Some Number Crunching on Gears

27-speed is not equal to 27 gears. How’s that?

I'm using 27-speed only as an example but the principles apply to almost all bikes with front and rear gear sets. If you have read about gear ratios, diligently derived every ratio that your bike offers and imagined using every combo in sequence, the ratios may have come out looking like this (I’m doing it for the first time myself, so please don’t mind the showing-off):

The graph above is simply a visual that represents this table of gear combinations.

Notice how some of the results are very close to each other? Any values lining up almost horizontally on the graph represent similar ratios. So here’s the disturbing fact - not every gear combination actually gives you a unique ratio across the range of 27 combinations.

That, combined with the ‘forbidden’ combinations that result in cross-chaining, effectively kills off many of the theoretical 27 gears possible. Take a look at this table – it suggests a sequence of gear combinations which:

1. Follows a linear sequence of shifts, switching between front and rear shifts.
2. Avoids any serious cross-chaining.
3. Achieves a pretty smooth progression of ratios from the bottom of the range to the top.

And here’s the (ahem, beautiful) chart.

Somehow makes a lot more sense, doesn’t it? And therein lives the mantra of a Good Shift Pattern. If you count the number of shifts it takes to cover this range, it comes to 10 (11 combinations minus 1) according to my chart, but could be 11, max 12, if you insist on a couple of overlaps ;) But there it is - more with less! No overlaps, no cross-chaining and a progressive rise of ratios across the range. You're getting the whole meal of 27 gears with just 10 shifts. The table and chart above translates to a shift pattern shown in the figure below:

If you read the shifts along the rear cogs - it reads 2, 4, 2 shifts. This pattern could very well change to 3, 2, 3 as long as you don't hear any cross-chain rattle. The thing to remember is to time your front derailleur shifts in accordance with the rear sequence.

Side note: Why is the 2^nd chainring combined with 5 cogs and the others only with 3 each? That's because from the 2^nd chainwheel’s chain-line the chain can be pushed either 2 cogs in or 2 cogs out at the rear (middle fig. below) . But from the 1^st chainring you should only go 2 cogs out (left fig.). From the 3^rd chainring you should only go 2 cogs in (right fig.). You could shift 3 cogs but that might risk cross-chaining or ratio overlaps, neither of which will get you top marks in bicycle heaven. Click on the figure below for a better view.

Hope that helped. I'm no engineer, but I love this stuff. If you want to talk more about this crazy topic do leave comments, suggestions, corrections etc. Hope that this write-up has shifted your view on gear shifting, for the better.