Bicycle Technology: Derailleur Gearing

Fig. 10.2 shows the components that make up a typical derailleur system. The rear wheel hub is equipped with a freewheel block with a whole range of different sized sprockets, while two or three different sized chainrings are used in the front. The front derailleur, or changer, shifts the chain sideways between the chainrings, while the rear derailleur selects the appropriate sprockets in the rear. These derailleurs are operated by means of shift levers on the down tube or the handlebars, to which they are connected by means of flexible cables.

Since the various sprockets and chainrings each have a different number of teeth, the ratio between the rate at which the cranks are turned and that at which the rear wheel turns can be varied accordingly. Given a certain pedaling rate, the speed with which the rear wheel turns is proportional to the quotient of the number of teeth in the front and the number of teeth in the back.

The number of different gearing options is expressed by the product of the numbers of sprockets and chain- rings: 2 chainrings and 5 sprockets gives ten speeds, 3 chainrings and 7 sprockets 21. Actually, there is a certain overlap, so the actual number of significantly different gears may be less than that. Racing bikes generally have 12 or 14 speeds (2 chainrings up front), while mountain bikes and touring machines generally come with 18 or 21 speeds (3 chainrings). On cruisers and similar simple bicycles, 5- and 6-speed systems are often used, using a single front chainring and thus eliminating the front derailleur as well — a sensible approach for inexperienced cyclists.

Gearing Theory

The principle of the gearing system is the idea of adapting the transmission ratio between cranks and rear wheel to the difficulty of the terrain. Under favorable conditions — when the resistances are low — the driven rear wheel can rotate quite a bit faster than the cranks, propelling the bike at a high speed without pedaling excessively fast. This is referred to as a high gear and is achieved when a large chainring is combined with a small sprocket. Under unfavorable conditions, when resistances are high, a low gear is selected, achieved with a small chainring and a large sprocket, so the rear wheel does not turn much faster than the cranks.

10.1. This is what happens when you change gear: The derailleur shoves the chain over onto the next smaller or bigger chainwheel.

10.2. Parts of the derailleur system

10.3. Gear combinations

10.4. Nothing new: This precursor of today’s derailleur was introduced around 1910.

It will be instructive to compare the situation on a level road with that on an incline. The example will be based on a cyclist who can maintain an output of 100W (i.e. about 0.13 hp). On a level road without head wind, this will suffice to progress at 30km/h (about 20mph). If the road goes up by 8%, the same output only allows a speed of 10km/h (about 6.5mph).

If the gearing ratio were fixed, the pedaling rate would have to be three times as high in the first case as it is in the second. Conversely, the forces applied to the pedals would be three times as high when pedaling slowly uphill as they would be pedaling fast on the level road. However, the muscles and joints work better if the pedal force is limited, even if this requires a higher pedaling speed. Thus, the uphill ride is particularly tiring, even though the same total output is delivered — not because of the output, but because of the high forces at low muscle speeds.

This predicament is solved with the use of gearing: it allows selecting the ratio between pedaling and riding speed in such a way that the pedaling force remains within the limits of comfort by allowing an adequately high pedaling speed, regardless of the riding speed. Conversely, it is possible to keep the pedaling rate within the comfortable range when conditions are so easy that one would otherwise have to pedal extremely fast to deliver the available output.

To achieve this, the relatively untrained fitness cyclist might select a gear in which he maintains a pedaling rate of 70rpm while each crank revolution brings him forward by about 7. 15m. This results in a speed of 70 x 7.15 x 60 = 30,030m/h, or 30km/h. On an incline, he may maintain the same pedaling rate and output level, but might select a gear that brings him forward only 2.40m per crank revolution, which results in a speed of 70 x 2.40 x 60 = 10,080m/h, or 10km/h. Either way, pedaling speed and muscle force remain unchanged.

Actually, it is unrealistic to assume that the same out put level and pedaling speeds are always maintained. All riders put in more effort when climbing than when riding on the level. The example shows what is possible, even though the actually selected gears and speeds may vary a little one way or the other. To ad here to the example would require a very wide range of gears, even for rather moderate terrain differences.

A typical configuration for a racing bike might include a range of 13 to 21 teeth in the rear and 52 and 42 teeth in the front, resulting in a top gear that is (52/13) / (42/21) = 2 times as high as the lowest gear. For a mountain bike, the range might be determined by front chainrings of 46, 36 and 26 teeth, rear sprockets ranging from 13 to 26 teeth, resulting in a top gear that is (46/13) / (26/26) = 3.54 times as high as the lowest gear.

Virtually all bicycles except the mountain bike are equipped with gears that are insufficiently spread for most applications. Even if you ride a racing bike, the range between favorable and unfavorable conditions is much greater than can be comfortably mastered with the narrow range of gears usually installed by the manufacturer. It is simple enough to adapt the system to more sensible gearing by installing a freewheel block with more widely spread sprockets.

Gear Designation

Although one could refer to the particular gear ratio by simply stating the size of chainring and sprocket, this is not a satisfactory method. It would not easily reveal that e.g. 52/26 gives the same gear ratio as 42/21 (curiously enough referred to as 52 X 26 and 42 X 21 respectively, whenever this method is used). Obviously, it becomes completely impossible to compare bikes with different wheel sizes. To overcome these problems, two methods have been developed, referred to as gear number and development, respectively. The two methods are illustrated in Fig. 10.5.

10.5. Development and gear number as designations for gearing ratios.

10.6. Graphic representation of the gearing steps using the combinations ‘half step plus granny.’

Gear number is a rather archaic method that is inexplicably used to this day in the English speaking world. It references the equivalent wheel size of a directly driven wheel that would correspond to the same gear. To calculate the gear number, use the following formula:

N = D(wheel) x T(front) / T(rear)

where:

N = gear number in inches

D(wheel) = actual outside wheel diameter in inches

T(front) = number of teeth, chainring

T(rear) = number of teeth, sprocket.

Typical high gears are in the vicinity of 100 inches, while very low gears may be nearer 30 inches.

The internationally used development designation is easier to visualize: it represents the distance traveled per crank revolution, measured in meters. To calculate it, use the following formula:

D = pi x D(wheel) x T(front) / T(rear)

where:

D = development in meters

pi = 3.14

D(wheel) = actual outside wheel diameter in m

T(front) = number of teeth, chainring

T(rear) = number of teeth, sprocket.

A typical high gear may be around 8 - 9m, while a typical low gear may be 2.5 - 3m.

Neither of these gear designations needs to be calculated once you know how they are determined. Tables 1 and 2 provide quick a reference for their determination on the basis of 27-inch and 700mm wheels, while they can be determined for other wheel sizes by multiplying with the following ratio:

X(wheel) = X / 0.675 x D(wheel)

where:

X(wheel) = the required value for the wheel size in question

X = the value for development or gear number for 27-inch or 700mm wheels

0.675 = the wheel size in meters on which the tables are based

D(wheel) = the actual outside diameter in meters of the wheel in question.

10.7. (Left and right) The optimal gearing progression provides closely spaced gears at the high end (small sprockets) and more widely spaced gears at the low end (large sprockets).

10.7. Chain deflection as a determining factor for the suitability of gearing combination.

The Gear Progression

Ergonomically, it is best to select the gears in such a way that the difference between them is larger in the range of low gears than it is in high gears. This is achieved by selecting the sprocket sizes so that the smaller sprockets differ less from each other than the biggest sprockets. The best ratio is obtained when the percentage steps of the sprocket sizes remains approximately the same. Thus, the high gears are closer together than the low ones.

10.9. Selection graph for sprocket sizes: Detail (copy and cut out); Example: 7-speed freewheel 13 - 24 teeth

Take, as an example, a series of 7 sprockets from 13 to 25. At first, it may seem logical to assign them as follows 13, 15, 17, 19, 21, 23 and 25. The difference is always 2 teeth. However, between 13 and 15 that amounts to 2/15 = 0.15, or 15%, while between 23 and 25 it is only 2/25 = 0.08, or 8%. This incongruity be comes even more dramatic as wider range gearing is used.

It will be more accurate to adhere to a progression that keeps the percentage steps similar throughout the range, using smaller steps between small sprockets than between big ones. An example for the range between 13 and 25 would be 13, 14, 15, 17, 19, 22, 25. In this case, the steps can be calculated to be 8%, 7%, 7%, 12%, 11% and 12%.

This too can easily be selected with the use of a graph, referring to Fig. 10.9. Place a copy of the strip over the graph in such a way that the first and last arrows (de pending whether it is a freewheel block with 5, 6 or 7 sprockets) coincide with the values for the smallest and biggest sprockets. At the intermediate points, read off the closest intermediate sprocket sizes, deviating slightly to the left or the right only if done consistently to the same side.

There are several different theories for the selection of the chainring sizes. My preference goes towards some thing referred to as half step for systems with two chainrings, to something called half step plus granny for systems with three chainrings (see Fig. 10.6). In both cases, the term half step refers to the principle of selecting the smaller chainring of such a size that intermediate gears between steps with different sprockets are achieved (this is done by choosing the second chainring only a few teeth smaller than the biggest). The term granny refers to a very small third chainring, that makes an entirely different low range available when it is combined with any of the sprockets.

The more common selection of chainrings results in achieving a different range of gears with the smaller chainring than with the larger. On mountain bikes, often ridden under conditions where shifting with the front chainring must be minimized, this makes perfect sense, but I find it a crying shame to equip touring bikes and fitness machines with the kind of gearing that provides such overlaps that fully 40% of them are wasted.

When selecting chainrings and sprockets, remember the comments about their wear: they wear less if they are selected with a number of teeth that represents a prime number. This is the reason why 41, 43, 47 or 53 tooth chainrings and 13, 17, 19 or 23 tooth sprockets should be selected in preference to slightly different sizes. They not only wear better, they also run more smoothly.

Finally, it should be pointed out that, especially when systems with seven sprockets are used, the extreme gears that cross over the chain from the smallest sprocket to the smallest chainring, or from the largest sprocket to the largest chainrings, should be avoided (see Fig. 10.8). The resulting lateral chain deflection causes both high wear and reduced efficiency of the drive train. It will be virtually impossible to adjust the derailleurs in such a way that the chain does not rub against the derailleur cage in the extreme gears.

The Rear Derailleur

Essentially every rear derailleur consists of a hinged, spring-tensioned parallelogram mechanism with which a spring-tensioned cage with its two chain guide wheels can be moved sideways, shifting the chain from one sprocket to another. The most significant difference in design is that between models with a hanging parallelogram and a more horizontal one, between models with long cages and short ones, between the location at which the cage is pivoted, and between straight and slanted parallelogram mountings (referred to as slant pantograph design).

10.10. Shimano SIS started the trend towards indexed shifting in the mid eighties. Today, hardly a bicycle is sold without index gearing, whether mountain bike or road machine.

10.11. Shimano Dura-Ace derailleur

Figures 10.12 and 10.13 show the two major types. In general, the models with nearly horizontal cages, referred to as pantograph types, lend themselves better to indexing (although the indexing is contained in the lever, rather than the derailleur). The slant design minimizes the distance between the chain and the sprocket teeth, making for more positive shifting. The models with a long cage, preferably pivoted at a point between the two chain guide wheels, are more easily adapted to large differences between sprocket sizes (i.e. wide-range gearing).

Most models are marked to show the range of sprocket sizes and the amount of chain wrap for which they are suitable. In some cases, the cage can be attached to the body in several different locations, each representing a certain range of sprocket sizes. The amount of chain wrap for which a derailleur is suitable indicates how big the difference between the combinations largest chainring, largest sprocket on the one hand, and smallest chainring, smallest sprocket on the other may be.

The most important adjusting device for the modern derailleur (certainly if it is suitable for index gearing) is the cable tension adjuster. In addition, the extreme limits of travel are adjusted with the set-stop, or limit, screws. In the case of the slant pantograph model there is an additional adjusting screw with which the angle between the parallelogram and the horizontal plane can be adjusted, as described in the manufacturer’s instruction leaflet, to achieve the greatest degree of chain-wrap around the sprocket consistent with smooth shifting.

10.12 and 10.13. The two basic rear derailleur types. Left: Conventional straight parallelogram derailleur as was long the standard for all European makers. Right: Pantograph model as used by all Japanese manufacturers and increasingly also by European companies.

10.14. Shimano wide-range derailleur

Although most derailleurs nowadays are installed directly to a threaded lug on the RH rear drop-out, simple bikes may lack this feature. In that case, the derailleur is mounted on an adaptor plate that is held between the drop-out arid the wheel axle nut or quick-release. Both adaptor plates and drop-outs are generally designed for specific derailleurs, which work best when certain distances are adhered to. This locks you into equipment from a specific manufacturer, so it is preferable not to experiment with a different make or model of derailleur than those for which the drop-out on the frame was designed.

10.15. Assembly of typical modern rear derailleur The mounting plate (lower left) is only used on frames without derailleur mounting lug (Shimano illustration).

The Front Derailleur

Fig. 10.16 shows a typical front derailleur. It simply consists of a hinge mechanism that moves another wise fixed cage sideways to guide the chain over one chainring or another. The differences between the various models are primarily associated with the size of the cage and the lateral travel: there are distinct differences between models suitable for triple chainrings and those suitable only for double chainrings. A long, low dropped cage indicates that it will shift down to a really small chainring, as is necessary for touring and mountain bikes. The adjustment mechanism is usually limited to a set of set-stop screws to adjust the range of lateral travel.

10.16. Front derailleur, showing installation position.

Most modern versions have a hinge mechanism that does more than just move the cage sideways. Instead, they tend to lift the chain towards the larger one as they move to the right, drop down as they move to the left. Especially for triple chainring use, the (long and thus sensitive) cage should be ruggedly constructed. Most racing models (for twin chainrings) are nowadays designed to be installed on a lug attached to the seat tube, while mountain bike mode always have a clamp with which they are attached to the seat tube, a solution that allows more flexibility, since the lugs brazed on to the frame tend to be suitable only for one particular make and model of the front derailleur.

Instead of a regular front derailleur, there is one system on the market that does the same job in a more sophisticated manner. This is the Browning system, available from SunTour under the name BEAST. It is an electrically controlled system in which sections of the chainrings are hinged and move sideways to deliver the chain to the next chainring. Although one may object to battery-powered technology on the otherwise perfectly manually operated bike, there is no doubt something to be said for the ease with which this system shifts the chain even under the most difficult conditions (all other front derailleurs shift only very reluctantly as long as the chain is under tension, as when cycling uphill).

10.17. Shimano-made bike front derailleur.

10.18. SunTour mountain bike front derailleur.

10.19. Assembly of conventional front derailleur. Nowadays, many road frames are equipped with a lug for front derailleur installation, so the mounting bracket is eliminated.

Derailleur Controls

Both front and rear derailleurs are operated by means of shift levers via bowden cables. The shift levers may be installed on the down tube, on the handlebars, on the stem or at the handlebar ends. The stem mounted location is inherently unsuitable and is only found on drop-handlebar bikes intended for people who don’t know how to handle them. Fig. 10.20 shows several versions.

In addition to these regular models, there is the so- called Grip-Shift for installation at the ends of forward reaching triathlon handlebars, such as used in time trial racing. Campagnolo and Sachs-Huret both have something similar for installation on the ends of regular mountain bike handlebars. Whatever design is used, the shifter for the rear derailleur is mounted on the right, the one for the front derailleur on the left. The Browning system (which only works in the front) is operated by means of a double push button switch.

10.20. Conventional (non-indexed) shifters. Downtube, Stem mounted, Bar-top

Index Derailleurs

The difference between the modern index derailleurs and old-fashioned friction models lies mainly in the shifters and the cables. These index shifters have a stepped .ratchet mechanism inside, which stops the cable in predetermined positions, coinciding with derailleur positions for particular sprockets. Most of the older versions have a supplementary lever that allows shifting between the index mode and a mode in which intermediate positions can be reached (to allow full use of the gears even when the Index system is out of adjustment).

The cables used for index gearing are thicker and stiffer than conventional cables to eliminate real or apparent stretch, which would throw the system out of adjustment. Their length is usually preset for a certain configuration, since they are very hard to cut. These cables also have a nylon low-friction liner and do not require lubrication.

Since 1990, most mountain bikes come with double-button levers mounted under the handlebars. These allow operation without moving the hands: push the top button to shift up, the bottom button to shift down. There are some differences between the available models, but most are so complicated that the manufacturers rightfully warn against taking them apart when they don’t work properly: you’ll have to replace the whole unit.

Shimano’s version no longer has a friction mode to allow for maladjustment, while it also is available only as a combined unit integrating brake lever and gear shifter. This is a particularly consumer hostile approach. SunTour’s version is mounted separately and also includes a small-step ratchet to allow non-index shifting, if necessary. Recently introduced Shimano shifters combined with racing brake levers work very well. Unfortunately they also force you into a certain system with specific brakes, and they are very heavy.

10.21. Early indexing: It had a ratchet mechanism in the derailleur.

10.22. Above-the-bar index shifter

10.23 and 10.24. Left: Under-the-bar shifter for mountain bikes. Right: Brake lever-mounted shifter for road bikes. (SunTour illustrations).

Derailleur Maintenance

Once a month, it will be smart to clean and, if necessary, lubricate front and rear derailleur and other associated parts, especially the chain, the pivot points, the pulleys, and the sprockets. Shifting depends on all of these components working properly. The other operation regularly necessary is adjustment if there is any deterioration of shifting. Non-index versions in particular may require re-adjustment of the set-stop screws if the chain is shifted too far or not far enough.

Adjusting Derailleur Travel

Sometimes the chain is shifted beyond the last chain- ring or sprocket or, conversely, not far enough. In the first case it will drop by the side and may get caught; in the second case certain gear combinations just cannot be reached as a result. These things can generally be corrected by adjusting the set-stop screws, shown in Fig. 10.27.

Before you resort to adjusting these little screws with the spiral springs under their heads on the rear derailleur, though, check to make sure the problem is not caused by a bent drop-out or adaptor plate. This may be the result of a fall, and will result in a non-perpendicular alignment of the derailleur cage, and no amount of set-stop screw adjustment will solve the problem: get the drop-out aligned instead. Similarly, the front derailleur may have shifted on the seat tube: the cage should be perfectly parallel to the chainrings.

10.25 and 10.26. Left: Sachs-Huret Elisee index derailleur with a cup-on cable attachment and adjusting mechanism. Right: Campagnolo Bullet twist grip for mountain bike use.

When you have established that the problem is not due to a bent or twisted derailleur, you will need a little screwdriver and sometimes a rag — needed if the chain has to be put back on sprocket or chainring. If the chain has got caught. you may have to loosen and re-tightens the wheel first to free it.

Adjusting procedure:

1. Establish what the cause and nature of the problem is:

- front or rear;

- too much travel or too little;

- on the inside (to the left) or the outside (right).

2. Seek out the appropriate set-stop screw and deter mine if it has to be screwed in (too much travel) or out (not enough travel).

3. Screw the appropriate set-stop screw in or out about half a turn at a time.

4. Lifting the rear wheel off the ground and pedaling forward while shifting, check operation of the gears In all combinations and if necessary repeat adjustment until all gears work properly.

10.27. Adjusting set-stop screws to limit derailleur range.

Adjusting Index Derailleur

Generally, the cause of index derailleur problems is either a bent or twisted attachment (see the preceding section for this), or — more typically — cable stretch. However, most of the cables used do not stretch all by themselves: the problem is probably due to the cable or any part being loose, or conversely the cable may have been caught or damaged at some point. First check all those possibilities and proceed to the adjustment process below only when you are sure nothing else is wrong. Generally, no tools are required for this.

Adjusting procedure:

1. If the shifter in question has an F-position for the non-indexed, or friction, mode, set the supplementary lever in this position first.

2. Select the highest gear (largest chainring and smallest sprocket) — if it cannot be reached, loosen the cable adjusting mechanism as necessary (if still no luck, also adjust the high range set-stop screw as described above).

3. Adjust the rear derailleur cable in this position so that it is just taut but not under tension.

4. Lifting the rear wheel and turning the cranks, shift into the lowest gear (smallest chainring, largest sprocket) — if necessary, adjust the set-stop screw. If still no luck, also tighten the cable just a little.

5. Shift back into the highest gear and now shift into the index mode (if appropriate).

6. If necessary, adjust the cable tension until the chain runs smoothly and noiselessly in this gear.

7. Shift the rear derailleur’s shifter down one step — if the derailleur does not follow perfectly, tighten the cable adjuster half a turn. If it shifts too far, slacken it half a turn. Repeat in quarter-turn steps if necessary.

8. Tighten the adjuster just enough that the chain runs noisily against the next larger sprocket. Then back off again until the noise subsides.

9. Once more check all the gears, paying particular attention to quiet running — repeat the last two steps, if necessary.

10.28 and 10.29. Left Automatic AIR–Shifter. Right: SunTour BEAST developed by Browning, which shifts the chain in the front by means of hinged chainring sections.

10.30 and 10.31. Left: The derailleur wheels usually run on sleeve bearings. To reduce friction, they can be replaced by models with ball bearings, such as these by Tacx (right).

Shifter Maintenance

From time to time, the gear shift levers must be tightened, assuming they are also kept clean and very lightly lubricated. To tighten them, there is a screw on top that holds the mechanism together. Index derailleurs can often be salvaged, for the time being, by simply shifting them into the friction mode until you have time to do a proper maintenance or replacement job on them.

Conventional models on which the manufacturer al lows for disassembly may be opened up if no satisfaction is obtained by tightening the screw on top. Clean, check, lubricate and reassemble to get it back in working order. If this still does not do the trick, check the cable before resorting to replacement of the shifter mechanism itself.

10.32 and 10.33 Left: SunTour above-the-bar index shifters for mountain bike use. Right: Under-the- bar mountain bike shifters.

10.34. Shimano Total Integration shifters combined with racing brake levers. Convenient but heavy.

Hub Gearing