will free riders from the burden of operating the gears so they are better able to enjoy the activity. And at that stage, there will be no need for them to ponder the nuances of gear ratios.