Gearing Choices

[Ted Durant]

This might be a fairly long post, apologies in advance, and just skip past it or delete if you’re not interested in another treatise on gearing.

I’m in line for a fancy custom bike and I’ve spent an inordinate amount of time (it’s good to be retired) working on the gearing. Part of the quest is that I want a normal-looking silver rear derailer. Given the direction the industry is headed, and the uncertainty over the fate of the OM-1, this has been keeping me up at night.

So, gearing….   I’ll start with the three basic quantitative decisions: 1) high and low gear, 2) how many cogs and chainrings, and 3) the spacing between each gear. In some sense you could say that (3) is dictated by (1) and (2), but a significant question is whether you want equal spacing across all gears or closer spacing in some and wider in others.

Starting with (1), we are immediately faced with how to measure a gear. Most people who spend any time with this still use “gear inches” which, while a quaint throwback to high-wheelers, is a reasonably intuitive metric and lots of people immediately know what you mean when you say you’re riding a 67” gear. For reference, in the 1980’s the standard 12-speed was set up with a 53/39 crankset and something like a 13-24 set of cogs in back. That’s a high gear (on 700x25c tires) of 108” and a low of 43”. 

St. Sheldon annointed the Gain Ratio as the preferred metric, and for a long time that’s what I tried to follow. It adds in the effect of crank length, and you can think of it as the distance the bike travels relative to how far your feet travel. That 80’s 12 speed, with a 170mm crank, has a high Gain Ratio of 8.1 and a low of 3.2. It’s clever and theoretically superior, and I know that a Gain Ratio a bit under 5.0 is my normal gear, but it just hasn’t taken root for me.

A simpler ratio would be the gear ratio itself, which doesn’t take into account wheel size or crank length. It’s pretty easy to calculate that a 52x13 is 4x, and 39x13 is 3x, and 39x24 is, well, a bit more than 1.5x. Different wheel sizes may or may not matter to you.

In my noodling on this I had a blinding flash of the obvious. What really matters is how fast (or slow) I am going. For that, of course, I need to know the cadence I am riding at. Everyone has (this is scientifically proven, seriously) a preferred cadence, and a comfortable range around that cadence. There is a pretty wide range among people of their preferred cadence and range. So, I decided on my comfortable cadence and range, and now I measure gears (taking into account wheel size) in the speed I am going at my comfortable cadence. 

The notion of comfortable cadence range then can play a major role in determining how much spacing you want between gears. For example, my comfortable cadence is around 87 rpm (aside - I’ve gone to shorter cranks), and the range is 75 - 100. An ideal shift for me is one that takes me from the limits of that range back to the center, which is a 14% difference. (footnote: I measure differences as the natural log of the ratio, happy to explain why but I don’t think it’s important here.)

Alas, we are limited to 1-tooth differences, and sometimes 2-tooth differences. And while a 10-11 change is 9.5%, a 14-15 change is 6.9%. The evolution to smaller smallest cogs in back has significantly increased the challenge to building a set of cogs with consistent differences across the range. If you want a 14% change, you’re kind of stuck down at the small end of the cogs, choosing between 10% or 20%. Even starting with a 12 tooth cog helps considerably, as the 12-14 jump is 15.4%, which is very close to ideal. On the other hand, starting with a larger small cog means having to go to even larger large cogs to get a desired low gear, or widening the gap in front, or going to a triple. 

Alright, so there are essentially two approaches to using multiple chainrings to arrive at a desired range of gears with even steps: crossover and half-step. In a crossover system, you try for even, acceptable steps between cogs in back, and when you run out of gears in back you cross over to the other chainring. In a half-step system, you try for even steps that are twice the desired difference and the chainring difference half of that. So, you are making rough adjustments in back and fine adjustments up front. A variation on that is to add a third, small chainring, known as “half-step plus granny”, in which you have a bunch of evenly spaced gears and then a handful of wider-spaced gears down low..

The development of higher cog counts in back has made crossover setups the standard. However, as John Allen has pointed out, the accompanying development of more flexible chains has made half-step gearing potentially a better option. If you were to build an ideal half-step system, say starting from 11 teeth and using 18% increments, you’d go from 11 to 34 in 7 cogs, 41 in 8, and 49 in 9. If you combined that with 44/40 up front, and like me you ride 650x38b tires at 75-100rpm, you would have 18 distinct gears in a range from 49.5.kph to 7.6kph with an average step of 9.3% and a standard deviation of steps of 0.9%. Good luck building a 1x system with that range, step size, and consistency!  And, good luck finding a 9sp 11-13-16-19-23-38-34-41-49 cassette! And, of course, if you want that setup you are forced to go with a butt-ugly modern derailer in back. The good news is you can use pretty much anything, including a stick, to shift up front!

That said, a large number of cogs in back can allow for something of a nice combination of half-step and crossover. Some people talk of a “1.5 step”, but I’ve evolved to a bit different way of thinking about it. In theory, because of the cubing effect of wind resistance as speed increases, you should want progressively smaller gear differences as the gears get taller for a consistent difference in pedaling effort. In practice, I find this is true, to some extent, but the more relevant factors are hills and wind. In a nutshell, sometimes I want bigger gaps, and sometimes I want smaller. What I DON’T want, is to have a big difference in gaps smack dab in the middle of where I usually ride. And, sure enough, on one of my bikes, I am usually right near where the cogs go 14-15-17. That’s gaps of 6.9% and 12.5% right next to each other, and it’s a jarring difference. 

So my new, patent-pending approach, is to think of the rear cogs as essentially two ranges, close steps on the smaller half and larger steps on the larger half. If I’m in conditions where I want small steps, I stay on the smaller half; if I want larger steps, I stay on the larger half. In practice it’s very similar to a “half step plus granny” setup. It turns out, I have a bike that has an almost perfect example of this setup, and I have subconsciously been using it this way.

An important part of this setup is that you cannot use the typical mindset of “maximize the drop from the big ring to the small” in current 2x setups. If you do that, you will probably take the gearing too low for the small steps to be useful. On the setup I have that works well, I chose to make the chainring jump less jarring than my other bike. A 42/26 combo is a giant 48% change. If I don’t shift at least two gears in back in conjunction with a front change, my cadence has to change way beyond my comfort level. A 44/32, on the other hand, is 32% and far more manageable. I have that on a bike with 650x48b tires and 11-32 11sp in back. That cassette is 11-15 in 1-tooth increments, then 17-32 in relatively even steps. If I cross over from the 44x15 to the 32x12, I have 9 gears that have an average 7.9% step between them (sd 0.9%). Staying on the small ring I have 7 more gears at an average 12.6% gap (sd 1.3%). Additionally, I can ride in the large chainring in the 44x17 at 28.7kph or 44x19 at 25.7 kph, the heart of my usual speed, and have consistent 2-tooth changes either direction in back. Or, I can ride in the 32x13 at 27.3 or the 32x14 at 25.3, with nice 1-tooth changes in either direction. The range total range is 9.6 to 51.0 kph for me. I’d want to get that down some if I was carrying a bunch of stuff off road in the mountains, but for riding around here that’s more than enough range.

Back to my dilemma … the large cog of 32 and total wrap of 33 teeth in that setup are easily managed by a SunTour Cyclone GT derailer from the late 70’s. Be still my beating heart! No ugly modern derailer necessary! 

I still think a 2x7 half-step setup, with 18% gaps in the rear and 9% up front, is a killer setup for most road and gravel riding that doesn’t involve, say, more than 10% extended climbing grades. You’ll have to build your own cassette, though. A 2x11 or 2x12 two-range setup as I’ve describe above, though, is very practical and pretty widely available. 

Spreadsheet available upon request.

Ted Durant

Milwaukee WI USA

[Piaw Na]

I'm a big fan of half-step + granny for 7-speed rear cassettes and freewheels. I think I even wrote an article about it for the Rivendell Reader at one point (good luck digging it up!). What killed it for me was once cassettes got to the point where constructing your cassette was no longer supported or too much work, it was no longer practical.

Around here in the Bay Area, I simply decided to go for the lowest gear possible, and live with suboptimal flat riding gearing. The reason for this is even if I can climb a 20% grade when fresh on a 34x34 drivetrain, there will come a day when I have to climb that grade tired, or when carrying a load, or when I just not feeling like working that hard. Going 1mph slower on the flat by contrast just doesn't bother me that much. Just the other day I took my wife on a ride up the Wallace Stegner trail. We'd hiked that trail a couple of times but to my surprise my computer read a 20% grade. Her ebike had to work to get over it and I got into my 40x51. Having that on my bike makes me more likely to ride trails like that. Those who live in places where 20+% grades are unusual or cannot be found probably won't bother with my low gears.

[Patrick Moore]

Piaw: It's easy and, thanks to AliExpress, relatively cheap to build your own cassettes from loose parts -- at least, perhaps not for really huge cogs. But a half step + granny could give me, anyway, nice close cruising gears in the 75" to 60" range plus a downhill gear or two and some low bailout gears.

I did this long ago for a commuter with 48/45 or 47/44 rings and a 7 speed cassette, something like 13-32, half-stepping (more or less) the middle 5 cogs with cruising gears in the middle, and using the small for a downhill gear and the big for a bailout gear:

25" wheel: 

	48	45
12	100
13	92	87
15	80	75
17	71	66
20	60	56
24	50	47
32		35

BTW, this shifted very nicely from hoods, ramps, and hooks with Kelley Take-Offs, on pavement; would not want KTOs on bumpy dirt.

Generally speaking, though, with 9 cogs or more I prefer crossover, and  I'll trade top high and bottom low for close middle ratios; with a 10 speed cassette giving many more possibilities and the new knobby 50 mm Oracle Ridges requiring slightly lower sandy dirt gearing,  my Matthews "road bike for (sandy) dirt" has a sub-compact plus granny:

28 1/2" wheel:

	44	28
14	90
15	84
16	78
17	74
18	70
19	66
20	63	40
22	57	36
25	50	32
28	45	29

[Bill Lindsay]

Ted

So, you have settled on what your gearing and derailleur choices will be?  If yes, what exactly will they be?  What rear wheel OLD will you be using?  Will it be a cassette rear hub or a freewheel?  How many cogs in back, what cogs?  If it's a contemporary 10 or 11speed cassette width, have you confirmed your Suntour RD will sweep that horizontal distance?  What shifters will you use?  

Bill Lindsay

El Cerrito, CA

[Ted Durant]

On Apr 3, 2024, at 11:54 AM, Piaw Na <pi...@gmail.com> wrote:

I'm a big fan of half-step + granny for 7-speed rear cassettes and freewheels. I think I even wrote an article about it for the Rivendell Reader at one point (good luck digging it up!). What killed it for me was once cassettes got to the point where constructing your cassette was no longer supported or too much work, it was no longer practical.

I remember that, and probably could dig it up! And, yeah, you really have to build your own. 

Those who live in places where 20+% grades are unusual or cannot be found probably won't bother with my low gears.

This is super important and where “YMWCV”! I should have prefaced my entire treatise by making it clear that most of my riding is in SE Wisconsin on mostly paved roads and crushed limestone trails. The limestone trails are abandoned railroad beds, so rarely exceed 2% grade. We have only a few hills that approach 20% and they are quite short. Mostly it’s rollers that are 5%, occasionally 10%. The wind, on the other hand ….  

Riding in the LA area, especially trying to go up avg 10% dirt/rocky trails that go on for miles, my gearing needs are somewhat different. One of the thoughts I’m keeping in mind as I spec a new bike is flexibility … if I travel with this bike, will I be able to easily modify the gearing/tires/fenders/racks/lighting to match the intended conditions. But then, I also have a few different bikes, so ultimate flexibility might not be paramount :-)

On Apr 3, 2024, at 12:33 PM, Bill Lindsay <tape...@gmail.com> wrote:

So, you have settled on what your gearing and derailleur choices will be?  If yes, what exactly will they be?  What rear wheel OLD will you be using?  Will it be a cassette rear hub or a freewheel?  How many cogs in back, what cogs?  If it's a contemporary 10 or 11speed cassette width, have you confirmed your Suntour RD will sweep that horizontal distance?  What shifters will you use?  

All TBD, but I can confirm that a Vx GT and a Cyclone MkII GT will cover 9 -11 cog cassettes. In fact, a Cyclone MkII GT executes flawless index shifting on a 9-speed 12-36 cassette using Shimano 10-speed bar end shifters. I’ve posted elsewhere about this … SunTour derailers should index perfectly on a Shimano-SRAM n speed cassette with Shimano n-1 speed shifters, where 7<=n<=9. By “index perfectly” I mean that the horizontal derailer movement is exactly the right amount given the cable pull. An odd and interesting historical math artifact.

What is also important is related to that. SunTour derailers have a high actuation ratio, meaning lots of horizontal movement relative to cable pull. As a result, “normal” shift levers are able to move a SunTour derailer across 8-12 cogs where other derailers would require a shift lever with more cable pull (a larger diameter drum around which the cable is wound). SRAM and newer Shimano derailers have much lower actuation ratios, driven (I hypothesize) by a desire to increase the amount of cable pull per shift and, consequently, increase the tolerance for imperfections in cable movement. Campagnolo, interestingly, _increased_ the actuation ratio slightly when they went from “old” 9 speed to “new” 9 speed and later. Always marching to their own beat, those Italians.

My choice of shifters will depend on several factors, including the gearing, the derailer, whether I feel indexing is important, and whether I want to deal with the additional complication of handlebar-mounted shifters on a bike that might get rinko’d. 

Ted Durant

Milwaukee, WI USA

[Nick Payne]

I've attached a gearing spreadsheet I use, which allows me to easily compare three different gearing setups in the one sheet. It's in ODS (OpenOffice) format, but I believe that Excel can open and read that format. It also shows speed in each gear at a specified cadence - I have speed as KPH because we use metric in this country - if you want MPH values, just modify the speed formulas to divide the KPH values by 1.609.

Nick Payne

[Bill Lindsay]

"All TBD,"

Even OLD is TBD?  135?  130?  126?  120?  something else?  I'm super into 120 and 126 lately, so I'll be interested to hear it if you are also considering a legacy OLD.

BL in EC

[Ted Durant]

On Wednesday, April 3, 2024 at 4:29:06 PM UTC-5 Ted Durant wrote:

 I can confirm that a Vx GT and a Cyclone MkII GT will cover 9 -11 cog cassettes. In fact, a Cyclone MkII GT executes flawless index shifting on a 9-speed 12-36 cassette using Shimano 10-speed bar end shifters.

After more experimentation I have to retract that. The Cyclone MkII GT covers 9, but 10 is just a bit too far. In theory it’s less than 1mm extra distance. In practice, it probably depends on the specific cassette and where that innermost cog lies relative to the face of the derailer hanger.  On a VO hub with a Shimano HG body, on my Terraferma, a Shimano 9-sp 12-36 worked okay, but a Shimano 10-sp 12-28 requires just a bit more sweep.

And I had trouble getting a new Silver (1) shifter to hold its position during the test. Beeswax or Loctite might have helped.

[Ted Durant]

On Wednesday, April 3, 2024 at 9:54:49 PM UTC-5 Bill Lindsay wrote:

Even OLD is TBD?

Yes, but I don’t have any specific requirements there. I don’t expect chainring clearance or chain deflection issues to cause me to lean in a particular direction. However, availability of compatible  components will be a factor.

[Bill Lindsay]

I admire how the entire build hinges on a rear derailleur that looks good, first and foremost, and everything else will fall into place after that.  ;-)

BL

[Peter Adler]

As Snoopy said long ago: "Some of us prefer to sacrifice comfort for style".

Peter "guilty more often than I care to admit" Adler

Berkeley, California/USA

[Ted Durant]

On Friday, April 5, 2024 at 3:17:24 AM UTC-5 divis...@gmail.com wrote:

As Snoopy said long ago: "Some of us prefer to sacrifice comfort for style".

I’m not comfortable riding a bike with an ugly derailer so I don’t have conflicting objectives.

:-)

[george schick]

I'm apparently of the same ilk as Bill.  I'm using a Shimano Crane RD (their predecessor to the Dura-Ace line) on a Fuji Finest of the same time period, very early 70's, and it looks just fine on there.

[Luke Hendrickson]

Bill,

I run the gearing that I do (13-34 7s with 46-34-22 up front) solely because it allows me to run my Suntour XC three-pulley rd! Admittedly the 45T chain wrap is nine above the stated 36T maximum but still :)

- Luke in San Francisco

[Ted Durant]

On Saturday, April 6, 2024 at 12:21:15 AM UTC-5 Luke Hendrickson wrote:

I run the gearing that I do (13-34 7s with 46-34-22 up front) solely because it allows me to run my Suntour XC three-pulley rd! Admittedly the 45T chain wrap is nine above the stated 36T maximum but still :)

Bravo! That derailer gets no love from Disraeligears but it has a warm spot in my heart. Wacky, clever engineering.

Also, an update here … I added a pristine Cyclone GT to my collection. I decided to put the SunTours on my Breadwinner, which has an 11-speed setup, to see how they’d manage the required sweep. They don’t. One of the issues on that bike is that it’s a 140mm through-axle rear, and the first cog is a pretty long way from the face of the derailer hanger. I did a quick look at some other bikes, and it appears the derailer hanger-to-first cog distance varies by quite a bit.  That will definitely have an impact on whether an old derailer has enough sweep for a given setup.  

[Ted Durant]

On Friday, April 5, 2024 at 7:44:35 PM UTC-5 george schick wrote:

I'm apparently of the same ilk as Bill.  I'm using a Shimano Crane RD (their predecessor to the Dura-Ace line) on a Fuji Finest of the same time period, very early 70's, and it looks just fine on there.

I’m working from a much more modern source of inspiration … my 1979 Fuji America.    :-) 

[Ted Durant]

On Wednesday, April 3, 2024 at 12:16:23 PM UTC-5 Patrick Moore wrote:

Piaw: It's easy and, thanks to AliExpress, relatively cheap to build your own cassettes from loose parts

Thanks to some coaching from Patrick and Garth, I sourced from Ali Express the necessary cogs and spacers to build a 7-speed 11-13-16-19-23-28-34 cassette. It looks pretty snazzy with the red spacers and silver cogs. It's not going to win any awards for light weight, but I mounted it to a standard 8-11 speed freehub (using an extra spacer and cog to fill the gap), and it shifts beautifully with a Cyclone GT rear derailer and Silver downtube shifters. I didn't get any ghost shifting, but I also 1) tightened the shifter a bit and 2) didn't stand on the pedals. I had 39 and 42 chainrings in inventory, so I mounted those, as well. Ideally I'd have a 4-tooth difference up front, but this is good enough to test the hypothesis.

I only did a quick neighborhood loop - flat, but with a fair amount of wind. My initial impression is that the steps are too small. Seems crazy, I know, but 10% steps feel small, and the ~20% steps in back feel only slightly too big. It feels amazing, though, to shift two cogs in back and get a huge change in effort. I played around with some alternatives, and I think 12.5% up front and 25% in back would be better for general riding (typical Wisconsin hills and wind, not trying to set Strava PRs). Any more than 6 cogs in back, though, and you'll be going to either a derailer dropper or a newfangled, ugly derailer with a big max cog clearance. If you're willing to go that route you can build a gearing setup with a massive range and perfectly even steps out of a 2x7.