For bikes with a front derailleur, I've noticed that the gearing ratios of most bicycles are not linear, and there is an odd "overlap" between those power ratios as you switch from one front gear to the other.

OK, it's hard to explain, but this chart shows what I mean:

https://i.stack.imgur.com/g3N73.png

This is just an example and actual ratios can vary, but this illustrates some extremely common problems:

  • The ratios aren't spaced out consistently
  • To go down through all the gears from highest to lowest, you will find yourself switching front gears several times back and forth while simultaneously switching the rear.
  • Many of these gears are so close as to be redundant.

So I'm just curious: why are the gears set up in this way?

  • 4
    Having triple chainring at the front was never an elegant solution, rather it was a successful hack to cover gearing range needed for MTB applications. These days, no high-end groupset comes with a triple at the front; everything is either 2× or 1×. Entry level groupset can still be seen with triple front chainring designs. – Grigory Rechistov Jun 13 at 17:20
  • 2
    What is important is not the number of teeth difference but the ratio. Going from 12 to 13 is the same as 24 to 26 or 36 to 39. The 12 to 13 shift is smaller than the rest, but 11 to 13 would be too large in this system. – Ross Millikan Jun 14 at 5:00
up vote 28 down vote accepted

Having an overlap between the ratio ranges available with each chainring means you don't have to use your front derailleur as much. Based on your understanding and expectations of the terrain and conditions ahead, you choose a chainring which gives you access to a useful set of harder and easier ratios.

The cassette ratios are spaced to achieve a vaguely consistent %-difference between adjacent gears, with the limits that you can't have fractions of a tooth and for smooth shifting the derailleur's upper pulley has a minimum and maximum distance from the teeth, so the derailleur's geometry needs to move that pulley through an arc that echoes the arc of the cassette.

Having ratios closer together means when accelerating you don't have to "spin out" one gear to avoid getting "bogged down" in the next harder gear, and when climbing you don't lose momentum with a sudden loss of resistance on each change down a gear.

Alternative 1: Internal hub gears

e.g Rohloff 14 speed, Shimano Alfine & Nexave 11,8 or 7 speeds. Low maintenance but heavy and make removing and fitting your rear wheel more difficult.

Alternative 2: Single-chainring MTB setup with a wide-ratio cassette

10 and 11 speed systems are available with smallest sprocket 9,10 or 11 teeth and largest sprocket between 40 and 50 teeth, for an overall ratio difference from hardest to easiest ratio of 4:1 - 5:1. The derailleur needs to be designed for the steeper cassette angle, of you can use a hanger extender (e.g the GoatLink) to move it down so it clears the largest sprocket, but in the hardest gears the upper pulley may be too far from the teeth to shift nicely.

  • 12
    Well put - to rephrase your first paragraph, the intent of the 3 x 7 gearing arrangement show in the question is NOT to have 21 usefully spaced ratios. Rather, it is to have three "sets" of 7 ratios each, with each set intended for a different general use. – dwizum Jun 13 at 16:36
  • These days, all three major bike gear manufacturers (SRAM, Campagnolo and Shimano) sell or at least have announced 12 speed systems, with ranges up to 10—50 and 10—52. Instead of increasing the range, Campagnolo uses 12 gears to decrease steps between adjacent gears. – Grigory Rechistov Jun 13 at 17:16
  • 2
    Alternative 1b: stick the gear in the bottom bracket. – gerrit Jun 13 at 18:55
  • I once saw a German-made internal hub gear being advertised that was boasting 100 gear ratios. Needless to say it was exorbitantly priced, but an impressive piece of machinery nonetheless. – Perkins Jun 14 at 0:10
  • goatlink and radcage's are a hack to get derailleurs deisgned for max. 36 tooth cassettes working on wide range cassettes. Derailleurs designed for wide range cassettes work fine. – mattnz Jun 14 at 4:05

The ratios aren't spaced out consistently

Actually, if you look at your diagram and exclude the smallest and largest cog on the cassette, the gears are more or less evenly spaced. What unevenness there is is an artefact of the requirement for whole-number ratios. Sure, replacing the 15t cog with a 14.5t cog would give better spacing between the 17t and 13t but there's no such thing as a 14.5t cog.

Typically, you wouldn't use the smallest cog, except with the large chain ring, or the largest cog except for with the small chain ring. This is known as cross-chaining and it puts the chain at an awkward angle where it tends to rub against the front derailleur and is generally inefficient, and you'd be better off using a different chain ring.

To go down through all the gears from highest to lowest, you will find yourself switching front gears several times back and forth while simultaneously switching the rear.

That's not how you use derailleur gears. Rather than thinking in terms of a sequence of 21 gears, you should think of three sequences of seven. Any time you run out of gears in one set, you move to the next chain ring and adjust the rear gear by a couple to compensate. So, in practice, shifting up through the gears would look something like (read left-to-right, top-to-bottom, as usual)

28:28 28:24 28:20 28:17 28:15
                  38:17 38:15 38:13
                        48:15 48:13 48:12.

Note that, unless you shift front and rear simultaneously, getting from 28:15 to 38:15 will involve spending a moment in 38:15 or 28:17. I'd make both shifts while turning the pedals without putting any power through them so it doesn't make much difference what order the shifts happen in.

Shifting back down again would probably look something like

48:12 48:13 48:15 48:17 48:20
                  38:17 38:20 38:24
                        28:20 28:24 28:28.

Notice that only about half of the possible combinations get used in each shift pattern. By the way, you wouldn't sit down and learn these sequences: they're just what happens when you change at the back where possible, and change at the front only when you need to.

In practice, if I was accelerating from a stop, I'd be much more likely to just shift one derailleur at a time and do something like

38:20 38:17 38:15             (accelerating fairly hard)
            43:15 48:13 48:12 (taking it easier; the first of
                               these is a big jump in ratio)

Many of these gears are so close as to be redundant.

This is the same misunderstanding as above.

  • In your last case you might actually go 38:15,48:15 (not apply full power), 48:**17** (immediately, a recovery shift), 48:15 etc. And one thing that's not as obvious to everyone as I reckon it is to you, is that it's the ratio between consecutive ratios that matters i.e. the step from 12 to 13 and the step from 24 to 26 are the same. +1,a very nice explanation – Chris H Jun 13 at 16:32
  • That would be essentially the first sequence, just starting on the middle chain ring. I added a note after the first about the double-changes. – David Richerby Jun 13 at 16:45
  • Got it, I was reading the overlaps in your example as alternatives (too much scrolling on this screen to keep track of what text corresponds to which example) – Chris H Jun 13 at 16:51
  • @J... Yes. Three-quarters or more of my answer is spent addressing that misconception. – David Richerby Jun 14 at 15:47
  • I'd say that with a 9-speed cassette one avoids the two cogs on the opposite side of the chain ring and both extreme cogs on the middle ring, unless one expects to switch off of them in a few seconds again. – Peter A. Schneider Jun 15 at 12:19

It used to be, back in the days of ten-speeds, that the tooth counts were carefully chosen so that one could shift a "half gear" by, say, shifting the rear two cogs to the right and shifting the front one cog to the left. Such a design allowed fine tuning of the gear ratio, while still allowing the gears to span a broad range.

However, when rears went to 6, 7, 8, 9, and 10, and fronts went to three, such design was not only incredibly difficult but also confusing and unnecessary -- simply shifting the rear up/down one cog was as fine of a control as most cyclists needed.

  • There was another (and perhaps simpler) 'half-a-gear' solution: closely-spaced chainrings. I had a road bike (circa 1968) with chainrings 48 and 51. This 3-tooth step approximately equals half a shift (~1 tooth) on the rear. – Zeus Jun 14 at 9:40
  • @Zeus - Yeah, but that didn't give you as much range. – Daniel R Hicks Jun 14 at 10:58
  • Half step where alternate shifts were chainring only and chainring-and-one-sprocket was the standard setup though, with a triple if you needed more range: sheldonbrown.com/gear-theory.html#halfstep – armb Jun 15 at 12:13

The overlap in gear ratios that are available with each chainring is mainly a consequence of the practicalities of building a derailleur gear system. I.e., how many sprockets and what sizes can be fit on the rear hub and on the crank, but it also has useful consequences.

Using the example you give above, the cassette has only 7 sprockets and a narrow range of sizes: 12-28. Picking a chainring size that gives ratios useful for most riding conditions - 38 teeth, we are left with insufficiently low and high ratios, so we have to add smaller and larger chainrings to provide them, which results in lots of overlap of ratios. Two chainrings could have been used but that would require the rider to constantly shift between chainrings when using the most commonly used 'middle' gear ratios.

As derailleur technology has improved, more sprockets can be added to the rear cassette, with a wider range of sizes. This allows having two chainrings because they can both provide coverage over the most commonly used 'middle' gear ratios.

The logical extension of this progression is of course the '1x' setups that have been appearing over the last few years.

Small gaps allow you to pedal at a suitable rate for your legs and the speed you're doing.

After breaking a rear gear cable, I did 70+km on a wide-ratio 3-speed recently. It was quite hard (but I was very glad I had 3 chainrings). I kept wanting a gear a bit higher or a bit lower, but only had a lot higher/lower.

You also don't want to have to change down a little by changing down a chainring and up all your sprockets, if you're climbing a hill.

  • I see the unstated answer about big gaps being bad, but someone's flagged this answer. Want to try rewording it ? – Criggie Jun 14 at 19:21
  • @Criggie I'm surprised by that, but obviously it's not clear enough for someone. – Chris H Jun 14 at 21:07

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