[Ken Kifer's Bike Pages]
ARTICLE: Cycling Cadence and Bicycle Gearing
The reason for talking about gearing, why bicycles have gears, gear and cadence defined, low-gear requirements, gear-planning strategies, and charts of high and low gears.

Why are few cyclists interested in bicycle gearing? Why is having the correct gears important? Why is getting the correct gearing for your bicycle difficult? Why do bicycle tourers especially need lower gears? What is gearing and why is it necessary? How can gears be computed? What is the meaning of: gear, gear inches, gear ratios, and development? What is cycling cadence? Why is a high cadence favored by experienced riders? What is wrong with low cadence on the hills? What low gear should your bicycle have? Why is strength an important factor in low gear choice? Why is a fitness run necessary to calculate your lowest gear? What high gear is appropriate? How many gears are needed? Why is an even progression of gears important? How can gearing be planned? What teeth are needed on the rear freewheel or freehub? How should the front chainrings be planned? Why go to all this trouble? Directories

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Cycling Cadence and Bicycle Gearing

If you want even the nerds to consider you a nerd, try getting enthusiastic about bicycle gearing.  There is probably no topic with poorer esteem or poorer coverage in any book on cycling.  There are three reasons for this low estate: 1) newbies don't understand it, 2) strong cyclists don't need it, and 3) most people dislike math.  If these things are true, why do I want to approach the task? -- simply because cadence and gearing are important for the newbie, the tourer, and the person with weak muscles.

The Value of Gearing

I became convinced that gearing was an important topic through experience. I had moved to an area with some long, very steep climbs, 12% and over, and I started having trouble; after making one climb, I would feel a popping and tearing of the muscles in my knees. However, my bike had impressively low gears, at least for a 10-speed, down in the low 30's.  Investigation on my part revealed to me that the bike had only six useful gears and I needed much lower gears for my climbs, so I purchased a 15-speed bike without paying much attention to its gearing. That did not solve the problem either, so I had to do further reading.  I ended up having to purchase new cranks, chainrings, rear derailleur, and freewheel to get the gears I needed, increasing the cost of my bike by almost 50%. But now I have a bike that can climb mountains.

Let me present a simple problem to illustrate the problem of gearing: imagine that you are going on a touring trip in Colorado and will be carrying your own gear and supplies.  On some days, you will be climbing for half a day on a 6% grade. Your current bike has a 28 tooth large cog in the back and a 32 tooth small chainring in the front.  Do you need to change your gearing or not?  If you know the answer to this question, then you can quit reading right now. Or if you would never be caught dead carrying a heavy load up a mountain, you should quit also.  On the other hand, if the prospect of such a trip sounds nice but you don't know the answer, reading what I have to say will be of value.  With the proper gears, the length of the climb and the height of the mountain are unimportant.

Problems in Getting the Right Gearing

There are three problems in the quest for the right gears.  First, the manufactures are very conservative about placing low gears on bikes.  Basically, if the range between high and low gear is modest, the derailleurs work a little better.  A wide gear range can require a slack chain, something no manufacturer is going to allow. Second, the cyclists who write cycling books tend to be very strong and therefore don't even recommend or even understand low gears.  For instance, in one book (which was much better than most), the author said that a 27-inch gear was the equivalent of walking.  Actually, a 12-inch gear would allow you to climb at 3 mph at 80 rpm, but I doubt that you could walk that fast while pushing your bike on the same hill. A 27-inch gear would be equivalent to jogging up the same hill.  Third, when you decide what you really need, then you might find that it's hard to achieve because the manufacturers have not been thinking along the same wavelengths.

Why Tourers Need Lower Gears

A mountain is a completely different obstacle to the racing cyclist and to the touring cyclist. The racing cyclist, the strongest of the strong, in the peak of condition, is riding an ultra-lightweight machine, with speed as his primary objective.  The touring cyclist, more of a Nature-lover than a jock, somewhat overweight and very tired, is riding a heavy bike with a heavy load, with pleasure as the primary object. The racing cyclist stands on his machine and speeds up the hill, running at his anaerobic threshold, averaging as fast a speed as the tourist does on flat ground. The tourist sits on the way up, riding at a pace he can maintain all day long, well below his threshold.

The Basics of Gearing

At this point, I am going to have to explain the basics of gearing, so if you find this unnecessary, please skip on down, because I will be getting beyond the basics after a few paragraphs.

What is gearing and why is it necessary?  Click and Clack had to answer this question about cars recently, and I was tickled to see that they used a bicycle to explain the point because I have always used a car.  Let me compare it to walking.  In walking up a hill, your pace will become shorter and your forward movement slower, while in walking down a hill, your pace will become longer and your movement quicker. If you tried walking up a steep hill without slowing down, you would rapidly become exhausted. However, on a bicycle, you don't slow down the speed of your legs, but you gear down to reduce the amount of pressure you have to apply to the pedals.  So a cyclist going up a hill and down a hill may be spinning his legs at the same pace and making the same effort, but the bike travels a shorter distance with every turn of the crank while going uphill and a longer distance with every turn of the crank while going down.  The cyclist on the uphill gives up speed to save effort, the same as the person walking up a hill.  The cyclist even has an advantage over the walker: because his legs are moving faster, the blood flow is better, and thus he doesn't have as much fatigue.

At one time, bicycle racers did not believe in multi-geared bikes.  But Velocio, who invented the derailleur, thought of a test to prove them wrong.  He challenged a champion racer to a race in the mountains with a young woman.  The champion had a single-speed bike; the woman a three-speed.  The champion lost.

Gearing is achieved by having chainrings on the front and cogs on the rear with various numbers of teeth.  Let us suppose that you are riding a bike, and the chain is on a 30-tooth sprocket on the front and a 30-tooth cog on the rear.  At this point you have a 1 to 1 drive.  What gear size is it? The gear that you're in at this point is the same as the tire size on the rear wheel.  If you have a 27-inch wheel or 700 C wheel, you are in 27-inch gear.  If you have a 26-inch wheel, you are in 26-inch gear, and so on.  Now let's shift gears until the sprocket in front is twice the size of the one in the rear, say a 52 chainring in the front and a 26 cog in the rear.  What gear is that?  Well, 52/26 X 27 = 54, so if you have 27-inch wheels, you are in 54 inch gear. This gear is the equivalent of having a direct drive bike (such as the old high wheeler) with wheels 54 inches in diameter.  If you then change gears in the back, so that you are on a rear cog of 13 teeth (the equation is 52/13 x 27 = 108), you now have the equivalent of wheels 108 inches in diameter.  Gear inches are proportional and are not an equal distance apart: thus a shift down from a 25 inch gear to a 20 inch gear is equivalent to a shift down from a 100 inch gear to an 80 inch gear, and the difference between an 11 inch gear and a 33 inch gear is the same as the difference between a 33 inch gear and a 99 inch gear.  Two other terms are also used instead of gears or gear inches.  Gear ratios refers to the ratio between the front sprockets and back cogs; this term is seldom used correctly. Development refers to the distance traveled when the cranks are rotated 360°; usually this is measured in meters because development is favored over gear inches in Europe, where the metric system is used.

The Importance of Cadence

In order to understand gearing, we also have to look at the mystery of cadence.  Cadence is very simply the speed at which you turn the cranks, measured in revolutions per minute (rpm). However, bound into the concept of cadence is the idea that some rpms are better than others. What difference does it make how fast you spin?  Well, try a very low gear, the smallest sprocket on the front with the largest cog on the back, and pedal very fast on flat ground.  The result is that you travel very slowly but your legs tire very quickly from having to spin that fast. Now try a very high gear, the largest sprocket on the front with the smallest cog on the back. Now, the problem is that you have to push very hard to move forward. This causes your legs to tire also. Therefore, a middle speed has to be found.  Most people who begin cycling like to spin at about 60 rpm, yet touring cyclists like to spin at about 80 rpm.

Why do cyclists prefer a higher speed?  The best cadence is a balance between leg speed and pedal pressure, but as a cyclist puts more energy into the task, both increase.  So, the non-cyclist will pedal at 60 rpm going 10 miles an hour, the tourist will spin at 80 rpm going 15 miles an hour, and the racer will twirl at 100 rpm going 20 miles an hour.

The cycling books like to pretend, however, that a touring cyclist will pedal 80 rpm in the flats and 40 rpm on the steep hills.  Now if touring cyclists were strong enough to stand and pedal the whole distance up the mountain, they could do that, but it makes much better sense to gear down, sit down, and keep the cadence up. The length of the climb makes a difference.  On a short climb, standing provides a good opportunity to stretch.  However, from observing myself closely, I am convinced that sitting and spinning is quicker and less tiring even for fairly short distances.

What Gears Are Appropriate?

Now we're ready for the $64,000 question: what gears do cyclists need?  Well, as you may have already figured out, the answer is not going to be the same for everyone.  Some people are stronger than others. In order to answer this question, I had to make the following chart:

The Lowest Gear Needed for a 200 lb. Rider/Bike Combination
Flat-ground speed and output Hill-climbing speed Gear @ 80 rpm
mph hp watts kCal fps fph +4% +6% +8% +10 +12 +4% +6% +8% +10 +12
10 .05   40   150   30   540 2.6 1.8 1.3 1.0 0.7 11 -- -- -- --
12.5 .08   60   225   40   792 3.8 2.6 1.9 1.5 1.3 16 11 -- -- --
15 .11   80   300   60 1080 5.1 3.5 2.6 2.0 1.7 21 15 11 -- --
17.5 .16 120   450   80 1584 7.5 5.1 3.8 3.0 2.5 32 21 16 13 11
20 .22 160   600 120 2160 --- 7.0 5.1 4.0 3.4 -- 29 21 17 14
22.5 .29 215   800 160 2880 --- 9.3 6.8 5.5 4.5 -- 39 29 23 19
25 .39 290 1100 215 3870 --- --- 9.2 7.3 6.1 -- -- 39 31 26
27.5 .52 390 1500 290 5220 --- --- --- --- 8.2 -- -- -- -- 34

Notes: hp = horsepower, kCal = calories, fps = foot pounds per second, and fph = feet climbed per hour. Gears below 11 are not calculated because they are impossible to achieve. Climbing speeds above 9.5 mph not calculated because they would require calculating wind drag. All calculations are my own except speed on flat ground was derived from a careful comparison of four published charts. The actual speed on flat ground will vary with a given horsepower due to differences in wind resistance. The calories here are output and are less than the number of calories you would actually burn.

In order to use this chart, it's necessary to take a little fitness run.  How long?  How long will it take to climb your chosen hill? In my own case, I find my maximum output is about 23 mph, but I can only keep that up for 20 minutes or so. On the other hand, I can keep up an 18 mph pace all day long around home; that doesn't mean that I will average 18 mph; my average speed will be lower, but that will be my speed on flat smooth ground. Looking at the chart, I see that at that output, I can climb a six percent grade hill at 5.1 mph in a 21 inch low gear.  However, these figures are for my weight, the weight of my bike, tools, bags, and water on a local ride.  When I am on a touring ride, I will be traveling 50 pounds heavier (total 250 lbs.). In that case, my speed will be 80% as great, thus I will need a low gear only 80% as high, thus a low gear of 16 is called for.  In figuring what low gears you need, be sure to convert for your weight.

Actually, I can climb 6% grades on my touring bike with a 20 inch gear. What I have to do is to make a harder effort, the equivalent of riding at 20 mph on level ground. This is also equivalent to climbing an 8% grade without my touring load, and I do that all the time too.  However, I am pushing myself to climb that hard, which is why I stop and walk a bit after half an hour or so. At that pace, I could climb a mile in 2 1/2 hours, not counting rests along the way. According to the chart, I can also climb a 12% grade on a local ride or 9% while touring by using my maximum 23 mph effort.  Actually, I can climb steeper grades than that around home by standing on my pedals and slowing down my cadence, but I can't climb anything as steep as 9% on a trip. My touring bike is too heavy for me to stand and ride for more than a few minutes and, while on a trip, I am always somewhat tired from the day before, so I can't exert my maximum effort.

Another question that could be asked is, what high gear is needed? This is really a question of how steep the downhills are or how strong the tailwinds are and how fast the cyclist wants to go.  A 100 inch gear, the normal high gear, allows the bike to travel at 25 mph @ 80 rpm and 30 mph @ 100 rpm.  I have been able to pedal up to 38 mph in that gear.  What touring cyclist would need to pedal faster than that?  Indeed, there is some justification for using a lower high gear. There are few opportunities to travel over 20 mph and then coasting would achieve about the same speed.  But downhill pedaling helps pump out of the legs some of the toxins acquired on the trip up the hill. The legs feel better and the next hill is easier if the legs have worked a little on the way down.

How Many Gears?

Assuming that we have decided on a high of 100 and a low of 20, now comes the hard step. How many gears are needed between 20 and 100?  I experimented with a good variety of cogsets and chainrings, the cogsets from 14-21 to 14-36. What I discovered was that a 10% change between these gears seemed the most natural. In fact, my son's bike was set up with a 12% change, my touring bike with a 10% change, and my around town bike with an 8% change, so I have had lots of time to test these assumptions. Here's what happens: if the gear range is too wide, I'm wanting to shift gears when no gear is available, and when the gear range is too narrow, I tend to skip over them. The perfect gear change seems to me to be 10% while my son prefers his wider setup. I am sure that anything wider than 16% would be too wide.

So, just having a lot of gears or even an even progression of gears is not what I want. I want a 10% change, or close to it, from bottom to top. Let me show you what a perfect set of gears would be, starting from the bottom, based on 10%:

20  22  24  27  29  32  35  39  43  47  52  57  63  69  76  84  92  101
And here's a second set of perfect gears based on 12%:
20  22  25  28  31  35  39  44  50  55  62  70  80  87  98
Of course, due to the small number of teeth on cogs and chainrings, this perfect set of gears can only be approximated.

Gear Planning

There are three possible ways to plan the gears. The first system is used with the current 7 to 9 cog freehubs. The last is used with the older 5 and 6 cog freewheels.

With the individual system, you go downhill in the big chainring, level with the middle chainring, and uphill with the small chainring. Most of the shifting is done with the rear derailleur. This is the method used on new bikes now days. A bike with this setup usually has many duplicate gears. With this method, the percent change between the teeth on the rear cogs should be 10% or 12%, but usually the chainrings are too close together in size and the change on the rear is much larger. This system has a major flaw of having too much duplication.

The jumping system is very similar to the individual system, except there is no overlap or a one cog overlap between the different sets. With this method in shifting down, when you get to the biggest cog that's used with the large chainring, you must shift to the smallest cog and the middle chainring. For example, you could use a 54-36-24 front with a 14-21 freewheel and get this gearing. You don't shift very often but, when you do, it's a major jump. This setup is rarely used and never on bikes sold in stores.

The alternating setup uses the front derailleur more. To shift downward through all the gears without skipping any of them, you would have to use both derailleurs on every other shift. Thus you would shift down with the front derailleur to get to the second lowest gear, and to get to the third, you would shift down with the rear derailleur and shift up with the front derailleur. While this method seems to require an awful lot of shifting, half of it double shifting, in actuality, no one ever shifts through all the gears like this. Instead, this setup makes finding the exact gear very easy, as they are in a logical progression. The chainrings must have a 10% or 12% difference in the number of teeth, but the teeth in the cogset must change by exactly twice that percentage. This system avoids duplication.

By the way, my own setup of 52-48-24 and 14-17-21-26-32 is both alternating (the outside pair of chainrings) and jumping (the inside pair). This means that there is double the gap between the lowest gears, something I'm not completely happy with. However, I do get 14 useful gears out of 15 this way. Also, the second chainring should be a 47, so with a 48, I alternate between 8% and 12%.

There are some odd arrangements too.  One is labeled as Alpine. In the old "Alpine" setup, an alternating setup was used with a greater difference in size between the two chainrings.  Finding the best gear with this setup required taping a chart to the handlebars because the pattern was so complicated. The new "Alpine" setup uses the individual setup with a greater proportional difference in size between the largest cogs.  This setup makes the shifting patterns unpredictable.  Much more common is duplicate gearing: that is, both the front chainrings and the rear cogs have the same percent difference, thus rather than the number of useful gears being a multiple of the number of sprockets (i.e. 2 X 5 = 10), they are the product of an addition (i.e. 2 + 5 - 1 = 6).  Thus a bike with "27 speeds" may have as few as eleven useful gears.  Finally, some bikes have no pattern at all.  Thus, the cyclist might find gaps in the high, middle, or low gears. Oval chainrings add another complication, since the actual gear changes during the pedal stroke.  Not all ovals mount the same way either.  In my opinion, none of these setups has any merit.

Planning the Rear Cogs

Now to give you the necessary teeth for the rear cogs (with a 10% change) for any of the three patterns, starting with a low of 32 (which allows a low gear of 20 with a 24 tooth front chainring):
Individual or Jumping 32 29 26 23 21 19 17 15 14 12
Alternating                 32      26     21      17     14
And here they are for a 12% change:
Individual or Jumping 32 28 25 22 19 17 15 13 12
Alternating                 32      25     19      15     12 

If you want to compute your own cogsets, starting from another size large cog, just multiply by .9 each time for a 10% change, .88 for a 12% change, .86 for a 14% change, or whatever you want. Round off to the nearest whole tooth after figuring out the whole series.

Planning the Front Chainrings

The front chainrings should 1) be spaced the appropriate distance apart and 2) allow you to achieve the high and low gear that you want. With the alternating system, the chainrings are only 10 or 12% apart; with the jumping system, the distance between them should match the jump between the largest and smallest cog ( in percent, not teeth), and with the individual system they can be whatever you want, as long as you achieve your high and low gears.

Determining High and Low Gear

Using this method to determine the gears for your bike avoids the necessity of having to figure out the gears for every combination. However, it is necessary to figure out two gears, your highest and your lowest.  As said earlier, the highest gear for a touring bike should probably be between 90 and 100.  And your low gear should come from the output chart.  All that is necessary now is to look at a chart of the possible cogs and sprockets (both of these charts assume 27 inch or 700 C wheels; 26 inch wheels will result in slightly lower gears):

High Gear from Chainring and Cog Combinations
Chainring   52 50 48 46 44
12 cog   117   112   108   104   99
13 cog   108   104   100    96   91
14 cog   100    96    93    89   85

Low Gear from Chainring and Cog Combinations
Chainring   30 28 26 24 22 20 18
26 cog   31   29   27   25   23   21   19
28 cog   29   27   25   23   21   19   17
30 cog   27   25   23   22   20   18   16
32 cog   25   24   22   20   19   17   15
34 cog   24   22   21   19   17   16   14

Now, if you choose a larger or smaller rear cog than 32, as I used earlier, you will have to refigure the cogs, as I did using the 32 cog earlier, but is not necessary to calculate the gears for every combination.

Why Go to the Trouble?

I have to warn you that after you go through the task of figuring out what would be ideal for you that you then have to find the corresponding chainrings and cassettes and also the derailleurs which will work with them, which is not a simple task.  Then why go to all this trouble?  The goal is easy to understand: a sweet collection of gears which allow climbing the highest hill and shifting without having to speed up or slow down or fumble around for the right gear. If you aren't interested in going to this trouble, it's no problem for me.  But I would recommend that, at the very least, you should figure how low your lowest gear should be.

In my own case, I happen to be pretty lucky in using the outmoded five cog freewheel. The amazing thing is that a near perfect arrangement and spacing is found on the most common five-"speed" sprockets, 14-32 and 14-28 (the 14-32 has a 10% change and the 14-28 an 8% change). I guess whoever decided on this arrangement had the same thoughts I had. Unfortunately, no bike ever sold in a store was given the correct chainrings to match them.  There's a reason for that too, as I have mentioned before.  In having my ideal gear combination with the wide range from 100 high to 20 low, I also have to accept another problem -- chain slap.  With some of my lowest gears, the chain runs loose because the derailleur does not have the ability to wrap that many teeth. The solution I use is to simply avoid swaying from side to side when climbing with those combinations. Future derailleurs might solve this problem.

Again I will ask: why be stubborn, figure out gear inches, and go against what the manufactures want?  Until people started defying the manufacturers, there was no such thing as triple gearing and as long as people will accept whatever they are given, there will be no future progress.  At any rate, I get my reward for being stubborn every time I climb a mountain and shift smoothly from gear to gear on even the steepest grades.


Bicycle Gearing for Wisconsin Hills  Scott Ellington explains gearing in much the same way I do. His web article lacks some of the explanations of this one, but is very clear and has a gear calculator that includes weight and power in the calculations.

The Cogulator, a Java Applet for computing gears and cadence, which you can copy.

Bicycle Analyzer Data Form  A gear and cadence calculator with some analysis added.

Analytic Cycling: Interactive Methods for Estimating Cycling Performance  This rather high-tech site allows you to compute your own figures; however, be prepared for meters per second figures (it's also more oriented to racing than to touring).

A Gear Inch & Shifting Pattern Calculator by Barry Masterson  Although not saying so in the title, this caculator allows you to use metric figures as well.

Machine Head Software  Some software programs to calculate gears and the energy involved in bicycling.

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