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In the gear comparison section I described my experiences with what feels comfortable with various systems such as 7 speed derailleur systems, 10 speed derailleur on a road bike, a 3 speed Sturmey Archer hub, and a single speed bike (actually a cassette with derailleur but fixed due to issues with shifting). I show there what influence you get on your speed and how each system feels in comparison to the others. Partially inspired by a response from Kindernay about the step size in gears with their 7 speed hub that they recommended because their 14 speed hub was not in stock, I decided to analyse it from the foundations, which is something I haven't seen anywhere. Are there specific preferable gear step sizes? There are various opinions, and one I saw in a video was that 'the optimal number of gears is 3' in a video on youtube. But that is optimal only in a specific sense, not to ride as effortless, as comfortable, and as fast as possible. My aim here is to see what would be optimal if you ride a lot and want to cycle quickly.
On this page I analyse this from principles instead of just experience of what works, this means to analyse what the step size between gears can be or should be for comfortable cycling, in relation to the cadence with which you find it comfortable to pedal. The only factor from experience to affect the outcome is thus the range of cadences with which a cyclist feels it is pleasant to ride. I take possible variations of that into account at the end when determining the optimal number of gears.
It turns out that there is a logical reason why a certain gear step size is optimal. I determine that to be gear_factor = √(comfortable_cadence_high / comfortable_cadence_low), i.e. gear_factor ^{2} (= applying 2 gear changes) = comfortable_cadence_high / comfortable_cadence_low. It even makes sense in the later refinement I made of half of that cadence region being your preferred region.
I thought about the issue of how to determine the optimal and good enough gear step size and proceeded to write a lot of it down while doing cadence measurements for what I consider to be a comfortable pedalling frequency, on my trip in Poland in August 2022, which was when I got Kindernay's response about the step size in gears with their 7 speed hub.
On my trips in Poland (about 500 km total, 250 km around Wroclaw, 250 km from Bialystok to Siedlce), I regularly measured my cadence by just counting how many rotations I made with the pedals in 20 seconds (sometimes 60 seconds). I got to 70 rpm being about the absolute minimum, I prefer 75 rpm, and I found it comfortable up to ca. 90 to 95 rpm. You can do this too if you don't have a bike computer with cadence measurement. Once I got a Cateye Padrone digital with cadence measurement I checked all these measurements, and got to slightly lower cadences, but in winter so I expect them to be as I measured again in summer.
I suspect that the more you have trained to ride fast that you will like a higher cadence region in which you feel comfortable. So it could be that for lower speed cyclists and those who don't ride a lot, that their preferred cadence is far lower, possibly 60-75?
Another issue is that the higher the power the higher you want the cadence (unless e.g. you are tired, then cadence will drop). You often see people riding at very low cadence at low speeds of ca. 14 km/h, and that is because the required power is very low so pedalling is then almost effortless, and to give an even more 'effortless' feel a lower cadence means less movement of the legs. This is something I may add a bit more about later but it won't affect the outcome.
I would be interested in the comfortable pedalling range of readers to be able to more specifically nail down what the maximal step range of especially a geared hub should be.
If you want to help, just send me an email about what cadence range you prefer, how much you ride and what speeds you like to ride (on flat straight sections).
My definition for comfortable cadence: You can ride at these cadences, and it feels fine, not forced. If going higher your attention is drawn to the fast pedalling which already means it's not comfortable, on the low end you could for example feel it is not comfortable from the force in your knees. If your attention goes to your knees, it's not comfortable...
[ for me this range is ca. 70-90 in winter, ca. 75-95 in summer) ]My definition for preferred cadence range: This is cadence that you tend to ride, i.e. at that you like most of all. I.e. if you don't pay attention to your riding then look at the cadence at which you ride after a while. This will be a smaller range than the above range.
[ For me this is in winter ca. 80 - 85, perhaps a bit lower on the low end, in summer not yet tested. ]To email me go to the email page
First we need to know the cadence range in which you feel comfortable cycling. Then:
Now in a lot more detail my explanations and calculations:
I noted in the comparison section that I found that on the road bike with 2x10 Campa (the cassette was probably 11-25), it often didn't feel that I switched.
Let's compare some cassettes of 7,9,10 speed and check the gear ratios between them, and then look at hubs such as from Rohloff and Kindernay, pinion gear boxes and I will include a Sturmey Archer 3 speed hub as well:
One commenter with one of my videos on youtube noted he found the step size of the Rohloff hub, so 1.136x, too big. Well:
I would thus say, from my experiences, that as I have no issues with the 7 speed 12-28 and 9 speed 11-32 cassettes, that the Rohloff hub's step size of 1.136x is fine. In actually using the Rohloff hub I feel no issues in this regard either, but I have to say that most of my attention goes towards the fooking rotational shifter! ;-) I will keep the step size in mind on further rides and then give a final verdict on whether it would be useful it that were smaller. I will already say: A little smaller is perhaps better but not too much to give small ratios that result in not being sure by feeling whether you shifted as I had on my road bike (from feeling it was no different in one gear vs. the next which means the step size was too small). It would probably not be useful therefore if ratios were below somewhere in the range 1.10-1.12. I don't know the exact cutoff where to me it feels as if I didn't shift, I can't check on the bikes I have at the moment as I'd need a close teeth count cassette (11-21 cassette on a 9 speed bike would be a good test).
Update 2024-2-17: I made a 28 km bike ride with my Cannondale Touring with 3x9 gears, and on this ride I felt that one jump in the gears was too big. I wasn't thinking about gears and step size but I just noticed, stepped off, and noted that this was the transition between the 5th and the 6th cog on the rear. I looked up the number of teeth: 18 and 21 so a factor 1.167. I didn't have this feeling with the next higher and lower cogs of 16 (factor 18/16/1=125) and 24 teeth (factor 24/21=1.143). This confirms that for me up to about 1.143 feels ok, and a factor 1.167 is too big.
What do we need to analyse: Cadence, power, speed: Choosing speed to give a comfortable power needed, while staying in a comfortable cadence region. There are 3 possibilities depending on 1) what is a comfortable cadence range for you, 2) the step size of the hub or cassette.
From my testing in Poland, I estimate the comfortable range was about 75-95 being optimal, 70 still fine, more than 95 not so good. I will just take 75-95 at the moment as being optimal, I may change this in future after doing some tests as the Cateye Padrone digital has a cadence sensor too so I've been checking and will update this if needed. Currently, in January (winter), I feel that 75-90 is good, and when switching gears with the Rohloff hub, 70-75 is still fine, and I usually switch gears when I get to pedal at 70 rpm, I usually end up at 80-85 rpm. Not sure yet about the upper limit, where I feel I want to change gears. This is slightly lower at the upper limit than I found good in summer in Poland and this is logical because of the cold. So perhaps the 'comfortable pedalling cadence range' should be restricted a bit at the top end due to needing to be comfortable in winter and summer. I will do more measurements in February, then when it gets warmer see what changes.
More cadence measurements, update 2023-4-21: Looking at averages on the Cateye app of all rides, I tend to end up at ca. 70 rpm average for shorter rides, and 75 rpm for longer rides, but this includes all the time I ride without pedalling such as when approaching traffic lights, when going downhill, or just when coasting because of doing some testing. The actual average is somewhere in the range of 80-85 rpm as that is where I ride normally, only occasionally below or above it. The highest cadence the Padrone measured was 115 rpm.
Note 2023-2-15: Have a look at the much older section of gear comparisons in one bike (Gears: How much do gears (number and gear step size) influence your speed, and what is optimal?, about a bike with 3x7 cassette, 3 speed Sturmey Archer hub, and single speed), which was at a time I was riding about 8000 km per year and at high speed, often as fast as most road bikes but on my touring bike. Since about early 2022 I don't ride much due to having finished renovations, preparing to sell my house and living elsewhere and then sold my house which completely removed the need to go ride to other cities for groceries (as I lived in a very small town) and that affects of course my endurance ability and speed. Note that I don't ride for sport, only to get somewhere... So things are a bit different now, and in that section I noted that with the Sturmey Archer 3 speed hub that if I were to be riding at 32 km/h then it would mean ca. 84 rpm which I found too low at that speed... My preferred cadence was high, ca. 95 rpm at high speeds, and more than 100 rpm was doable but not comfortable. The preferred range in cadence for me at that time was a bit higher at lower speeds already, and it was a bit higher in the high end too, and just as now, it was higher the faster I went (this is still true but not so often noticeable as I don't ride much at 30+ km/h the last year), which is I think true for most people from what I've seen: The higher the power output the more you want it at higher cadence, probably because this means less force on the pedals.
Cadence = pedal frequency.
At the moment I will take:
- 'comfortable cadence range' (CCR) in my case: 75-95 rpm.
- cadence limits, 'CCmin' (for me 75), 'CCmax' (for me 95).
- very important: The factor from low to high which I call 'cadence step' (CS), for me CS = 95/75=1.27.
- gear step (GS) = step (well, factor) from one gear to the next gear. For the Rohloff hub this is 1.136, for 3 speed Sturmey Archer hubs this is 1.33. For cassettes and Nexus 7 and 8 speed hubs this step varies per gear.
1. In any given gear you can, without changing gear, stay within the CCR and change your pedal frequency to cycle at various different speeds that all feel good (if the power required is below what you find comfortable).
2. The speed you can achieve depends on the power that you can and want to supply.
Now imagine this:
1. You ride in a certain gear in your minimum of the CCR, so for me 75 rpm, this happens at a certain speed 'v1' [ so speed = v1 at cadence = CCmin ].
2. you then speed up your pedal frequency to go faster, up to the maximum speed without changing gear so while staying within the CCR. The speed you reach is then v2 = v1 x 1.27. Suppose speed 1 = 15 km/h, then speed 2 = 19.05 km/h. [ so speed = v2 = v1 x CS at cadence = CCmax ]
3. To go faster than 19.05 km/h, to 19.06 km/h, you would go outside the CCR if you don't change gears, so what you do is that you change gear to the next one, then adjust your pedal frequency to go 19.06 km/h.
4. Now note: If the gear step is a smaller step than the CS, this cadence will be in your CCR. If the gear step is bigger, it means your cadence needs to be adjusted to go to lower than is comfortable, namely like this:
4.1. GS>CS: Suppose the gear step is bigger than the cadence step: With CS =1.27, let's say GS = 1.33 (such as with a Sturmey archer 3 speed hub). So you ride 19.06 km/h but now in the bigger gear, and you need to adjust your pedalling cadence to ride 19.06 km/h, to CCmax/gear_step = 95/1.33 = 71.4 which is below CCmin. This means you need to ride faster to be in the CCR. You need to ride 20.01 km/h or more to be within CCR. This means that there is a gap in the speed range, namely 19.06-20.00 km/h in which you cannot ride with a comfortable cadence...
4.2 GS=CS: Suppose the gear step GS = the cadence step CS: With CS =1.27, this is what would be the case for me with the Kindernay 7 speed hub. Then you can ride at a certain speed at a given cadence, but at CCmax you switch to a higher gear (and at CCmin to a lower gear), and you get into a speed where you need to ride with CCmin (respectively CCmax), i.e. from the upper limit to the lower limit and vice versa. This means if you get onto a slight incline or slight change of wind and you want to go faster while at the upper limit CCmax or you want to go slower while at the CCmin, you will get out of range of CCR and you need to switch back again. So there is no margin range around certain speeds, where you can adjust speed/cadence for changing circumstances without having to change gear, while keeping within CCR.
4.3. GS<CS: Suppose the gear step GS is smaller than the cadence step CS: With CS =1.27, and GS = 1.136 of the Rohloff hub. Now you get into a cadence that is above the CCmin when switching down a gear. If you are pedalling at 15 km/h at your CCmin, go to 14.99 km/h and then switch down a gear, it means you need to speed up your cadence to ride that speed, which is CCmin x (14.99/15.00) x GS = 85.14 which is below CCmax (95).
This has an advantage over case 4.2 when CS = GS, namely that at the lower end you can slow down in case of a slight hill or a small change of wind without having to change gears and at the higher end you can speed up, then don't need to immediately switch gears down again if there is a slight incline or headwind, i.e. there are 2 overlapping ranges with gear 1 and a higher cadence + higher gear 2 + lower cadence. You have 2 choices of ranges to be in for the same speed, and you only need to switch once you reach the end of the CCR.
All in a picture for an overview:
From the above it follows that for me, where cadence step CS = 1.27 (at least in summer), a gear step size GS of 1.27 is not optimal and I decided against buying the Kindernay 7.
I've ridden for years in my youth with a Sturmey Archer 3 speed hub, and it works fine but the gear steps are nowhere near optimal. This is fine within the given restrictions but here I am trying to find the optimal situation and optimal gear step sizes and seeing what the impact is of using a non-optimal gear step size, while you presumably have other options to give better gear selection that may prevent those issues as I mention in situation 4.1 and 4.2. In those cases where the gear step size is too big there are issues where you feel you can't ride comfortably at certain speeds and certain speeds in 4.2 where you need to switch back and forth between gears.
From the above considerations in general it follows that gear step size GS should be smaller than the cadence step size CS.
Note further that what the cadence step size is depends on the environment (winter/summer) but also on power that you produce. A lot of people like to ride slowly in the city at 15 km/h with a low cadence, as that feels effortless, but the more power you put out, and the more you ride, the more a somewhat higher cadence feels better.
Then we have the minimal GS, which from my experiences should not be too small as then you won't feel enough difference in switching gears, which obviously means that the gear switch wasn't needed... The exact limit is not clear, but likely around 1.10-1.12.
From what I found useful with 7 and 9 speed cassette systems, I think the Rohloff's GS=1.136 is fine. It could be slightly lower, as per above, but I find it works well enough.
Summarising the above: With my cycling CS=1.27, this means GS should be smaller than CS, but not smaller than a factor of what I estimate to be somewhere in the range 1.10-1.12.
To be added: The 'comfort range factor': This is a factor of a certain size that says how much overlap there is in pedalling range at the speeds around a given gear at the CCmin and CCmax. I thought this should be at least about a factor 1.07 which is about 1/4 of the range in cadence.
This picture shows what happens with overlap in gears:
With the first picture I put the overlapping gears above/below the speed arrow, but to see (= to visually make you understand) what is going on, it is better to put each gear below the previous one, like a ladder, with speeds that can be achieved in that gear using a comfortable pedalling cadence, and realise that lowering the gear step size means the start of the next block is closer to the start of the current block in each case, and thus that the overlap changes.
It seems to me useless to have 3 gears overlap, it's not so that the comfortable cadence range is so small that you continually need to shift for small changes, only for big changes such as hills or speeding up after a traffic light.
Therefore the optimal gear step size in relation to cadence range is about sqrt(cadence range step) which is in my case ca. sqrt(95/75) to sqrt(90/75) so in the region 1.125 to 1.095 so you have 2 gears for all speeds.
More on gear step size: If GS is too small you not only get the feel that "did I switch, or not?" but you will need to switch more gears for switching to a low gear to a traffic light and for getting back up to speed, and for hills. Suppose there is a hub with step size of 1.10, then 4 gears up with the Rohloff hub = factor 1.665, but you need 5.35 gear switches with the hub with 1.10 steps.
If [ cadence_low ... cadence_high ] is the range in which you comfortably cycle, then the gear step factor of about √(cadence_high/cadence_low) gives an overlap of 2 gears for each cadence that you find comfortable. This gives you room to change your cadence according to what you expect might happen or what you would prefer, e.g. go to a lower gear and higher cadence if you expect to get into rough terrain, such as sandy/muddy road.
But there is a 2nd advantage to use this gear step size (and not bigger nor smaller): If you take the comfortable cadence range you will likely have a preference for a smaller range within that comfortable range, that is approximately half this range. For example in winter I like it a bit lower than in summer: About 70 for the low limit, and 90 for the high limit. And I find it fine to ride at these cadences, but when I ride I tend to end up in a range of around 80-85, perhaps a bit lower. This is approximately the centre of the cadence range, and almost half that range. This means that within this preferred range within the comfortable range, I can always get very close to that preferred range after switching gears and staying approximately the same speed. 90/70 =1.28, √(1.28)=1.134 = optimal gear step size (optimal in the sense that we then have 2 gears overlap everywhere). Taking that optimal gear step size then from the cadence of 85 we then get to 85/1.134=75 when switching to a higher gear, which is near the bottom of the preferred range within the comfortable range.
It could be that I'm an exception in that my comfortable cadence range is larger than with most people, and that thus that a step size of 1.136 of the Rohloff hub, though fine for me, may not be fine for others, but I doubt it. However, if you feel this way, let me know, I would be interested in ranges of cadences that others find comfortable. I expect that the factor cadence_high/cadence_low will be similar to mine, i.e. about 1.28 for what is acceptable, and likely about half that range for what you prefer most of all.
The above takes as an assumption that:
What range would you want in a hub, gear box, or cassette system? I will deal here with touring: I've done loaded touring and on very steep hills in Germany I sometimes went no faster than 6-7 km/h with 30+ kg of luggage in my panniers and in the backpack on top of the rear panniers. I would say for heavy loaded touring and going comfortably up mountains and steep hills, 6 km/h at 75 rpm would be the minimum so that you can ride at steep inclines at 4km/h with 60 rpm. But what is the highest speed at which you can then ride with CCmax?
Ranges:
I felt the Shimano Alfine 11 on the bike that I used in Poland in 2022 has a too small range, the upper end was ok, but I didn't get into high gears enough with touring. That bike is being used for city use so for that it was ok.
Max speed with given ranges, and CCmax = 95 rpm, max speed = (6/75)*95 * gear_range:
For touring with bags and heavy loads, I would only select: Rohloff 14, Kindernay 14, Pinion 12 or 18. A cassette system is also possible, say 3x9 speed which is cheap and has a reasonable range (though limited at the low end compared to what is possible with the other systems), but I am tired of changing chains and to a lesser extent cassettes, so when selecting a more expensive bike I would go for one with a hub or gear box and with belt, no chain. See also my chain wear listing on the chains/chain checker page.
Note that a downside to the Pinion and Rohloff is a rotational shifter. With the Rohloff it is heavy going, a lot heavier than with the Pinion (at least with the current versions of 2023, earlier versions may have been heavier going, not sure). There is the option of installing a Gebla Rohbox for the Rohloff hub to use trigger shifters. The Kindernay comes with trigger shifters which is far superior. Unfortunately the Kindernay 14 is still not available in Feb. 2023.
2023-3-22: I watched a video in 2021 on youtube from the channel 'Shifter' which stated "The perfect number of gears for your urban bike is three. Here's why.".
He starts by mentioning (ca. 2:23) that in the book "Just ride" by Grant Peterson the optimal number is gears is described as 8. He then states (ca. 4:23) that his view is that it is 3.
Both are wrong. I already deduced that the first is wrong in 2021 from my experiences on the page Gears: How much do gears (number and gear step size) influence your speed, and what is optimal?, where I came to the conclusion that for optimal speed you need around 11-14 gears.
Here for the optimal number of gears I'm doing it in a far more strict derivation using the analysis above of the comfortable cadence region, the gear range you want for travelling with heavy loads uphill too, and the optimal gear step size:
1. The optimal number of gears for relaxed city riding for the purpose of transportation is 2:
Here you need to take into account that optimal cadence is not really relevant for low power output. You can then ride at lower cadences. Higher (optimal) cadence becomes important with high power output.
I used to have a Dutch city bike which I used from when I was 12, which had a 3 speed Sturmey Archer hub. I was one of the few people actually using 3rd gear to ride fast. Generally people do not ride fast and they mainly use gears 1 and 2, rarely gear 3 with a tailwind to ride without effort at a low cadence.
2. The number of gears for a touring bike where you don't always ride fast but want to ride fast where possible to travel the biggest distance in a day on a trip that can be days or weeks, follows from my analysis about cadence and gear step size. With:
cadence_factor = CCmax/CCmin = 95/75 = 1.27,
we get:
optimal_gear_step = sqrt(cadence_factor) = 1.127,
which means if you want to ride at 6 km/h uphill at CCmin, and ca. 40 km/h at CCmax in the highest gear (to get as far as possible with a strong tailwind, after all you want to ride long distances so everything that helps is good, higher speeds than 40 km/h are unlikely to be useful), you need:
gear_range = (max_speed/min_speed) / cadence_factor = (40/6)/1.27 = 5.25,
Switching gears 'gear_steps' times should give the gear_range:
gear_factor ^{gear_steps} = gear_range,
i.e. gear_steps = ln(gear_range)/ln(gear_factor),
and:
gear_steps = gears -1,
So you need ln(5.25)/ln(1.127) = 13.87 gear steps. Round that so you need 14 steps from the initial ratio, and thus 15 gears in total...
You could perhaps lower the maximum speed for loaded touring but if you want to use a bike for multiple purposes then the given speed range makes sense. You could limit the speed to ca. 30 km/h in which case you can reduce the number of gears by 2. So 12 gears is possible assuming a comfortable cadence region of 70-90, but slightly limited, and thus not optimal.
The issue of comfortable cadence range is related to why the Moeve cyfly crank could persuade people to ride faster than they would normally... There are several factors that determine what a person finds comfortable in riding a bicycle:
1. Force on the pedals (a longer crank means less force, however with a fixed crank it means a longer pedal/foot movement (bigger circle that you need to move your feet) and thus larger leg movement which is felt as negative).
2. pedal movement curve (shortest is best).
3. cadence frequency within the CCR (I suspect this changes with the length of the pedal movement curve: the longer the curve, the lower the CCmin and CCmax). As the Moeve cyfly reduces the curve length, I suspect that not only will the force required to pedal feel lower but the cadence could be higher. Note that none of these factors influence factor 4, the power that a cyclist feels comfortable to put out, but it can persuade a cyclist to put out more power as the cadence and force limits are higher and lower respectively, i.e. they do not give a feel of "I don't like this" as quickly to a given cyclist (Moeve doesn't understand this but neither do the critics, as you can see from some comments with my video on this topic):
4. power within the range that is comfortable, i.e. such that you don't get exhausted, don't sweat, etc.
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Last modified: 2024-2-20