### An article fromBicycling! magazine

(They have dropped the ! now)

## Metric Gear Ratio Measurements

#### by Randolph A. Swart

American bicyclists might find the European system of measuring gear ratios more useful than our own "inches" system. Few cyclists now ride high wheelers, and the theoretical height of a wheel is of little use to most of us.

The European system simply measures, in meters, the distance a bicycle travels for each revolution of the cranks. This distance, generally called here a "development" after the French word, is computed by multiplying the ratio of front chainwheel teeth to rear sprocket teeth, times the circumference of the rear wheel (in meters). Sew-ups and 700C tires generally have a diameter of 2.13 meters. For a 50-14 combination the development is:

Front 50 divided by Rear 14 = 3.57
3.57 x 2.13 = 7.6 meters development

The accompanying computer-calculated chart gives developments for a wide range of gear ratios, based on a 2.13 meter wheel circumference. It has a more extended range of ratios than most European charts and is more accurate than some (the Huret catalog chart, for example).

This system has two advantages. For those who are setting up a new bicycle or replacing a freewheel cluster, it allows the choice of gear ratios which give a smooth progression from the lowest to the highest gear needed. The intervals between developments can be equalized so that the rider who encounters a little stronger headwind or a slightly steeper slope can reach for his derailleur controls with confidence that changing down one ratio will always give the same change in his pedaling cadence.

The second advantage is the easy translation of development and cadence to cycling speed. A cadence of 70, for example, with a 5 meter gear gives 70 x 5 = 350 meters (.35 kilometers) per minute forward speed. Speed thus is 60 x .35 = 21 kilometers per hour (13 mph). This not only makes speedometers unnecessary; it also allows the cyclist to choose his highest and lowest gears depending on his cadence and the maximum and minimum speeds he will want to maintain. (This can all be accomplished by the "inches" system, but requires more computation. Who can divide by 12, multiply by pi and figure fractions of 5280 while pedaling? How many feet high is a 100 inch wheel?)

This method will be even more useful when the U.S. converts to the metric system and road signs are changed to kilometers. Cyclists in this country are in the vanguard of other movements and can point the way here, too.

(Chart of gear ratios appeared here.)

Choosing Gear Ratios

The choice of gear ratios for a bicycle is as personal a decision as the choice of the bicycle itself or its components. There are many theories of gear selection. Using the metric development system, we can show how one of them works.

Start by assuming that the gear range should be determined by choosing a high ratio and a low ratio and spreading the other ratios as evenly as possible in between. Using the chart of developments we can select front chainwheels and a rear freewheel cluster through a trial and error process.

Choice of the high and low developments depends on such personal factors as the use planned for the bike (touring, commuting, cyclecamping, racing), the loads to be carried, terrain the rider wishes to conquer and the rider's weight, strength and physical condition. The derailleur used must also be capable of handling the range of gears chosen, and an excessively wide range may make the intervals between gears too great.

For a five speed bicycle we can show the gear selection process very simply. Assume we pick a low ratio of 3.5 meters (we are in good shape and do not climb mountains with heavy packs). Assume further that we want a high gear of 6 meters (which gives, with a cadence of 80, a speed of about 30 kilometers per hour-18 mph). A good solution for our five speed would be a 45-tooth front chainwheel and a freewheel cluster of 16-18-20-23-27. This will spread the developments evenly with an interval of approximately .6 meters. (The interval is computed by dividing the difference between the highest and lowest developments by the number of intervals-the number of gears less one.)

Choice of 10 and 15 speed developments is complicated by the overlap problem. Due to chain misalignment when the outer front chainwheel is used with the inner freewheel cog (and vice versa) most 10 speeds have only 8 useful gears while 15 speeds generally have 9. Use of the additional available ratios results in increased friction and rapid chain and sprocket wear. The middle freewheel cogs, however, are used with more than one chainwheel, so must be chosen to give the right development with each one. This makes it necessary to try many different possible combinations before finding the best solution.

My own bicycle can serve as an example of this process. I wanted ratios adequate for cyclecamping with up to 20 pounds of gear. l also commute daily to work with much lighter loads. I expect to climb some small Eastern mountains on camping tours and I hate to get off and push. Finally, I sometimes use a commuter path to work which follows a creek bed down a gentle slope for several miles. For that stretch I need a fairly high gear for speed when I am late for work. My physical condition varies, and I tend to need higher gears as the season progresses.

Based on these considerations I chose developments that start at just above one turn of the wheel for each revolution of the cranks (2.13 meters) and end at a little over 7.5 meters. To keep the interval between developments small I decided on a 15 speed system, using 9 of the available ratios. The intervals between developments should then be about .68 meters (7.6- 2.13 = 5.47 meters total range, divided by 8 intervals-between 9 gears gives S847 = .68). I chose front chainwheels of 29-40-50

with rear cogs of 14-16-18-21-29. The useful developments are as follows:.

14 16 18 21 29
29--3.432.942.21
40-5.334.734.06-
507.616.665.92--

There are some compromises necessary. Maintaining the perfect interval for the lower gears will give wider intervals in the higher gears when the rear cogs are used with larger chainwheels. Again, this is a personal choice. I wanted the mid-range intervals to be the most uniform. l decided I could tolerate a little wider intervals in the higher developments, when I am mostly riding without loads, than in the lower and midrange. The 50-14 is good for a downhill run (at a cadence of 100 I get 29 mph), although with the 50-tooth front chainwheel the jump from 16 to 14 is nearly a whole meter.

The developments suit my needs, and I have been pleased with the results. My own solution is obviously not the ideal set of ratios for everybody else's 15 speeds. It only illustrates the process I am recommending.

Computerizing the choice of chainwheels and cogs is time consuming. The program must take account of all the personal factors mentioned above and thus requires considerable changes for each cyclist. It is probably more efficient to make the choice by trial and error, although the computer can give a range of combinations for final selection.

This is one means of choosing ratios. It points up the usefulness of the metric developments system. People who cycle in flat country may find that low ratios are unimportant. Racers may want to place their emphasis on a greater concentration of gear choices in the mid-range for more subtle changes in pedaling cadence. I believe this system works well for the tourist or commuter, however, and hope it may be useful to others

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Editor's Note: For those who are used to expressing gear in inches, "development" in meters can be obtained by mentally multiplying your gear by 0.08, which is close enough for all practical purposes. After all, true gear should be calculated on the basis of the actual rolling radius of the tire under the load and inflation pressure used. This may differ considerably from 27 inches. Fred DeLong