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I’ve come across 2x12 and 3x11 triple cranksets. Can these systems necessarily provide more range than 2x11 and 3x10 @ > 700%?
Edit: My question is really what can practically be accomplished, with factors such as derailleur cage length and derailleur capacity. Do all such related factors of practicality mean each of these systems have the same range limit? If not, then what are the practical range limits?
Cage length doesn't directly dictate overall gear range, but under some safety constraints can dictate the overall gear range.
First, instead of "cage length", it's best to talk about "derailleur capacity", which correlates to cage length, but also includes factors such as placement of the derailleur relative to the rear axle and the size of the pulley wheels.
To see why, we can start with a 1x (single chain ring) system. In this case, the derailleur capacity tells us how how different the largest and smallest cogs on the cassette can be.
If we go to a 2x or 3x system, the capacity tells us the maximum range in (chainring teeth + cog teeth) we can access without making the chain too tight or too loose.
For a given cassette, the capacity thus determines the maximum difference between the chainring sizes that can be accommodated, and thus the maximum gear range if the system is required to function in all gear combinations.
If the rider can be trusted not to cross-chain the system into a big-big or small-small configuration, however, the range can be expanded so that capacity dictates the difference between [smallest chainring + smallest cog allowed with that chainring] and [largest chainring plus largest cog allowed in that chainring].
It’s difficult
What really limits you is derailleur capacity. Take for example a Shimano SLX rear derailleur with long cage (RD-M7000-10-SGS). It has 43 teeth of capacity. Let’s pair it with a crankset which has 36 and 22t chainrings. The crankset ”eats up” 36t-22t=14t of our capacity. So we have 43t-14t=29t of capacity remaining. There are no 10–39 cassettes, but a 10–40 would probably work fine.
The resulting gear range is 654%.
You could achieve >700% gear range by ignoring manufacturer limits. For example you could install a 10–50 cassette for 818% gear range. The chain with such a setup would either be too short in the big/big combination (very bad) or too long in the small/small gear combination (kind of bad).
Edit: Just noticed that the Shimano SLX rear derailleur only allows 11t small sprocket and 36t big sprocket. The other rear derailleurs only have 41t capacity which would reduce your gear range further.
Edit2: I should probably also add that the lowest speed with the above mentioned gear ratio is around 5.5km/h (at 75 rpm cadence) and the highest speed is 55km/h (at 110rpm cadence). That’s actually not that unrealistic or undesirable.
Let's see what I can come up with here.
Now for the math:
Therefore, using this setup gives you 1051% range!
Note that at the lowest gear, pedaling at 80rpm would only propel you at 4.7km/h. In this gear, pedaling from a standstill would also yield around 200ft∙lb (~270Nm) of torque at the rear hub even for my 140 pound body weight, so the bike would probably not enjoy this treatment.
No, not necessarily. It would be technically possible to have a super wide range 2x11 or 3x10 drivetrain, but at the cost of wide steps between gears.
As cassettes have gained more and more sprockets, they have offered more drivetrain options, allowing for either a moderately wide range with close jumps between gears, or a very wide range with moderate jumps between gears (for example, Microshift offers a 12-46 8-speed cassette, but the jumps are big).
So the number of available ratios is a soft limit in the sense that wide jumps between gears are undesirable, and a harder limit in the sense that it's difficult to move the chain up big jumps, but this wouldn't technically prevent you from having a very wide range with relatively few gears.
A hard limit is derailleur cage length. At some point, the derailleur would need to wrap up so much chain (and hang underneath a big enough sprocket) that the cage would be at risk of dragging on the ground.
Another range limit is the jumps between gears in front. Front derailleurs are fairly crude devices, and don't shift well with steep jumps between gears—if you make a bad shift under heavy load, you can break the derailleur. Current state of the art is 14t 16t steps between chainrings, although that has been cheated with some success. And the rear derailleur's chain wrap comes into play here as well.
I came across one combination that allows a 700% range, within reasonable specs deviations of commercially available parts: 36/26 chainrings and a 9/46 cassette (detailed in this question) — it could work in either 11 or 12 speed. But it's not what I did in practice: the implication of such combination would require to use components that only exist from one manufacturer (cassette and rear hub), which I don't like given the current supply situation.
With this combination, the way to circumvent the limit of the derailleur capacity is to "go smaller". On the upper range, having a cassette with 9 teeth sprocket allows you to keep a ratio of 4 with 36 teeth chainring. And the 26 teeth chainring gives you a ratio of 0.57, which is similar to a 30 teeth chainring with a 51 teeth sprocket on the cassette. The benefit of going smaller is that the effects of 1 tooth difference are more significant than with "larger" components. For example, using a 38/28 cassette gives you a 693% range.
