Gain Ratios--
A New Way to Designate Bicycle Gears
A New Way to Designate Bicycle Gears
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Cyclists often find it useful to have a numeric representation of the gearing provided by their bicycles. This allows them to make meaningful choices in customizing their gearing, and can be useful in comparing the performance of one bicycle with another.
There are several systems for doing this, none of them entirely satisfactory. I would like to propose a new, more accurate and more universal system.
Cyclists who are only associated with one narrow ghetto of the cycling world frequently make do by just naming the chainwheel and rear sprocket they are using. This is a bit cumbersome, using two numbers where only one is really needed, and can also be confusing. For example, a 39/14 is the same as a 53/19, but this is not obvious. Since there are only 4 chainwheel sizes in common use on road racing bikes (39,42,52 & 53) this is still usable for the cyclist who only deals with this type of machine.
More well-rounded cyclists, who are likely to deal with wider variations in chainwheel and tire size, need a more sophisticated system to realize that the 46/16 on their mountain bike, and the 52/12 on their Moulton and the 52/14 on their Bike Friday are all about the same as the 53/19 and 39/14 on their road racer.
This system is also pretty much useless when planetary gears are involved.
The simplest system in common use is the "gear inch" system. This dates back to before the invention of the chain-drive bicycle. It originally was the diameter of the drive wheel of a high-wheel bicycle. When chain-drive "safety" bikes came in, the same system was used, multiplying the drive wheel diameter by the sprocket ratio. It is very easy to calculate: the diameter of the drive wheel, times the size of the front sprocket divided by the size of the rear sprocket. This gives a convenient two- or three-digit number. The examples listed above are all around 74-75 inches. The lowest gear on most mountain bikes is around 22-26 inches. The highest gear on road racing bikes is usually around 108-110 inches. Unfortunately, the handwriting is on the wall for all inch-based measurement systems.
In countries that use metric measurements, the usual system is "development" in meters. This is the distance that the bicycle moves with each revolution of the pedals. This system is a bit more cumbersome than the gear inch system, for two reasons. First, it is a little more difficult to calculate: wheel diameter in meters x front sprocket / rear sprocket x pi. Having to multiply by a constant (an irrational one, no less!) needlessly complicates things. Also, the resulting value is a less-convenient number to work with, a single digit plus two decimals. For example a road bike's 52/13 would be expressed: 8.64. A mountain bike's 24/28 would be: 1.78.
All of these systems share a common inadequacy: none of them takes crank length into account! The fact is that a mountain bike with a 46/16 has the same gear as a road bike with a 53/19 only if they have the same length cranks. If the mountain bike has 175's and the road bike 170's, the gear on the mountain bike is really about 3% lower!
I would like to propose a new system, which does take crank length into account. This system is independent of units, being expressed as a pure ratio.
This ratio would be calculated as follows: divide the wheel radius by the crank length; this will yield a single radius ratio applicable to all of the gears of a given bike. The individual gear ratios are calculated as with gear inches, using this radius ratio instead of the wheel size.
You can calculate gain ratios, gear inches or meters development with my
A road bike with 170 mm cranks: (The usual generic diameter value for road wheels is 680 mm, so the radius would be 340 mm.)
340 mm / 170 mm = 2.0. (The radius ratio)
2.0 X 53 / 19 = 5.58
This number is a pure ratio, the units cancel out. I call this a "gain ratio" (with thanks to Osman Isvan for suggesting this term.) What it means is that for every inch, or kilometer, or furlong the pedal travels in its orbit around the bottom bracket, the bicycle will travel 5.58 inches, or kilometers, or furlongs.
A mountain bike with 26 inch wheels (13 inch radius) and 6 3/4" cranks:
13" / 6 3/4" = 1.93
1.93 X 46 / 16 = 5.54
Remember, the "radius ratio" only has to be figured out once for a given bike, because it is the same in all gears. Any individual gear is calculated as:
Radius ratio X front(teeth) / rear(teeth)
Any measurement units may be used, as long as the same units are used for both the wheel diameter and crank length.
You can calculate gain ratios, gear inches or meters development with my
| Tire Size |
Tire Radius |
165 mm | 170 mm | 172.5 mm | 175 mm | 180 mm |
|---|---|---|---|---|---|---|
| I.S.O. 630: | ||||||
| 27 X 1 3/8 | 345 | 2.091 | 2.029 | 2.000 | 1.971 | 1.917 |
| 27 X 1 1/4 | 343 | 2.079 | 2.018 | 1.988 | 1.960 | 1.906 |
| 27 X 1 1/8 | 342 | 2.073 | 2.012 | 1.983 | 1.954 | 1.900 |
| 27 X 1 | 340 | 2.061 | 2.000 | 1.971 | 1.943 | 1.889 |
| I.S.O. 622: | ||||||
| 700 X 56 | 370 | 2.242 | 2.176 | 2.145 | 2.114 | 2.056 |
| 700 X 50 | 365 | 2.212 | 2.147 | 2.116 | 2.086 | 2.023 |
| 700 X 44 | 354 | 2.145 | 2.082 | 2.052 | 2.023 | 1.967 |
| 700 X 38 | 347 | 2.103 | 2.041 | 2.012 | 1.983 | 1.927 |
| 700 X 35 | 345 | 2.091 | 2.029 | 2.00 | 1.971 | 1.917 |
| 700 X 32 | 342 | 2.073 | 2.012 | 1.983 | 1.954 | 1.900 |
| 700 X 28 | 336 | 2.036 | 1.976 | 1.948 | 1.920 | 1.867 |
| 700 X 25 | 335 | 2.030 | 1.971 | 1.942 | 1.914 | 1.861 |
| 700 X 20 | 332 | 2.012 | 1.953 | 1.925 | 1.897 | 1.844 |
| I.S.O. 559: | ||||||
| 26 X 2.125 | 330 | 2.000 | 1.941 | 1.913 | 1.886 | 1.833 |
| 26 X 1.9 | 324 | 1.964 | 1.906 | 1.878 | 1.851 | 1.800 |
| 26 X 1.5 | 312 | 1.891 | 1.835 | 1.809 | 1.783 | 1.733 |
| 26 X 1.25 | 311 | 1.884 | 1.829 | 1.803 | 1.778 | 1.728 |
| 26 X 1.0 (559 mm) | 305 | 1.848 | 1.794 | 1.768 | 1.743 | 1.694 |
| I.S.O. 571: | ||||||
| 26 x 1 (650C) | 311 | 1.884 | 1.829 | 1.803 | 1.778 | 1.728 |
| Other: | ||||||
| Wide Tubular | 338 | 2.048 | 1.988 | 1.959 | 1.931 | 1.878 |
| Narrow Tubular | 335 | 2.030 | 1.971 | 1.942 | 1.914 | 1.861 |
| 26 X 1 3/8 (590 mm) | 330 | 2.000 | 1.941 | 1.913 | 1.886 | 1.933 |
| 24" | 305 | 1.848 | 1.794 | 1.768 | 1.743 | 1.694 |
| 24 x 1 (520) | 279 | 1.691 | 1.641 | 1.617 | 1.594 | 1.550 |
| 20 X 1.75 (406 mm) | 254 | 1.539 | 1.494 | 1.472 | 1.451 | 1.411 |
| 20 X 1 1/4 (451 mm) | 257 | 1.558 | 1.512 | 1.490 | 1.469 | 1.428 |
| 17 x 1 1/4 (369 mm) | 211 | 1.279 | 1.241 | 1.223 | 1.206 | 1.172 |
| 16 x 1 3/8 (349 mm) | 204 | 1.236 | 1.200 | 1.183 | 1.166 | 1.133 |