Sequential shifting

The future of electronic groupsets and the new goal for gear ratio progressions

By Simon Paterson
Engineering Design
Sydney, March 21, 2011

A look at the potential future for electronic groupset gear shifting components such as Shimano's Di2.

Introduction

The release of Shimano's electronic groupset, Di2, into the hands of the cycling public triggered some logical analysis of the future of this technology.

Seemingly the next logical step is to interface a cyclocomputer with the brains of the electronic shifters to start to control the behaviour or receive feedback from the system. This relatively minor technological feat opens the door to many possibilities.

Feedback

Since the brain of the electronic shifting system would be aware of the gear in use, it seems a relatively minor technological step to announce the setting via an ANT+ link which could then be displayed on any ANT+ compatible computer.

Automatic shifting

One of the first things that came to mind was the concept of automatic shifting. It would be an interesting system. For new riders who can’t figure out those confounding gears, it could be quite useful.

Automatic shifting might be re-phrased as semi-automatic shifting which would appeal to a more serious cyclist and might also have a place in the professional peleton. Another article in this series goes into some depth on the concept and even deals with the core maths which would make the system work.

Sequential shifting

This is perhaps the area into which I have put most thought. I believe it is the place where electronic shifting will lead us.

It may be useful to define exactly what is meant by ‘sequential shifting’, since this is a concept with more than one interpretation. Sequential shifting is a term used a lot in reference to car gear boxes. It makes sense, since car gears are numbered, that a shift ‘up’ would take the car from, say, 1st gear to 2nd gear. Bike gears are not numbered, so this concept isn’t as straightforward. But the basic idea of using a button for shifting ‘up’ and a button for shifting ‘down’ can certainly be applied to electronic gear systems like Di2.

If we apply this concept to a bicycle, then sequential shifting would take us from the small chainring / large cog combination through the gears to the large chainring / small cog combination; swapping in the middle at small chainring / small cog to large chainring / large cog. This describes a kind of sequential movement through the gears and would be extremely simple to achieve with electronic shifting. It would even be possible to avoid so-called ‘cross-chain’ combinations automatically.

This is a simplistic application of sequential shifting which is not really analagous to car gears. In a car gear system, the change in gear is always to a different gear. If you go up from 3 to 4, you arrive at a different gear. On a bicycle, however, there is an overlap of gears between chainrings. Let’s look at that overlap for a moment using gear inch (or sometimes chain inch) calculations, a fairly common way of quantifying gear ratios which can be calculated using chainring and cassette tooth count. There are several calculators available on the web, such as Sheldon Brown’s gear inch calculator. If you dial in your sprocket settings you will get a table of numbers with the gear inch settings for each chainring/cog combination. Here is an example:

Gear-inch
  Chainring teeth
Cassette teeth 39 52
12 6.81 9.08
13 6.29 8.38
14 5.84 7.79
15 5.45 7.27
16 5.11 6.81
17 4.81 6.41
19 4.30 5.74
21 3.89 5.19
23 3.55 4.74
25 3.27 4.36
Wheel Circumference: 2096 mm

If you look at these numbers you can see that there is a fair amount of overlap between gears accessed from the small and large chainrings. For instance, the gear inch setting of 5.11 with the 39 front and 16 rear combination is virtually the same as 5.19 gear inches with 52 front and 21 rear. Technically, then, our system of ‘sequential’ shifting is not really sequential in terms of actual gear ratios. It is sequential in terms of our motion through the gears, but not in terms of true gear ratios.

If you examine the gear inch table it is possible to chart a technically sequential gear inch progression. It is interesting to see that this sequence would require movement of both the front and rear derailer with virtually every gear change. For example, the sequence might be like:

  1. 52/23 = 4.74
  2. 39/17 = 4.81
  3. 39/16 = 5.11
  4. 52/21 = 5.19
  5. 39/15 = 5.45
  6. 52/19 = 5.74
  7. 39/14 = 5.84

As can be seen, the chain may be moving from the inside front chainring to the outside chainring between one sequential gear and the next. At one moment we have 4.74 gear inches with 52 front chainring and rear 23 cog and the next moment we move to 4.81 gear inches with 39 front chainring and a big jump down to the 17-tooth cog. That’s a lot of movement for true sequential shifting. Although this kind of sequential shifting would be possible with an electronic groupset, it may not be desirable, regardless of the smoothness and reliability of the shifting. The small changes in actual gear ratios offered by this pure sequential shifting are probably not required, nor desired, either. What would be more interesting is a sequential shift in gear ratios that did not require jumping between large and small chainrings.

For that, we need to look at a better distribution of gear ratios.

A closer look a gear ratios

The challenge, then, is to create a gear ratio distribution or progression which avoids overlap. Once I worked it out, it was the inspiration for a new approach to gearing ratios.

Distributing the ratios

It took a little work to discover a new distribution of gear ratios with little or no overlap. I considered the desire to avoid cross-chaining, and looked for a distribution of gears that was sequential once the cross-chaining combinations were removed.

Gear-inch
  Chainring teeth
Cassette teeth 32 53
11 6.1 10.1
12 5.59 9.26
13 5.16 8.54
14 4.79 7.93
15 4.47 7.41
16 4.19 6.94
17 3.94 6.54
18 3.73 6.17
19 3.53 5.85
21 3.19 5.29
Wheel Circumference: 2096 mm

After removing the cross-chain combinations of 32/11 (6.1) and 53/21 (5.29), we end up with an entirely linear set of ratios with no overlap. Now we can implement a truly sequential shifting system using Di2 or EPS. (Although, this would also work for mechanical systems.)

There are significant advantages. This distribution provides at least 18 fully-functional and unique gears without couterparts—compared with 13 gears without counterpart in the typical gearing system now in use. (How many people realise their 20-speed bikes are really only 13-speed bikes?)

Electronic shifting with 11-speed cassettes

Although Campagnolo’s offering of electronic shifting came some time after Shimano, the industry was poised and certainly assumed, correctly, that their system would use an 11-speed cassette.

More pertinant to our current discussion, I realised we could now have a true 20-speed bicycle. There’s no great significance, it’s just a nice round number.

My tweaked combination with 11-speed cassette is shown in the following table. Even though electronic gear shifting has eliminated some of the issues with cross-chaining, I think it is still worthwhile avoiding these combinations for the benefit of noise and chain wear. I have deliberately included an overlap of gears on the cross-chaining combinations and anticiapte that these would be electronically excluded from any sequential shifting system (as I’ve visually excluded them from this table). This gives us a true 20-speed system. That’s 20 useable, non-crossed, unique gears arranged sequentially. I think it’s awesome, and I’m keen to build one.

Gear-inch
  Chainring teeth
Cassette teeth 32 54
11 10.29
12 5.59 9.43
13 5.16 8.71
14 4.79 8.09
15 4.47 7.55
16 4.19 7.07
17 3.94 6.66
18 3.37 6.29
19 3.53 5.96
20 3.35 5.66
21 3.19
Wheel Circumference: 2096 mm

I like this combination because it gets us down to 3.19 gear inches at the low end, which is just lower than a standard combination of 39/25 and up to 10.29 gear inches at the high end which is above the standard combination of 53/11. A broad gearing range is one of the significant advantages of this system.

One additional point which I really love about this system is the ‘flatness’ of the cassette. In many cassettes, we see large jumps in teeth count, especially as the cassette cogs get larger. In the Campagnolo 12-29, for example, we have a 3-tooth jump from 23 to 26 to 29. (We’re not discussing aesthetics, but if you’re like me, you think those smaller, flatter ones look better.) These jumps make the change between gears more pronounced, which is exaggerated at low speeds. With this cassette, the distribution is always one cog. It is interesting that this does not, as one might expect, create a truly flat distribution of gear ratios, but it does create a very desirable one. As with any current setup, the increment between gear inches is higher as the gears get higher.

The jump from 52/13 to 52/12, for instance, is 0.7 gear inches. At the lower end, from 30/20 to 30/21, the jump is only 0.15. (Compare this, for instance, to a jump from 34/26 to 34/29, which is 0.28 gear inches; nearly twice the size.) This is a good thing. In the lower gears, used when climbing, it is advantageous to have a small change because you are going slower and the changes in gradient are often very small. The perceived effect to your cadence is similar to the larger jumps experienced in higher gears whilst travelling at higher speeds. It’s a winning situation in every respect.

Options

Truly sequential gearing ratios are harder to calculate out than conventional systems and are slightly more rigid in their formulation. Since the range of gears is so remarkable—because we have no overlap and no redundant gears—it is possible to have a ‘regular’ crankset which will suit the vast majority of riders, while still providing options for racing as well as the replacing the need for triple cranksets. Amazing, but true.

Double (‘race’)

The ratios described so far would really suit the super strong riders and professionals. And, from this perspective, could easily replace all the variations currently in use in professional cycling. Yep, all of them. Let’s call it the ‘race’ model.

On fast, flat days, mechanics with the professional teams will fit the larger 54-tooth chainring for the 10.29 gear inches of top gear. We’ve got that covered. On very steep days, the pros will go down as low as 25 or 26 on their cassette for the particularly steep parts of a special climb. Got that covered, too. The configuration described above covers this entire range without losing anything. It’s close to perfect for this level of cycling.

Compact (‘standard’)

Those who currently ride compact cranksets will want lower ratios in their lower gears. This can be achieved while still extending the high gear beyond the current capability of a compact crankset; a definite advantage for those short, swift descents. Below is the configuration that I believe could be considered ‘regular’ (forget the ambiguous term ‘compact’) which is sure to suit more than 90% of road cyclists. (Those who need the higher ratios would know it, and purchase the ‘race’ version described above.)

30/52 chainring

12-24

Gear-inch
  Chainring teeth
Cassette teeth 30 52
12 9.08
13 4.84 8.38
14 4.49 7.79
15 4.19 7.27
16 3.93 6.81
17 3.7 6.41
18 3.49 6.05
19 3.31 5.74
20 3.14 5.45
22 2.86 4.95
24 2.62
Wheel Circumference: 2096 mm

This combination does not go quite as high as the current ‘double’ crankset 53/11 combination, but it is close. Moreover, it extends the lower end down to 2.64 gear inches, just below a ‘compact’ 34/27 combination. It doesn't quite go all the way to a 34/29 combination but the largest 24-tooth cog could be replaced with a 25-tooth cog which would provide an equivalent gear ratio.

As far as this ‘regular’ 30/52 crankset setup goes, there are still options, depending on the rider’s needs:

  • 11-21 (11-12-13-14-15-16-17-18-19-20-21)
  • 11-22 (11-12-13-14-15-16-17-18-19-20-22)
  • 12-23 (12-13-14-15-16-17-18-19-20-21-23)
  • 12-24 (12-13-14-15-16-17-18-19-20-22-24)
  • 12-25 (12-13-14-15-16-17-18-19-20-22-25)

These are all possible combinations which simply shift the ratios towards the lowest gears and cover the full gamut of current ‘compact’ setups. Notice how the range 12-20 is standard in every set? This is necessary for truly sequential gear ratio progressions and, in fact, the ratios shown here are the only ones possible for the 30/52 crankset without breaking the sequential progression.

It is also possible to replace the need for triple cranksets. Let’s not get started on how much overlap there is in a triple crankset; there’s a lot (only 20 unique gear ratios from a total of 33). The real benefit of triples is being able to get really low gears, while still having a reasonable high end. The following sequential progression addresses those needs and spans virtually the same range as a 30/39/52 triple crankset while providing the same 20 unique gear ratios.

Gear-inch
  Chainring teeth
Cassette teeth 25 47
11 8.96
12 4.37 8.21
13 4.03 7.58
14 3.74 7.04
15 3.49 6.57
16 3.27 6.16
17 3.08 5.79
18 2.91 5.47
19 2.76 5.18
21 2.5 4.69
23 2.28
Wheel Circumference: 2096 mm

No need for those hideous triple cranksets any more, and nobody will be disadvantaged. Manufacturers are going to love that. Less materials, same cost.

So...

Can this system get any better? Yep. The smaller chainring and smaller cogs will have inherent weight saving advantages! It’s truly awesome in every way, don’t you think?

In practice

It’s not all as good as it seems. What is?

The first technical challenge is how to shift the chain between a small 32-tooth chainring and a large 53-tooth chainring. Normally the difference is as small as 10 teeth between chainrings; up to 16 teeth for compact chainrings. But our difference is around 20 teeth.

Update: Problem of shifting from small to big has been solved by WickWorks.

We would need to use a medium-sized rear derailer arm, rather than the standard ‘short’ size currently in use on most road bikes. The total capacity of the drivetrain would always be above 30, so a medium-arm is a necessity since short-arm derailers for road bikes can handle a capacity of 29 or less.

Besides the challenge of moving between a (very) small and large front chainring, there is also the challenge of implementing a smooth movement from small cog / small chainring to big cog / big chainring, as will happen in the middle of the sequence. This is a significant movement in the sequential progression. We are moving across 9 cassette cogs and shifting between chainrings. The benefit of doing this electronically is that the action can be coordinated. Think along the lines of ‘when the rear derailer is has moved 5 gears, the front derailer will begin to move’. The actual motion is likely to be far more complex than this, but there is no doubt that the action could be coordinated electronically between the front and rear derailers. The objective would be to give the rider the sense that the gear change was smooth and effortless, and that their cadence was not adversely effected. It’s a serious challenge. I’m sure this action will be difficult to execute smoothly under any significant load. Indeed, the complexity of this action and the impact on riding could be such a serious issue that it may make this system impractical. But these are just the challenges to overcome, not to shy away from—it just takes focus. We need to move that rear derailer very fast across the cassette and time the front derailer movement appropriately. It seems possible, but I could also be naive.

Wanna give it a try?

Hey, if anyone would like to work with me to give it a try, send me a message at bhsimon |at| gmail |dot| com. We could get some Athena triples, do some work to remove the middle chainring and adjust the distance between the 30 and 52; then build our own cassette from individual cogs, and give it a try. We’d soon learn the outcome. I’m certainly keen and I’d like to collaborate with someone who is equally interested.

Other topics

(Semi)-Automatic shifting

Tacx VR Trainers and Kurt Kinetic Rock ’n’ Roll mechanism

Where is the weight on your bike?

Rear derailer hanger alignment

Tubulars and clinchers; weights and real-world measures


© Simon Paterson, 2011