Riding doesn’t have to be difficult and exhausting; it all depends on your gears. If you’re a contender in the Tour de France, don’t waste your time reading this. This page discusses bicycle gearing for the rest of us.
The terminology is perhaps somewhat arbitrary, but it’s important to be clear and consistent. Let’s call the rear gears –the cassette on the freewheel – cogs; sometimes they’re also known as sprockets |
In front, on the crankset, we’ll use the term chainring. When we compute ratios, or percentages, we will always put the larger number in the numerator. We could put the smaller number on top and reach the same results, but the numbers would be just slightly different. |
All right! Let’s get on with it!
Gearing can make a big difference in the pleasure and effectiveness of cycling. With a good selection of gears, you’ll enjoy the fact that the hills are prettier than the flatlands, you’ll be able to deal with headwinds when they happen, your knees will get stronger instead of weaker, and you’ll ride further and faster before you run out of steam. You’ll discover that you were stronger than you thought. Even if you only ride around the neighborhood at a leisurely pace, you’ll find you enjoy it more. And who knows? – you may get addicted, and start doing more riding!
Most bicycles, and most riders, are geared too high. This means you’re using the anaerobic muscles for pure strength, instead of the aerobic muscles for endurance. The anaerobic muscles exhaust their energy stores early on, lose their strength, start to hurt. The aerobic muscles just keep going. And the difference in knee stress is important, especially for those of us who used to be runners – cycling can be either the best, or the worst, thing for bad knees, depending on how hard you push.
With the right gearing, you’ll not only go further, but also faster. You’ll start taking it for granted that not very many people are going to pass you on the uphills, and those who do will be the 20-year-olds with the perfect knees.
Pedalling cadence is partly a matter of habit. But there’s also one important aspect of the bike itself: foot restraints. When you’re pedalling slowly, there’s weight on both pedals all the time (another waste of energy), and your feet stay on the pedals through natural friction. Once you pick up the pace, you’ll naturally find that there’s less weight on the rising pedal – in fact, you’ll want to kick forward, rather than pushing down – and your foot will come off the pedal if it isn’t restrained.
Now I’m certainly not a clipless pedal bigot. I don’t even insist on tight-strapped toe clips. Open, loose toe clips – you can even remove the strap entirely – work perfectly well to hold your foot in place, especially as you develop the habit of kicking forward. Easy to get into, easy to step out of.
What’s a good cadence? 100 rpm is a good number (this is sitting – you’ll crank much slower when you stand out of the saddle). 90 is fine. 80 is ok, but don’t plan for it – there will always be hills steeper than you expected, and it’s nice to have a few rpm in reserve before the knees explode. Get a bicycle computer that displays cadence, and get used to the feel. After a while, you’ll be spinning at a good and comfortable rate without needing the cadence display, and next time you buy a computer, maybe you won’t want to bother. If you’re pushing, gear down! It should be an easy spin.
Ok, that’s the rider. Now for the bike. Why are bicycles geared too high? Because that’s what people buy:
“How fast can I go?”
“Man, with this gearing?! You can get it up to 50 miles an hour!”
“Great! I’ll take it!”
But most of your normal riding will be at 10-15 mph, or maybe 14-18 as you get stronger and spin faster. If you like hills, you’ll spend hours climbing at less than 10 mph – and minutes going down the other side. Gear ratios are a finite resource – where do you really want them? Above 30 mph, take a rest, let ’er roll. Going down the hairpin roads of the mountains, your problem isn’t going faster – your problem is brakes!
Another problem with most bikes is that the gears are redundant. That is, for some combination of small-small (front and rear), there’s also a combination of large-large that gives pretty much the same ratio. So you’re wasting an opportunity. What you’d really like is an infinite range of gear choices (well, maybe not above 50 mph!), with infinitely-fine steps between gears. Why?
Go back to the human engine powering all this. If you’re comfortable spinning at 100 rpm, for example, you’re likely to feel pretty good in the range 90-105 rpm. That’s a range of about 15%.
In contrast, your car’s engine runs happily and efficiently over the range – pick your own numbers – 2000-5000 rpm? 1800-6000 rpm? At least a range of two or three to one. And your car has what? – 5 speed gearing? The point is clear: your human motor doesn’t have a wide range of speeds; instead, you want lots of gears on your bike, spaced close together. Your legs will tell you soon enough: nothing is as frustrating as to be spun out on one gear and find you can’t comfortably push the next higher gear.
Finally, a quick note about what’s possible. Start by figuring out what you’d really like. Then talk with a bike shop, or check the catalogs or the web, to find out what’s commercially available. Some ratios don’t work numerically – we can only get gears with an integer number of teeth. Other combinations don’t work for mechanical reasons, going beyond the limits on combining really big and really small. We’ll talk about some of the constraints below, but the available components change constantly. A good bike shop can also tell you about mix-and-match possibilities that you won’t learn about from the catalogs.
If you’re buying a new bike, check the gearing before you buy. Chances are, it isn’t what you really want. But the bike shop will change it for you, if you ask. The charge depends on how badly they want to sell you the bike; something small such as swapping a chainring may well be free. In any case, it won’t cost very much, and it’s well worth it. Get good gears and you’ll be spinning them for a long time! Bad gears, and the bike will collect dust in the garage!
If you already have a bike, you can upgrade. Best case, you perhaps need a new chainring up front. Worst case, it could cost a new crankset, new front derailleur, new rear hub, new rear cluster, new rear derailleur, new chain and new shifters. If it’s a fine frame, even this set of changes could be worthwhile. Don’t give up until you try. Even if you ultimately decide to replace the whole bike, you still need to understand what to look for in the next one.
Let’s do a little background work. Start by thinking about your capabilities and ambitions. Where do you want to ride? If you like the mountains, you’ll make decisions different from those for flatland country with its everlasting headwinds. It’s ok to upgrade an existing bike to deal with today’s ambitions. If you get really hooked and decide to do loaded touring in the Sierra Nevada (highly to be recommended, by the way), you can look at further upgrades or even a new bike, later on.
How strong are you, really? Be honest – in the office on Monday morning, you can be as macho as you like, but what really matters is what your legs tell you as you work your way up that last hill late Saturday afternoon. I don’t mind admitting that I have the lowest granny gears I can find, and I use them.
The first step is to decide what speed range you want to be able to cover, and what range of cadences. Here are my own preferences – adapt them or adopt them as you like. I’d like to be able to deliver power up to 32 mph at a cadence of 105 rpm. Faster than that, I’m content to let ’er roll. This is line A on the nomograph:
At the low end, I’d like to be able to maintain a cadence of 85 rpm down to 5 mph (line B). Just as a reference, I typically ride in the range 14-18 mph with a cadence of 90-100, lines C-C'.
If your low-end ambitions are around 10 mph – flat country with headwinds – you can probably do just fine with a double crankset. We might ask for a low end of 10 mph at a cadence of 90, as shown by line D.
For a low-end well below 10 mph, there’s no question: we want a triple up front. There’s nothing like Granny in the mountains. Don’t leave home without her. Assuming we’re going for the granny, the nomograph says we’d like a high-end gear ratio of 102 inches, a low end of 20, and a comfortable mid-range in the 50s and 60s. Pick your own numbers, draw your own lines!
What do the gear-inch numbers mean? Viewed one way, they really don’t mean much of anything, any more than miles or pounds means anything. They’re just a convenient unit of measurement that helps you compare ratios. In fact, the number is the equivalent diameter of a 27-inch wheel. 54 gear-inches, for example, is really a 2:1 ratio that effectively doubles the diameter of the physical wheel. For 26- or 24-inch wheels, the numbers scale accordingly: a 2:1 ratio becomes 52 or 48 gear-inches, respectively. (Think of the old boneshakers: they had gear-inch sizes around 60 inches because that was the actual size of the wheel!)
On road bikes, the off-the-shelf crankset is likely to have something like 52-42 or 53-39 chainrings. Unless you’re riding the Tour, a 52 or 53 chainring is either a waste of good teeth or an invitation to knee damage. (We’ll do an example below that uses a 53-39 in a sensible way.)
Here’s a useful chart that allows you to easily evaluate combinations of various gears. Draw a vertical line for the chainring (52 or 53). Where it intersects the diagonal lines corresponding to the various cog sizes, look horizontally for the gear-inch result of that particular combination. If our top-end requirement is 102 inches, cogs smaller than 14 make no sense for a 52/53 – and we are going to want smaller cogs!
The mountain bike folks offer triple cranks with more reasonable sizes, things like 42-32-22. The extremes of this combination give us the following results. (Note: we usually can’t match a particular ratio exactly because we can only get cogs with an integral number of teeth.)
|
Desired gear size |
Front chainring |
Cog |
Actual gear size |
|
102 |
42 |
11 |
103.1 |
|
|
32 |
|
|
|
20 |
22 |
30 |
19.8 |
This looks pretty good! The top and bottom ratios just happen to match what we said we wanted. (Reality check: larger cogs only come in multiples of two teeth.)
|
What does an 11-30 cluster look like in detail? It depends on how many speeds we want: |
|
See anything wrong with this picture? On the 7-speed cluster, the steps from one ratio to the next increase by 2, 2, 3, 3, 4 and 5 teeth. That last step is a lulu! This is a lot of range to cover with a 7-speed. The 8- and 9-speed clusters aren’t bad.
Where do these numbers come from anyway? A little background: we’re trying to spread cogs out logarithmically; that is, the ratio between each pair of adjacent cogs should be the same. That’s what the step size row indicates in the table above. As a simple example, if we had a 10-tooth cog with a 20% step, the next larger cog would be 10*120% = 12 teeth. Next we’d want a 14.4-tooth cog, which is impossible, so we’d settle for 14 teeth. The next cog would be 14.4*120% = 17.28 teeth, and so on.
Look at the 8-speed cluster. Its mean step size is 15.4%; that is, the average ratio between adjacent cogs is 1.154. A half-step is 7.4%, from the square root of 1.154 (remember, it’s a logarithmic scale). We’ll use the half-step number later on.
Here’s the table again, forgetting the 7-speed, showing each individual step size. This illustrates the effect of rounding to the nearest integer. Even on the 9-speed, with a nice, tight average step of 13.4%, that jump from 12 to 14 is pretty good-sized.
|
Speeds |
8 |
Step, % |
9 |
Step, % |
|
Cogs |
11 |
18.2 |
11 |
9.1 |
Mean step size, % |
15.4 |
13.4 |
||
Half-step, % |
7.4 |
6.5 |
The appendix at the end of this page discusses cog selection further, with several tables that identify some reasonable clusters, and a convenient tool to look at step sizes.
Back to our example: we concluded that we wanted an 11-30 cluster. Let’s go for an 8-speed. Anything wrong with that? By itself, it’s just fine, but with the 42-32-22 crankset? Well, for example, the 42-17 combination is almost identical to the 32-13. In fact, four of our precious ratios are essentially wasted by redundancy. Here’s how it looks graphically (this is why the graphs are useful – we can see problems instantly):
Ideally, the horizontal lines should be uniformly spaced over the range we’re interested in. But this set-up gives us redundant ratios in the middle of the range that do us no good; at the same time, those last steps on both the high and low ends are pretty big. Even where the ratios aren’t redundant, they aren’t uniformly spaced. Very typical gearing – you can almost certainly buy this bike off the shelf, if you’re so inclined – but far from optimal. Can we spread them in a more useful way?
Yes, we can. Suppose instead of 32 in front, we choose a chainring that has 42/107.4% = 39 teeth? Where did that 107.4% come from!? – That’s the half-step size! What we’re doing is spacing the rear cogs a whole-step apart, and selecting chainrings to be a half-step apart. Here’s how it looks:
Notice how uniformly the horizontal lines are arranged. That’s the basic idea of the half-step: a wide range with lots of tightly-interspersed choices. It’s also an easy shifting pattern to remember, a whole step in the back, a half step in the front. That’s important at the end of a long, hard day!
On the bike itself, half-step gearing looks a little funny: the large chainring is smaller than usual, and the chainrings are so close to the same size that lots of people won’t get the point. Let them laugh – your legs will thank you!
If you don’t need a granny, omit it – you just happen to have exactly the range you wanted at the beginning, a low end around 35 gear inches! (Funny about that, eh?!)
But how ’bout that granny! That’s a low end you can pull stumps with! Or haul a loaded touring bike over Sonora pass!
Shifting back and forth on the two larger chainrings is no big deal, but when we drop into granny, we’ll want to simultaneously shift the rear end up by three clicks; same rule when we come up off granny. That’s not hard to do, but it does mean we won’t be shifting up and down from granny all the time, so it’s nice to have a substantial overlap – which we do. On the 13 cog at 105 rpm, we can do 14.3 mph, which ought to be enough for the occasional gentler part of a continuing climb.
13 teeth? Why not the 11? Time for a couple more reality checks...
We’ve assumed that we can pretty much use all the combinations front-to-rear. If there’s no granny, that certainly ought to be true. With a triple, you are likely to find that the inside-outside combinations just don’t work, or make so much noise that you don’t want to use them. (That’s why we only count on the 13.) As we work the chain across the rear, it is very likely that we’ll need to trim the precise position of the front derailleur to avoid chain rub. Today’s integrated road bike brake-shifter controls (Ultegra STI, for example) support triples with a bit of trim. You may also prefer a friction shifter for the front, so you can trim it yourself.
Front derailleurs are rated by the maximum difference in chainring size they can control. In our example, we need a derailleur rated for 42 - 22 = 20 teeth. Did I mention that we’re talking mountain bike components here, even on a road bike? Anyone have a problem with that? But Shimano’s mountain bike derailleurs expect at least 10-12 teeth difference between the two larger chainrings – no chance to use half-step gearing. Back to the road side: the triple front derailleurs of, for example, the Ultegra line, are likely to be a better choice.
The rear derailleur needs a long tensioner arm to soak up the difference between the small-small and the large-large combination. Our small-small is 22 + 11 = 33; the large-large is 42 + 30 = 72; the difference is 39 teeth. Definitely in mountain bike territory here – Shimano’s high-end XTR mountain bike rear derailleurs are rated for 43 teeth difference with the right chain. The Deore XT also accepts 43, and SR Suntour, if you decide to go that route, has derailleurs that will accept a 41-tooth difference.
Finally, a note about that long, long drop from the middle chainring into granny. You really are launching the chain into mid-air when you do this shift. One of those chain-watcher gadgets* is a really good idea, so the chain can’t fall off the inside and jam in the bottom bracket! (Does it sound like I’ve been there?)
* I've used the Third-Eye chain watcher for years with no complaints. Recently (February 2005), Nick from NGear encouraged me to try the Jump Stop. It includes a couple of very nice design ideas, it's easy to install and adjust, and as expected, it worked fine in the limited amount of riding I've done with it to date.
A couple of comments from years of driving this gearing:
Although half-step, with or without granny, is almost perfect gearing, it doesn’t have wide market acceptance. If you have older components that will support a half-step, treat them like the rare, irreplaceable jewels that they are. Today’s components, particularly front derailleurs, won’t support this arrangement – they are likely to insist on at least 10, or in some cases 12, teeth difference between the two larger chainrings. The idea in today’s market is to put lots of close-spaced ratios in back, with two or three widely-overlapping ranges in front, and not worry about redundant combinations. This arrangement starts to become feasible with 8-speed clusters, but really comes into its own with 9-speeds. Our flatland case might look something like this:
True, there are a lot of redundant ratios. But there are so many that maybe it doesn’t matter – the largest step size is 13.8%, and we covered the flatlands range we asked for at the beginning. Although we used components from today’s lists of options, we did have to pick a mountain-bike rear end to go with our road-bike crankset. This is not an off-the-shelf bike; the 53-39 flatlands bikes are likely to default to something like a 12-23 cluster, which is fine if you’re planning to spend lots of time above 30 mph, but doesn’t do the rest of us much good.
Since we won’t be shifting the front very often, it’s important to check that at least one of the chainrings spans the 50-70 range where we expect to do most of our riding. Yes, check, that works. Flatland riders: we’re done!
The big problem with this arrangement is extending it down into the granny range. For a low-end of 20 gear-inches, we’d need a 24-tooth granny gear. In itself, that’s not a problem, but the front derailleur would have to handle a difference of 53-24 = 29 teeth – not likely! Today’s Shimano XTR and XT derailleurs will handle a difference of 22 teeth!
Back to the drawing board. Forget the road-bike triple cranksets: Shimano’s Ultegra, for example, has a 30-tooth granny gear. Let’s talk mountain-bike components, say a 22-32-44 crankset. We’re almost back to the example at the beginning, where we wanted an 11-30 in back (make it an 11-32 to match what’s widely available in 9-speed clusters today).
The problem with 9-speed cog spacing is the first step. A one-tooth step is too small, two teeth are awkwardly large. The problem is visible in the 14-32 example above, and it gets worse with smaller cogs.
Since we can’t build a true half-step bike anyway, how about treating that ninth (small) cog as a half-step, and spacing the other ratios one-and-a-half steps apart? To do that, think of our 11-32 9-speed as an 11-tooth cog plus a 12-32 8-speed. How does that look? Like this:
This may be acceptable, though a 31 middle ring would interleave the ratios a bit better. It more than covers the range we asked for, at both the top and bottom ends. It works with today’s components. The whole-step sizes are okay, and there are reasonable half-steps over most of the range, most importantly the mid-range where we’ll be spending most of our time. By the way, if we bring the top end down to our target number by using only a 42 chainring, the picture becomes considerably uglier; in particular, we end up with only about two mid-range ratios.
That wasn’t bad. Here’s another one (experimentation is key!). Try a 12-34 on the back, with a 24-34-46 in front. (This just happens to correspond to the XTR gruppo, for example.) Here’s how it looks:
At last: an off-the-shelf bike that does (almost) what we want. Yes, it’s a mountain bike – but you could surely put the same components on a road frame, if it’s designed for a triple.
What’s different about mountain bikes? We already asked for the lowest low-end gearing we could get, so that isn’t different. But the fact that the tires incur greater rolling resistance and the upright position increases wind resistance, both mean the high end should be a little lower. I like about 95 - 98 inches myself. With smaller tires, that’s just about the same gearing as the 102 I like on my road bike.
On the mountain bike, off-road, you’re unlikely to get very many long uniform stretches where the half-step would help. But there’s still no reason to waste possible ratios. Here, the one-and-a-half-step gearing works well. You still get the interleaved ratios and you can still remember how to shift, even after a long, difficult day.
On a conventional bike, you always have the choice to stand out of the saddle for grades too steep for your gearing. With a recumbent, you pedal sitting, or you walk. My experience is that the same ratios work well for recumbents, though the very long chains make for fewer problems between inside on the front and outside on the rear.
Likewise with tandems. For tandem riding where one partner is substantially stronger than the other, or loaded tandem touring, the same ratios are likely to be just about right. If you have two strong riders, your wind resistance will be lower, and you could reasonably take the top end up to 110 gear-inches.
The moral of the story is that it’s unlikely we can get everything we want, at least not the first time out; but with persistence and willingness to prioritize, we can do pretty well.
If you have Visio, and would like a vector drawing of any of these charts (which will print and display clearer than gif), please drop me an email.
Here are some convenient numbers for rear clusters. There are two ways to derive them: analytic and synthetic. The analytic method picks the end-points, divides the range into the appropriate number of steps for a 7-, 8- or 9-speed application, and finds the nearest integer cog size. The results are then filtered according to the rule of monotonic and reasonable step size.
Here are most of the reasonable combinations of 7, 8 and 9-speed clusters, covering the ranges wide enough to be interesting.
|
Cogs |
11 |
11 |
11 |
11 |
12 |
12 |
12 |
12 |
12 |
12 |
|
Step, % |
13.1 |
15.4 |
16.1 |
16.8 |
11.5 |
12.2 |
13.8 |
14.5 |
15.2 |
16.5 |
|
Half-step |
6.3 |
7.4 |
7.8 |
8.1 |
5.6 |
5.9 |
6.7 |
7.0 |
7.3 |
7.9 |
|
Cogs |
13 |
13 |
13 |
13 |
13 |
14 |
14 |
14 |
14 |
|
Step, % |
10.8 |
11.5 |
13.0 |
13.6 |
15.0 |
10.1 |
12.2 |
13.5 |
14.8 |
|
Half-step |
5.2 |
5.6 |
6.3 |
6.6 |
7.2 |
5.0 |
5.9 |
6.6 |
7.1 |
|
Cogs |
11 |
11 |
12 |
12 |
12 |
12 |
13 |
13 |
13 |
13 |
14 |
14 |
14 |
|
Step, % |
12.4 |
15.4 |
11.7 |
12.3 |
14.0 |
15.0 |
11.0 |
12.7 |
13.7 |
14.7 |
10.4 |
12.5 |
13.5 |
|
Half-step |
6.0 |
7.4 |
5.7 |
6.0 |
6.8 |
7.3 |
5.4 |
6.2 |
6.6 |
7.1 |
5.1 |
6.1 |
6.5 |
|
Cogs |
11 |
11 |
12 |
12 |
13 |
13 |
14 |
|
Step, % |
12.4 |
15.1 |
12.1 |
13.9 |
11.0 |
12.8 |
5.8 |
|
Half-step |
6.0 |
7.3 |
5.9 |
6.7 |
5.4 |
6.2 |
2.9 |
Lots of numbers here. What do they all mean?
The idea in this approach to constructing clusters is to take a starting point, say the smallest cog (it works equally well starting from the largest cog, or indeed, starting in the middle and working outward in both directions). We then pick the maximum step size we’re willing to tolerate, and build the cluster by choosing the largest possible step that does not exceed the threshold. That is, rather than trying to match a mean step size as closely as possible, we focus on not exceeding some maximum step size. The analytic approach works very well up into the 7- and 8-speed clusters; the synthetic approach works much better when we talk about 8- and 9-speeds.
This approach is immune to both the problems of monotonic step size and of unreasonable step size, though it can also lead to cogs or combinations that aren’t available. The disadvantage of the synthetic approach is that you can only pick one cog a priori; since all the others are derived, you may have to iterate with different thresholds to reach the endpoint you have in mind. And it’s still possible that no sensible combination matches the endpoint you have in mind.
The synthetic approach is the way to understand why, on the market, you may find components that don’t follow the analytic rules for uniform step size. Here’s another handy chart; it shows the percentage change between pairs of cogs for 1-, 2-, 3- and 4-tooth steps.
As an example of how this works, let’s build a 9-speed 12-23. Start with the 12-tooth cog and a threshold of 12%. If the next cog were 14, the step size would be 16.7%, greater than our threshold. So the second cog has to be a 13. Can the next cog be 15? No, that would be a 15.4% step; it has to be a 14. And so on. We don’t know in advance where the endpoint will be; in this case, it’s 23. It’s interesting to observe that, although the mean step size is only 8.5%, we had to tolerate a 12% threshold to build the cluster.
Similarly, we can synthesize an 11-28, which has a mean step size of 14.3%, using a threshold of 16.7%.
Shimano also offers an 8-speed “recreational” cluster, the Nexave. It looks like a fairly conventional 7-speed 11-26 – and then it has a 34. I guess the idea is that you will be riding either on the flats or up 12% grades, with nothing in between. I have to admit, I don’t see the point of this combination.
For reference, here are some of the components and combinations available when this was written. Since product offerings change all the time, check the manufacturer’s link or a bike shop. Be aware that you cannot necessarily mix-and-match these components; they are listed to give you an idea of what’s available.
With 5-, 6-, and 7-speeds gone, and 8-speeds going fast, you are likely to find pre-manufactured cassette assemblies, rather than do-it-yourself loose components. A cog is nowadays designed differently, depending on the size of its neighbors. No longer can you arbitrarily mix a random collection of loose cogs into whatever you happen to want.
Special thanks to Mike at Chain Reaction for a very helpful discussion as this page was being constructed. And to Ric at Wheelsmith for years of unerringly finding components for me that actually worked, as I pursued my dreams of ever wider ranges, ever smaller steps.