Bicycle gearing

Transmission types
Manual Sequential manual Non-synchronous Preselector
Automatic Manumatic
Semi-automatic Electrohydraulic Dual clutch Saxomat Zeroshift
Continuously variable
Bicycle gearing Derailleur gears Hub gears

A bicycle with a hub gear.

Shimano XT rear derailleur on a mountain bike

A bicycle gear or gear ratio refers to the rate at which the rider's legs turn compared to the rate at which the wheels turn. Bicycle gearing refers to how the gear ratio is set or changed. On some bicycles, there is only one gear so the ratio is fixed. Most modern bicycles have multiple gears, so multiple gear ratios are possible. Different gears and ranges of gears are appropriate for different people and styles of cycling.

Multi-speed bicycles allow selection of the appropriate gear ratio for optimum efficiency or comfort, and to suit the circumstances, e.g. it may be comfortable to use a high gear when cycling downhill, a medium gear when cycling on a flat road, and a low gear when cycling uphill. The difference between the highest and lowest gears is known as the gear range, which may be expressed either as a percentage (500%) or as a ratio (5:1).

A cyclist's legs produce power optimally within a narrow pedalling speed range. Gearing is optimized to use this narrow range as best as possible. As in other types of transmissions, the gear ratio is closely related to the mechanical advantage of the drivetrain of the bicycle. On single-speed bicycles and multi-speed bicycles using derailleur gears, the gear ratio depends on the ratio of the number of teeth on the chainring to the number of teeth on the rear sprocket (cog). For bicycles equipped with hub gears, the gear ratio also depends on the internal planetary gears within the hub. For a shaft-driven bicycle the gear ratio depends on the bevel gears used at each end of the shaft.

For a bicycle to travel at the same speed, using a lower gear (larger mechanical advantage) requires the rider to pedal at a faster cadence, but with less force. Conversely, a higher gear (smaller mechanical advantage) provides a higher speed for a given cadence, but requires the rider to exert greater force. Different cyclists may have different preferences for cadence and pedaling force. Prolonged exertion of too much force in too high a gear at too low a cadence can increase the chance of knee damage; cadence above 100 rpm becomes less effective after short bursts, as during a sprint.

Measuring gears

There are at least four different methods for measuring gear ratios: gear inches, metres of development (roll-out), gain ratio, and front/rear (racing-style). The first three methods result in each possible gear ratio being represented by a single number which allows the gearing of any bicycles to be compared; the numbers produced by different methods are not comparable, but for each method the larger the number the higher the gear. The fourth method uses two numbers and is only applicable to racing bicycles with derailleur gears which have a specific wheel size (rim diameter 622 mm, often referred to as 700C).

Front/rear measurement is of limited use and only considers the sizes of a chain ring and a rear sprocket. Gear inches and metres of development also take the size of the rear wheel into account. Gain ratio goes further and also takes the length of a pedal crankarm into account.

Gear inches and metres of development are closely related: to convert from gear inches to metres of development, multiply by 0.08 (more exactly: 0.0798, or precisely: $0.0254\pi$).

The methods of calculation which follow assume that any hub gear is in direct drive. Multiplication by a further factor is needed to allow for any other selected hub gear ratio (many online gear calculators have these factors built in for various popular hub gears).

• Gear inches = Diameter of drive wheel in inches × (number of teeth in front chainring / number of teeth in rear sprocket). Normally rounded to nearest whole number.
• Metres of development = Circumference of drive wheel in metres × (number of teeth in front chainring / number of teeth in rear sprocket).
• Gain ratio = (Radius of drive wheel / length of pedal crank) × (number of teeth in front chainring / number of teeth in rear sprocket). Measure radius and length in same units.

Both metres of development and gain ratios are normally rounded to one decimal place.

Gear inches corresponds to the diameter (in inches) of the main wheel of an old-fashioned penny-farthing bicycle with equivalent gearing. Metres of development corresponds to the distance (in metres) traveled by the bicycle for one rotation of the pedals. Gain ratio is the ratio between the distance travelled by the bicycle and the distance travelled by a pedal, and is a pure number, independent of any units of measurement.

• Front/rear gear measurement uses two numbers (e.g. 53/19) where the first is the number of teeth in the front chainring and the second is the number of teeth in the rear sprocket. Without doing some arithmetic, it is not immediately obvious that 53/19 and 39/14 represent effectively the same gear ratio.

Examples

The following table provides some comparison of the various methods of measuring gears (the particular numbers are for bicycles with 170 mm cranks, 700C wheels, and 25mm tyres). Speeds for several cadences in revolutions per minute are also given. On each row the relative values for gear inches, metres of development, gain ratio, and speed are more or less correct, while the front/rear values are the nearest approximation which can be made using typical chain-ring and cassette sizes. Note that bicycles intended for racing may have a lowest gear of around 45 gear inches (or 35 if fitted with a compact crankset).

Gear	Gear inches	Metre development	Gain ratio	Front/ rear	60 rpm		80 rpm		100 rpm		120 rpm
					mph	km/h	mph	km/h	mph	km/h	mph	km/h
Very high	125	10	9.4	53/11	22.3	36	29.7	47.8	37.1	59.7	44.5	72
High	100	8	7.5	53/14	18	29	24	38.6	30	48.3	36	57.9
Medium	70	5.6	5.2	53/19 or 39/14	12.5	20	16.6	26.7	21	33.6	25	40
Low	40	3.2	3.0	34/23	7.2	11.6	9.6	15.4	11.9	19.2	14.3	23
Quite low	20	1.6	1.5	n/a	3.5	5.6	4.7	7.6	5.9	9.5	7.1	11.4

General considerations

The gearing supplied by the manufacturer on a new bicycle is selected to be useful to the majority of people. Some cyclists choose to fine-tune the gearing to better suit their strength, level of fitness, and expected usage. When buying from specialist cycle shops, it may be less expensive to get the gears altered before delivery rather than at some later date. Modern crankset chainrings can be swapped out, as can cogsets.

While long steep hills and heavy loads may indicate a need for lower gearing, this can result in a very low speed. Balancing a bicycle becomes more difficult at lower speeds. For example, a bottom gear around 16 gear inches gives an effective speed of perhaps 3 miles/hour (5 km/hour) or less, at which point it might be quicker to walk.

Relative gearing

As far as a cyclist's legs are concerned, when changing gears, the relative difference between two gears is more important than the absolute difference between gears. This relative change, from a lower gear to a higher gear, is normally expressed as a percentage, and is independent of what system is used to measure the gears. Cycling tends to feel more comfortable if nearly all gear changes have more or less the same percentage difference. For example, a change from a 13-tooth sprocket to a 15-tooth sprocket (15.4%) feels very similar to a change from a 20-tooth sprocket to a 23-tooth sprocket (15%), even though the latter has a larger absolute difference.

To achieve such consistent relative differences the absolute gear ratios should be in logarithmic progression. Because sprockets must have a (relatively small) whole number of teeth it is impossible to achive a perfect progression; for example the seven derailleur sprockets 14-16-18-21-24-28-32 have an average step size of around 15% but with actual steps varying between 12.5% and 16.7%. The epicyclic gears used within hub gears have more scope for varying the number of teeth than do derailleur sprockets, so it may be possible to get much closer to the ideal of consistent relative differences, e.g. the Rohloff Speedhub offers 14 speeds with an average relative difference of 13.6% and individual variations from this average of at most 0.1%.

Racing cyclists often have gears with a difference of around 7%; this allows fine adjustment of pedalling speed to suit the conditions. Mountain bikes and hybrid bikes often have gears with a difference of around 15%; this allows for a much larger gear range without excessively large steps between gears. 3-speed hub gears may have a difference of around 30%; such big steps require a very substantial change in pedalling speed and often feel excessive. A step of 7% corresponds to a 1-tooth change from a 14-tooth sprocket to a 15-tooth sprocket, while a step of 15% corresponds to a 2-tooth change from a 13-tooth sprocket to a 15-tooth sprocket.

By contrast, car engines deliver power over a much larger range of speeds than cyclists' legs do, so relative differences of 30% or more are common for car gearboxes.

Usable gears

On a bicycle with only one gear change mechanism (e.g. rear hub only or rear derailleur only), the number of possible gear ratios is the same as the number of usable gear ratios, which is also the same as the number of distinct gear ratios, which is also the same as the number of easily usable distinct gear ratios.

On a bicycle with more than one gear change mechanism (e.g. front and rear derailleur), these four numbers can be quite different, depending on the relative gearing steps of the various mechanisms. The number of gears for such a derailleur equipped bike is often stated simplistically, particularly in advertising, and this may be misleading.

Consider a derailleur-equipped bicycle with 3 chain rings and an 8-sprocket cassette:

the number of possible gear ratios is 24 (this is the number usually quoted in advertisements);

the number of usable gear ratios is 22;

the number of distinct gear ratios is typically 16 to 18;

the number of easily usable distinct gear ratios is typically only 12.

The combination of 3 chainrings and an 8-cog cassette does not result in 24 usable gear ratios. Instead it provides 3 overlapping ranges of 7, 8, and 7 gear ratios. The outer ranges only have 7 ratios rather than 8 because the extreme combinations (largest chain-ring to largest rear sprocket, smallest chain-ring to smallest rear sprocket) result in a very diagonal chain alignment which is inefficient and causes excessive chain wear. Due to the overlap, there will usually be some duplicates or near-duplicates, so that there might only be 16 or 18 distinct gear ratios. It may not be feasible to use these distinct ratios in strict low-high sequence anyway due to the complicated shifting patterns involved (e.g. simultaneous double or triple shift on the rear derailleur and a single shift on the front derailleur). Avoiding these complicated shifting patterns results in having only some 12 easily usable distinct gear ratios. In the worst case there could be only 10 distinct ratios, if the percentage step between chainrings is the same as the step between sprockets. However, if the most popular ratio is duplicated then it may be feasible to extend the life of the gear set by using different versions of this popular ratio.

Gearing range

The overlapping ranges with derailleur gears mean that 24 or 27 speed derailleur gears may only have the same total gear range (about 5:1) as a (much more expensive) Rohloff 14-speed hub gear. Internal hub geared bikes typically have a more restricted gear range than comparable derailleur-equipped bikes, and have fewer ratios within that range.

Types

External (derailleur)

Main article: Derailleur gears

External gearing utilizes derailleurs, which can be placed on both the front chainring and on the rear cogset, to push the chain to either side, derailing it from one sprocket to a neighboring sprocket. The sides of the sprockets may be sculpted to help catch the chain, pulling it up onto their teeth to change gears. There may be 1 to 3 chainrings, and 5 to 11 sprockets on the cogset. Derailleur type mechanisms of a typical mid-range product (of the sort used by serious amateurs) achieve between 88% and 99% mechanical efficiency at 100W. In derailleur mechanisms the highest efficiency is achieved by the larger sprockets. Efficiency generally decreases with smaller sprocket and chainring sizes. Derailleur efficiency is also compromised with cross-chaining, or running large-ring to large-sprocket or small-ring to small-sprocket. This cross-chaining also results in increased wear because of the lateral deflection of the chain.

As mentioned above, derailleur gears may result in many duplicated gears. One archaic tactic for avoiding this duplication is to use chainrings of similar size. On a modern bicycle, it might be possible to move from one speed to its duplicate by shifting to the next smaller chainring and the third smaller sprocket. This would be because the chainrings have large gaps in their size: In this example, the ratio of the chainrings is approximately three times the ratio of the sprockets. This would be called a crossover gearing configuration, specifically a "three-step crossover." A bicycle with two chainrings that were close to each other in size would theoretically avoid duplication. The ratio of the chainrings would need to be approximately half that the sprockets. In this configuration, the half-step configuration, the speeds on one chaining would be between those on the other chainring, eliminating duplication. This configuration was complicated to design, since the "step" is actually an exponent, not a multiple. That is, (sprocket ratio)³ for a three step or (sprocket ratio)^(1/2) for a half step. Since limited sprocket options prevented a constant ratio between the sprockets, there would still be duplication in practice. Getting a low gear combination would require a third, much smaller chainring; a configuration derogatorily called a half-step-plus-granny. The frequent front-shifting and combined front-and-rear shifting made these configurations generally impractical.

Internal (hub)

Main article: Hub gear

Internal hub gears work by internal planetary, or epicyclic, gearing, in which the hub outer turns at a different, but adjustable, speed relative to the sprocket. Rear hub gears commonly come in 3 or 7 speeds but with many variations and up to 14 speeds.
Internal hub gears are more reliable than derailleurs, clean, almost weather-proof and require little maintenance. Only the most expensive offer as wide a range of gear ratios as derailleurs.
In a typical hub gear mechanism the mechanical efficiency will be between 82% and 92% depending on the ratio selected. One to one ratios are generally the most efficient, while systems employing several epicyclic trains in series (compound gears) are the least efficient.
Internal hub gearing predominate in bicycles used for city-riding and commuting, not least for the great convenience of changing down ratios while stationary. External derailleur systems predominate in competition and leisure use.

Internal (bottom bracket)

These systems have a 2-speed hub gear incorporated in the crankset or bottom bracket.

The Schlumpf Mountain Drive and Speed Drive have been available since 2001 and offer direct drive plus one of three variants (reduction 1:2.5, increase 1.65:1, and increase 2.5:1). Changing gears is accomplished by using your foot to tap a button protuding on each side of the bottom bracket spindle. The effect is that of having a bicycle with twin chain rings with a massive difference in sizes.

Another system entered the market in 2010.

Fixed gear

Fixed-gear track racing bikes can achieve transmission efficiencies of over 99% (nearly all the energy put in at the pedals ends up at the wheel). Biomechanical factors however determine that a human can deliver maximum power only over a narrow range of crank rotational speed or cadence. To match the power source with the load under varying conditions, a variable gear ratio is needed, and they work very well, though at the expense of mechanical efficiency. The efficiency varies considerably with the gear ratio being used.

Internal and external combined

It is sometimes possible to combine a hub gear with deraileur gears, but care is needed when selecting the rear cassette to avoid duplicate gear ratios. There are several commercially available possibilities:

• The Brompton folding bicycle uses a 3-speed hub gear (roughly a 30% difference between gears) in combination with a 2-speed deraileur gear (roughly a 15% difference) to give 6 distinct gears. This is an example of half-step gearing, where one set of gears has an inter-gear step half of that on the other set of gears. Some Brompton suppliers offer a 2-speed chain ring 'Mountain Drive' as well, which results in 12 distinct gears with a range exceeding 5:1. However, the change from 6th to 7th gear involves changing all three sets of gears simultaneously. Many hub gears are capable of accepting two dished sprockets, allowing this system to be easily replicated.
• The SRAM DualDrive system uses a standard 8 or 9-speed cassette mounted on a three-speed internally-geared hub, offering a similar gear range to a bicycle with a cassette and triple chainwheels.
• Less common is the use of a double or triple chainring in conjunction with an internally-geared hub, extending the gear range without having to fit multiple sprockets to the hub. However, this does require a chain tensioner or some sort, negating some of the advantages of hub gears.
• At an extreme opposite from a single speed bicycle, hub gears can be combined with both front and rear derailleurs, giving a very wide-ranging drivetrain at the expense of weight and complexity of operation- there are a total of three sets of gears (four if a 2-speed bottom bracket is also used.) This approach may be suitable for recumbent trikes, where very low gears can be used without balance issues, and the aerodynamic position allows higher gears than normal.

Others

There have been, and still are, drivetrains that are quite different from those above:

• Retro-Direct drivetrains used on some early 20th century bicycles have been resurrected by bicycle hobbyists. These have two gears but no gear lever; the operator simply pedals forward for one gear and backward for the other.
• Automatic transmissions have been demonstrated and marketed for both derailleur and hub gear mechanisms, often accompanied by a warning to disengage auto-shifting if standing on the pedals. These have met with limited market success.
• Continuously variable transmissions are a relatively new development in bicycles (though not a new idea). Mechanisms like the NuVinci gearing system use a ball connected to two disks by static friction - changing the point of contact changes the gear ratio.

Efficiency of the two common gearing systems

Chester Kyle and Frank Berto reported in "Human Power" 52 (Summer 2001) that testing on three derailleur systems (from 4 to 27 gears) and eight gear hub transmissions (from 3 to 14 gears), performed with 80W, 150W, 200W inputs, gave results as follows:

Transmission Type	Efficiency (%)
Derailleurs	87-97
Gear Hubs	86-95

Efficiency testing of bicycle gearing systems is complicated by a number of factors - in particular, all systems tend to be better at higher power rates. 200 Watts will drive a typical bicycle at 20 mph, while top cyclists can achieve 400W, at which point one hub-gear manufacturer (Rohloff) claims 98% efficiency.

At a more typical 150W, hub-gears tend to be around 2% less efficient than a well-lubricated derailleur.

Examples of gear measures

The table below shows distance traveled in metres per pedal revolution for a typical sprocket configuration on a 27 inch bicycle. Note that the two highest gears use the large front sprocket, the two lowest gears use the small front sprocket, while for all other gears, it is necessary to shift both front and rear sprockets to access the next higher or lower gear ratio. Some gears, indicated by asterisks (*) may have less favorable chain geometry due to crossover between inner and outer sprockets.

Rear hub teeth	51 tooth front outer sprocket (high)	40 tooth front inner sprocket (low)
13 (highest)	8.49 metres	6.61 metres **
15	7.33	5.75 *
17	6.46	5.06
20	5.49	4.31
24	4.58 *	3.59
28 (lowest)	3.91 **	3.08

Only those who want to go really fast will need a gear much above 100, though gears as high as 250 have been reported for specialist racing. Cyclists who are fit and strong will find that a low gear of around 40 -50 gear-inches is quite adequate for almost all on-road use. Other cyclists may prefer a somewhat lower gear, perhaps around 20 or 30. The lowest feasible non-specialist gear (as of 2005) is around 15. Tricycles can be bought with gears as low as 8, but such low gears are not really suitable for bicycles due to the problems of balancing at very slow speeds.

As a person ages, their necessary low gear may change. Suppose a cyclist at age 40 regularly commutes by bicycle 11 miles each way without doing any other cycling or exercise. He/she might need a low gear of 45 for the 58-mile London to Brighton charity bike ride, with no need to stand on the pedals even over Ditchling Beacon. Twenty years later the same cyclist (then commuting only 5 miles each way) might need a low gear of 27 for the ride. Another five years later the same cyclist (then commuting 7 miles each way) might feel happier with a low gear of 19 for the ride.

Several gear ratio calculators are linked below. Such calculators are more useful if they show the percentage difference between gears as well as the nominal gear ratios. These calculators require the number of teeth on each gear wheel on the bicycle and the diameter of the back wheel. Standard road wheels, labeled 700c are 70 cm in diameter with the tire; the smaller 650c wheels are 65 cm in diameter. Mountain, cruiser, and most other types of wheel are 26 inches with tire.

For gain ratios they also need to know the length of the pedal cranks in millimetres (crank lengths are normally some multiple of 2.5 mm). If the bicycle has an enclosed gear system (hub or bottom bracket), then details of these gears are also needed (make and model is enough for some calculators).

See also

• Bicycle
• Bicycle drivetrain systems
• Cadence
• Cogset
• Crankset
• Derailleur gears
• Gear inches
• Hub gear
• NuVinci
• Recumbent bicycle

External links

About bicycle gearing:

• Cadence training
• Cycling glossary, links to articles
• Derailleur Gears: A practical guide to their use and operation.
• Detailed discussion on gearing
• Gear theory for cyclists
• Gearing 101

Online gear ratio calculators:

• Calculate your gear ratios, as numbers
• Calculate your gear ratios, as numbers and graphs