Bicycle gearing

Overview

Bicycle

A bicycle, also known as a bike, pushbike or cycle, is a human-powered, pedal-driven, single-track vehicle, having two wheels attached to a frame, one behind the other. A person who rides a bicycle is called a cyclist, or bicyclist....

**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.

Unanswered Questions

Encyclopedia

A bicycle

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

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 transmission

s, the gear ratio

is closely related to the mechanical advantage

of the drivetrain of the bicycle. On single-speed bicycle

s 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 gear

s, 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.

, 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).

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).

s 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 chainring and cogset 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).

Extra features which can be helpful include:

Before using such a calculator you need to know the number of teeth on each sprocket on the bicycle, the size of the back wheel, and the size of the tires. The wheel size, rim diameter, and tire size can usually be found embossed on the side of a tire. If gain ratios are to be calculated you 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 a hub gear then details of this mechanism are also needed (make and model is enough for some calculators). Some calculators require the effective (wheel+tire) diameter; this can be determined as the rim diameter plus twice the tire size, e.g. a 700C wheel has an effective rim diameter of 622mm, when fitted with 35 mm hybrid-style tires the effective diameter is 622+35+35 = 692mm; dividing by 25.4 gives an effective diameter of about 27.24 inches.

, hub gear

ing or other methods for varying the gear ratio of the bicycle. Adult single-speed bicycles typically have a gear ratio of between 55 and 75 gear inches, depending on the rider and the anticipated usage.

There are many types of modern single speed bicycles; BMX

bicycles, some bicycles designed for (younger) children, cruiser type bicycles

, classic commuter bicycles

, unicycle

s, bicycles designed for track racing

, fixed-gear road bicycle

s, and fixed-gear mountain bicycles.

The fixed-gear

single-speed bicycle is the most basic type of bicycle. A fixed-gear bike does not have a freewheel mechanism to allow coasting.

While long steep hills and/or 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.

To achieve such consistent relative differences the absolute gear ratios should be in logarithm

ic progression; most off-the-shelf cogsets do this with small absolute differences between the smaller sprockets and increasingly larger absolute differences as the sprockets get larger. Because sprockets must have a (relatively small) whole number of teeth it is impossible to achieve 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 of around 0.1%.

Racing cyclists often have gears with a small relative difference of around 7% to 10%; this allows fine adjustment of gear ratios to suit the conditions and maintain a consistent pedalling speedIn cycling, cadence is the number of revolutions of the crank per minute; roughly speaking, this is the rate at which a cyclist is pedalling/turning the pedals...

. Mountain bikes and hybrid bikes often have gears with a moderate relative difference of around 15%; this allows for a much larger gear range while having an acceptable step between gears. 3-speed hub gears may have a relative difference of some 33% to 37%; 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

.

On a bicycle with more than one gear change mechanism (e.g. front and rear derailleur), these three 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 chainrings and an 8-sprocket cogset:

The combination of 3 chainrings and an 8-sprocket cogset 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 chainring to largest rear sprocket, smallest chainring 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). In the worst case there could be only 10 distinct gear ratios, if the percentage step between chainrings is the same as the percentage 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.

The overlapping ranges with derailleur gears mean that 24 or 27 speed derailleur gears may only have the same total gear range 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.

The approximate gear ranges which follow are merely indicative of typical gearing setups, and will vary somewhat from bicycle to bicycle.

Gear ranges around 600% can be achieved on derailleur setups by careful choice of (non-standard) chainrings and rear cogsets, but this may result in some rather large steps between gears or some awkward gear changes, e.g. 3 chainrings 22-32-44 and 9-speed cogset 12-36. Somewhat higher gear ranges can be achieved either by using larger steps between gears or by using a 2-speed bottom bracket hub gear in conjunction with a suitable derailleur or rear hub gear, but the practical usefulness of such a setup is uncertain, since anyone strong enough to use the high gears at the top of the range is unlikely to need the low gears at the bottom of the range.

and hub gear

s. These two systems have both advantages and disadvantages relative to each other, and which type is preferable depends very much on the particular circumstances. There are a few other relatively uncommon types of gear change mechanism which are briefly mentioned near the end of this section. Derailleur mechanisms can only be used with chain drive transmissions, so bicycles with belt drive or shaft drive transmissions must either be single speed or use hub gears.

mounted on the down tube, handlebar stem, or handlebar. A shifter may be a single lever, or a pair of levers, or a twist grip; some shifters may be incorporated with brake levers into a single unit. When a rider operates the shifter

Most hybrid, touring, mountain, and racing bicycles are equipped with both front and rear derailleurs. There are a few gear ratios which have a straight chain path, but most of the gear ratios will have the chain running at an angle. The use of two derailleurs generally results in some duplicate or near duplicate gear ratios, so that the number of distinct gear ratios is typically around two-thirds of the number of advertised gear ratios. The more common configurations have specific names which are usually related to the relative step sizes between the front chainrings and the rear cogset.

, but any change of chainring must be accompanied by a simultaneous change of 3 or 4 sprockets on the cogset if the goal is to switch to the next higher or lower gear ratio.

Megarange cogsets, where most of the sprockets have roughly a 15% relative difference, except for the largest sprocket which has roughly a 30% difference; this provides a much lower gear than normal at the cost of a large gearing jump.

which alters the speed of the hub casing and wheel relative to the speed of the drive sprocket. They have just a single chainring and a single rear sprocket, almost always with a straight chain path between the two. Hub gears are available with between 3 and 14 speeds; weight and price tend to increase with the number of gears. All the advertised speeds are available as distinct gear ratios controlled by a single shifter (except for some early 5-speed models which used two shifters). Hub gearing is often used for bicycles intended for city-riding and commuting.

or bottom bracket

. Patents for such systems appeared as early as 1890. 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 chainrings with a massive difference in sizes. Pinion GmbH introduced in 2010 an 18 speed model, offering an evenly spaced 636% range.

include rolling resistance and air resistance:

Human factors can also be significant. Rohloff demonstrates that overall efficiency can be improved in some cases by using a slightly less efficient gear ratio when this leads to greater human efficiency (in converting food to pedal power) because a more effective pedalling speed is being used.

Factors which have been shown to affect the drive-train efficiency include the type of transmission system (chain, shaft, belt), the type of gearing system (fixed, derailleur, hub, infinitely variable), the size of the sprockets used, the magnitude of the input power, the pedalling speed, and how rusty the chain is. For a particular gearing system, different gear ratios generally have different efficiencies.

Some experiments have used an electric motor to drive the shaft to which the pedals are attached, while others have used averages of a number of actual cyclists. It is not clear how the steady power delivered by a motor compares with the cyclic power provided by pedals. Rohloff argues that the constant motor power should match the peak pedal power rather than the average (which is half the peak).

There is little independent information available relating to the efficiency of belt drives and infinitely variable gear systems; even the manufacturers/suppliers appear reluctant to provide any numbers.

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

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:

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.

Online gear ratio calculators:

Bicycle

A bicycle, also known as a bike, pushbike or cycle, is a human-powered, pedal-driven, single-track vehicle, having two wheels attached to a frame, one behind the other. A person who rides a bicycle is called a cyclist, or bicyclist....

**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

Cadence (cycling)

In cycling, cadence is the number of revolutions of the crank per minute; roughly speaking, this is the rate at which a cyclist is pedalling/turning the pedals...

. Gearing is optimized to use this narrow range as best as possible. As in other types of transmission

Transmission (mechanics)

A machine consists of a power source and a power transmission system, which provides controlled application of the power. Merriam-Webster defines transmission as: an assembly of parts including the speed-changing gears and the propeller shaft by which the power is transmitted from an engine to a...

s, the gear ratio

Gear ratio

The gear ratio of a gear train is the ratio of the angular velocity of the input gear to the angular velocity of the output gear, also known as the speed ratio of the gear train. The gear ratio can be computed directly from the numbers of teeth of the various gears that engage to form the gear...

is closely related to the mechanical advantage

Mechanical advantage

Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. Ideally, the device preserves the input power and simply trades off forces against movement to obtain a desired amplification in the output force...

of the drivetrain of the bicycle. On single-speed bicycle

Single-speed bicycle

A single-speed bicycle is a type of bicycle with a single gear ratio. These bicycles are without derailleur gears, hub gearing or other methods for varying the gear ratio of the bicycle....

s and multi-speed bicycles using derailleur gears

Derailleur gears

Derailleur gears are a variable-ratio transmission system commonly used on bicycles, consisting of a chain, multiple sprockets of different sizes, and a mechanism to move the chain from one sprocket to another...

, 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 gear

Hub gear

A hub gear, internal-gear hub, or just gear hub is a gear ratio changing system commonly used on bicycles that is implemented with planetary or epicyclic gears. The gears and lubricants are sealed within the hub-shell of the bicycle's rear wheel, as opposed to derailleur gears, where the gears and...

s, the gear ratio also depends on the internal planetary gears within the hub. For a shaft-driven bicycle

Shaft-driven bicycle

A shaft-driven bicycle is a bicycle that uses a drive shaft instead of a chain to transmit power from the pedals to the wheel. Shaft drives were introduced over a century ago, but were mostly supplanted by chain-driven bicycles due to the gear ranges possible with sprockets and derailleurs...

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

Cadence (cycling)

In cycling, cadence is the number of revolutions of the crank per minute; roughly speaking, this is the rate at which a cyclist is pedalling/turning the pedals...

, 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.

### Methods

There are at least four different methods for measuring gear ratios: gear inchesGear inches

Gear inches is a system that assigns numerical measurements to bicycle gear ratios, to indicate how low or high a gear is.Gear inches has no current physical significance; it corresponds to the diameter in inches of the main wheel of an old-fashioned penny-farthing bicycle with equivalent gearing...

, 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

Bicycle wheel

A bicycle wheel is a wheel, most commonly a wire wheel, designed for bicycle. A pair is often called a wheelset, especially in the context of ready built "off the shelf" performance-oriented wheels....

size (rim diameter 622 mm, often referred to as 700C).

- Front/rear measurement is of limited use and only considers the sizes of a chainring 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: ).

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 wheelDrive wheelA drive wheel is a roadwheel in an automotive vehicle that receives torque from the powertrain, and provides the final driving force for a vehicle. A two-wheel drive vehicle has two driven wheels, and a four-wheel drive has four, and so-on....

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-farthingPenny-farthingPenny-farthing, high wheel, high wheeler, and ordinary are all terms used to describe a type of bicycle with a large front wheel and a much smaller rear wheel that was popular after the boneshaker, until the development of the safety bicycle, in the 1880s...

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 cadenceCadence (cycling)

In cycling, cadence is the number of revolutions of the crank per minute; roughly speaking, this is the rate at which a cyclist is pedalling/turning the pedals...

s 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 chainring and cogset 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 |

### Gear ratio calculators

A few good gear ratio calculators are linked below. These can display gear ratios in any or all of the measurement methods.**Caution**: if a calculator does not have any option for specifying tire size (or wheel size including tire) then the numbers it produces are suspect - variations in tire size can lead to results differing by as much as 10% throughout the range.Extra features which can be helpful include:

- Drop-down menus to select common cogsets.
- Display percentage differences between gear ratios.
- Plot gear ratios using a semi-log graph; equal percentage differences then appear as equally-spaced ratios, duplicate gears are obvious.
- Cater for both major types of gear-change mechanism (or even combinations thereof): derailleur and hub.
- Display riding speed for a given pedalling speed (or range thereof).
- Display required derailleur capacity.

Before using such a calculator you need to know the number of teeth on each sprocket on the bicycle, the size of the back wheel, and the size of the tires. The wheel size, rim diameter, and tire size can usually be found embossed on the side of a tire. If gain ratios are to be calculated you 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 a hub gear then details of this mechanism are also needed (make and model is enough for some calculators). Some calculators require the effective (wheel+tire) diameter; this can be determined as the rim diameter plus twice the tire size, e.g. a 700C wheel has an effective rim diameter of 622mm, when fitted with 35 mm hybrid-style tires the effective diameter is 622+35+35 = 692mm; dividing by 25.4 gives an effective diameter of about 27.24 inches.

## Single speed bicycles

A**single-speed bicycle**is a type of bicycle with a single gear ratio. These bicycles are without derailleur gearsDerailleur gears

Derailleur gears are a variable-ratio transmission system commonly used on bicycles, consisting of a chain, multiple sprockets of different sizes, and a mechanism to move the chain from one sprocket to another...

, hub gear

Hub gear

A hub gear, internal-gear hub, or just gear hub is a gear ratio changing system commonly used on bicycles that is implemented with planetary or epicyclic gears. The gears and lubricants are sealed within the hub-shell of the bicycle's rear wheel, as opposed to derailleur gears, where the gears and...

ing or other methods for varying the gear ratio of the bicycle. Adult single-speed bicycles typically have a gear ratio of between 55 and 75 gear inches, depending on the rider and the anticipated usage.

There are many types of modern single speed bicycles; BMX

BMX

Bicycle motocross or BMX refers to the sport in which the main goal is extreme racing on bicycles in motocross style on tracks with inline start and expressive obstacles, and it is also the term that refers to the bicycle itself that is designed for dirt and motocross cycling.- History :BMX started...

bicycles, some bicycles designed for (younger) children, cruiser type bicycles

Cruiser bicycle

Cruiser bicycles, also known as beach cruisers, combine balloon tires, upright seating posture, single-speed drivetrains, and straightforward steel construction with expressive styling...

, classic commuter bicycles

Bicycle commuting

Bicycle commuting is the use of a bicycle to travel from home to a place of work or study — in contrast to the use of a bicycle for sport, recreation or touring....

, unicycle

Unicycle

A unicycle is a human-powered, single-track vehicle with one wheel. Unicycles resemble bicycles, but are less complex.-History:One theory of the advent of the unicycle stems from the popularity of the penny-farthing during the late 19th century...

s, bicycles designed for track racing

Track bicycle

A track bicycle or track bike is a bicycle optimized for racing at a velodrome or outdoor track. Unlike road bicycles, the track bike is a fixed-gear bicycle and so has a single gear and neither freewheel nor brakes. Tires are narrow and inflated to high pressure to reduce rolling resistance...

, fixed-gear road bicycle

Road bicycle

The term road bicycle is used to describe bicycles built for traveling at speed on paved roads. Some sources use the term to mean racing bicycle...

s, and fixed-gear mountain bicycles.

The fixed-gear

Fixed-gear bicycle

A fixed-gear bicycle is a bicycle that has no freewheel, meaning it cannot coast, as the pedals are always in motion when the bicycle is moving....

single-speed bicycle is the most basic type of bicycle. A fixed-gear bike does not have a freewheel mechanism to allow coasting.

## 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/or 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 logarithm

Logarithm

The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: More generally, if x = by, then y is the logarithm of x to base b, and is written...

ic progression; most off-the-shelf cogsets do this with small absolute differences between the smaller sprockets and increasingly larger absolute differences as the sprockets get larger. Because sprockets must have a (relatively small) whole number of teeth it is impossible to achieve 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

Rohloff Speedhub

The Rohloff Speedhub is an epicyclic internal hub gear for bicycles, developed and patented by Rohloff AG. It has been manufactured and marketed by the German company since 1998. The Speedhub 500/14 has 14 equally-spaced sequential gears with no overlapping ratios and is operated by a single...

offers 14 speeds with an average relative difference of 13.6% and individual variations of around 0.1%.

Racing cyclists often have gears with a small relative difference of around 7% to 10%; this allows fine adjustment of gear ratios to suit the conditions and maintain a consistent pedalling speed

Cadence (cycling)

. Mountain bikes and hybrid bikes often have gears with a moderate relative difference of around 15%; this allows for a much larger gear range while having an acceptable step between gears. 3-speed hub gears may have a relative difference of some 33% to 37%; 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

Sprocket

A sprocket or sprocket-wheel is a profiled wheel with teeth, cogs, or even sprockets that mesh with a chain, track or other perforated or indented material. The name 'sprocket' applies generally to any wheel upon which are radial projections that engage a chain passing over it...

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

Transmission (mechanics)

A machine consists of a power source and a power transmission system, which provides controlled application of the power. Merriam-Webster defines transmission as: an assembly of parts including the speed-changing gears and the propeller shaft by which the power is transmitted from an engine to a...

.

### 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**.On a bicycle with more than one gear change mechanism (e.g. front and rear derailleur), these three 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 chainrings and an 8-sprocket cogset:

- the number of
**possible gear ratios**is 24 (=3×8, 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 combination of 3 chainrings and an 8-sprocket cogset 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 chainring to largest rear sprocket, smallest chainring 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). In the worst case there could be only 10 distinct gear ratios, if the percentage step between chainrings is the same as the percentage 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 gearing range indicates the difference between bottom gear and top gear, and provides some measure of the range of conditions (high speed versus steep hills) with which the gears can cope; the strength, experience, and fitness level of the cyclist are also significant. A range of 300% or 3:1 means that for the same pedalling speed a cyclist could travel 3 times as fast in top gear as in bottom gear (assuming sufficient strength, etc.). Conversely, for the same pedalling effort, a cyclist could climb a much steeper hill in bottom gear than in top gear.The overlapping ranges with derailleur gears mean that 24 or 27 speed derailleur gears may only have the same total gear range as a (much more expensive) Rohloff 14-speed

Rohloff Speedhub

The Rohloff Speedhub is an epicyclic internal hub gear for bicycles, developed and patented by Rohloff AG. It has been manufactured and marketed by the German company since 1998. The Speedhub 500/14 has 14 equally-spaced sequential gears with no overlapping ratios and is operated by a single...

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.

The approximate gear ranges which follow are merely indicative of typical gearing setups, and will vary somewhat from bicycle to bicycle.

- 180% 3-speed hub gears
- 250% 5-speed hub gears
- 300% 7-speed hub gears
- 350% 8-speed hub gears; derailleur with 2 chainrings; continuously variable transmission
- 530% derailleur with 3 chainrings; 14-speed hub gear
- 636% 18-speed bottom bracket gearbox

Gear ranges around 600% can be achieved on derailleur setups by careful choice of (non-standard) chainrings and rear cogsets, but this may result in some rather large steps between gears or some awkward gear changes, e.g. 3 chainrings 22-32-44 and 9-speed cogset 12-36. Somewhat higher gear ranges can be achieved either by using larger steps between gears or by using a 2-speed bottom bracket hub gear in conjunction with a suitable derailleur or rear hub gear, but the practical usefulness of such a setup is uncertain, since anyone strong enough to use the high gears at the top of the range is unlikely to need the low gears at the bottom of the range.

## Types of gear change mechanisms

There are two main types of gear change mechanisms, known as derailleursDerailleur gears

Derailleur gears are a variable-ratio transmission system commonly used on bicycles, consisting of a chain, multiple sprockets of different sizes, and a mechanism to move the chain from one sprocket to another...

and hub gear

Hub gear

A hub gear, internal-gear hub, or just gear hub is a gear ratio changing system commonly used on bicycles that is implemented with planetary or epicyclic gears. The gears and lubricants are sealed within the hub-shell of the bicycle's rear wheel, as opposed to derailleur gears, where the gears and...

s. These two systems have both advantages and disadvantages relative to each other, and which type is preferable depends very much on the particular circumstances. There are a few other relatively uncommon types of gear change mechanism which are briefly mentioned near the end of this section. Derailleur mechanisms can only be used with chain drive transmissions, so bicycles with belt drive or shaft drive transmissions must either be single speed or use hub gears.

### External (derailleur)

*External gearing*is so called because all the sprockets involved are readily visible. There may be up to 3 chainrings attached to the crankset and pedals, and typically between 5 and 11 sprockets making up the cogset attached to the rear wheel. Modern front and rear derailleurs typically consist of a moveable chain-guide that is operated remotely by a Bowden cable attached to a shifterShifter (bicycle part)

A bicycle shifter or gear control or gear levers is a component used to control the gearing mechanisms and select the desired gear ratio. Typically, they operate either a derailleur mechanism or an internal hub gear mechanism. In either case, the control is operated by moving a cable that connects...

mounted on the down tube, handlebar stem, or handlebar. A shifter may be a single lever, or a pair of levers, or a twist grip; some shifters may be incorporated with brake levers into a single unit. When a rider operates the shifter

*while pedalling*, the change in cable tension moves the chain-guide from side to side, "derailing" the chain onto different sprockets. The rear derailleur serves double duty: as well as moving the chain between rear sprockets it also has some spring-mounted jockey wheels which take up any slack in the chain.Most hybrid, touring, mountain, and racing bicycles are equipped with both front and rear derailleurs. There are a few gear ratios which have a straight chain path, but most of the gear ratios will have the chain running at an angle. The use of two derailleurs generally results in some duplicate or near duplicate gear ratios, so that the number of distinct gear ratios is typically around two-thirds of the number of advertised gear ratios. The more common configurations have specific names which are usually related to the relative step sizes between the front chainrings and the rear cogset.

#### Crossover gearing

This style is commonly found on mountain, hybrid, and touring bicycles with three chainrings. The relative step on the chainrings (say 25% to 35%) is typically around twice the relative step on the cogset (say 15%), e.g. chainrings 28-38-48 and cogset 12-14-16-18-21-24-28. This results in overlapping gear ranges with a lot of duplication or near-duplication of gear ratios. The advantage of this arrangement is that there is seldom any need to change both front and rear derailleurs simultaneously so it is generally more suitable for casual or inexperienced cyclists.#### Multi-range gearing

This style is commonly found on racing bicycles with two chainrings. The relative step on the chainrings (say 35%) is typically around three or four times the relative step on the cogset (say 8% or 10%), e.g. chainrings 39-53 and close-range cogsets 12-13-14-15-16-17-19-21 or 12-13-15-17-19-21-23-25. This arrangement provides much more scope for adjusting the gear ratio to maintain a constant pedalling speedCadence

Cadence may refer to:Music:*Cadence , a melodic configuration the end of a phrase, section, or piece of music*Cadence Magazine, a monthly review of jazz, blues and improvised music...

, but any change of chainring must be accompanied by a simultaneous change of 3 or 4 sprockets on the cogset if the goal is to switch to the next higher or lower gear ratio.

#### Alpine gearing

This term has no generally accepted meaning. Originally it referred to a gearing arrangement which had one especially low gear (for climbing Alpine passes); this low gear often had a larger than average jump to the next lower gear. In the 1960s the term was used by salespeople to refer to then current 10-speed bicycles (2 chainrings, 5-sprocket cogset), without any regard to its original meaning. The nearest current equivalent to the original meaning can be found in the ShimanoShimano

Shimano, Inc. is a Japanese multinational manufacturer of cycling components, fishing tackle, and rowing equipment.In 2005, the company had net sales of US $1.4 billion. Bicycle components provided 75% of its sales income...

Megarange cogsets, where most of the sprockets have roughly a 15% relative difference, except for the largest sprocket which has roughly a 30% difference; this provides a much lower gear than normal at the cost of a large gearing jump.

#### Half-step gearing

This style is not available off the shelf. There are two chainrings whose relative difference (say 10%) is about half the relative step on the cogset (say 20%). This was used in the mid-20th century when front derailleurs could only handle a small step between chainrings and when rear cogsets only had a small number of sprockets, e.g. chainrings 44-48 and cogset 14-17-20-24-28. The effect is to provide two interlaced gear ranges without any duplication. However to step sequentially through the gear ratios requires a simultaneous front and rear shift on every other gear change.#### Half-step plus granny gearing

This style is not available off the shelf. There are three chainrings with half-step differences between the larger two and multi-range differences between the smaller two, e.g. chainrings 24-42-46 and cogset 12-14-16-18-21-24-28-32-36. This general arrangement is suitable for touring with most gear changes being made using the rear derailleur and occasional fine tuning using the two large chainrings. The small chainring (granny gear) is a bailout for handling steeper hills, but it requires some anticipation in order to use it effectively.### Internal (hub)

*Internal gearing*is so called because all the gears involved are hidden within a wheel hub. Hub gears work using internal planetary, or epicyclic, gearingEpicyclic gearing

Epicyclic gearing or planetary gearing is a gear system consisting of one or more outer gears, or planet gears, revolving about a central, or sun gear. Typically, the planet gears are mounted on a movable arm or carrier which itself may rotate relative to the sun gear...

which alters the speed of the hub casing and wheel relative to the speed of the drive sprocket. They have just a single chainring and a single rear sprocket, almost always with a straight chain path between the two. Hub gears are available with between 3 and 14 speeds; weight and price tend to increase with the number of gears. All the advertised speeds are available as distinct gear ratios controlled by a single shifter (except for some early 5-speed models which used two shifters). Hub gearing is often used for bicycles intended for city-riding and commuting.

### Internal (bottom bracket)

Current systems have a 2-speed hub gear incorporated in the cranksetCrankset

The crankset or chainset , is the component of a bicycle drivetrain that converts the reciprocating motion of the rider's legs into rotational motion used to drive the chain, which in turn drives the rear wheel...

or bottom bracket

Bottom bracket

The bottom bracket on a bicycle connects the crankset to the bicycle and allows the crankset to rotate freely. It contains a spindle that the crankset attaches to, and the bearings that allow the spindle and cranks to rotate. The chainrings and pedals attach to the cranks...

. Patents for such systems appeared as early as 1890. 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

Bottom bracket

The bottom bracket on a bicycle connects the crankset to the bicycle and allows the crankset to rotate freely. It contains a spindle that the crankset attaches to, and the bearings that allow the spindle and cranks to rotate. The chainrings and pedals attach to the cranks...

spindle. The effect is that of having a bicycle with twin chainrings with a massive difference in sizes. Pinion GmbH introduced in 2010 an 18 speed model, offering an evenly spaced 636% range.

### Internal and external combined

It is sometimes possible to combine a hub gear with deraileur gears. There are several commercially available possibilities:- One standard option for the Brompton folding bicycleBrompton BicycleBrompton Bicycle is a manufacturer of folding bicycles based in Brentford, London.The Brompton folding bicycle and accessories are the company's core product, noted for its self-supporting compact size when stored. All available models of the folding bicycle are based on the same hinged bicycle...

is to use a 3-speed hub gear (roughly a 30% difference between gear ratios) in combination with a 2-speed deraileur gear (roughly a 15% difference) to give 6 distinct gear ratios; this is an example of half-step gearing. Some Brompton suppliers offer a 2-speed chainring 'Mountain Drive' as well, which results in 12 distinct gear ratios with a range exceeding 5:1; in this case, the change from 6th to 7th gear involves changing all three sets of gears simultaneously. - The SRAM DualDrive system uses a standard 8 or 9-speed cogset mounted on a three-speed internally-geared hub, offering a similar gear range to a bicycle with a cogset and triple chainrings.
- 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 of 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. 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, some quite different methods of selecting a different gear ratio:- Retro-directRetro-DirectRetro-direct is a gearing mechanism used on some bicycles in the early 20th century, which provides a second gear ratio when pedaled backwards.-History:...

drivetrains used on some early 20th century bicycles have been resurrected by bicycle hobbyists. These have two possible gear ratios but no gear lever; the operator simply pedals forward for one gear and backward for the other. The chain path is quite complicated, since it effectively has to do a figure of eight as well as follow the normal chain path. - Flip-flop hubFlip-flop hubFlip-flop hubs, also called double-sided hubs, are rear bicycle hubs that are threaded to accept fixed cogs and/or freewheels on both sides.There are several different types of flip flop hubs available for different applications...

s have a double-sided rear wheel with a (different sized) sprocket on each side. To change gear: stop, remove the rear wheel, flip it over, replace the wheel, adjust chain tension, resume cycling. Current double sided wheels typically have a fixed sprocket on one side and a freewheel sprocket on the other.

- Prior to 1937 this was the only permitted form of gear changing on the Tour de France. Competitors could have 2 sprockets on each side of the rear wheel, but still had to stop to manually move the chain from one sprocket to the other and adjust the position of the rear wheel so as to maintain the correct chain tension.
- Continuously variable transmissionContinuously variable transmissionA continuously variable transmission is a transmission that can change steplessly through an infinite number of effective gear ratios between maximum and minimum values. This contrasts with other mechanical transmissions that offer a fixed number of gear ratios...

s are a relatively new development in bicycles (though not a new idea). Mechanisms like the NuVinci gearing system use balls connected to two disks by static friction - changing the point of contact changes the gear ratio. - 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 transmission

## Efficiency

The numbers in this section apply to the efficiency of the drive-train, including means of transmission and any gearing system. In this context efficiency is concerned with how much power is delivered to the wheel compared with how much power is put into the pedals. For a well-maintained transmission system, efficiency is generally between 86% and 99%, as detailed below.### Aside

Other**very significant**factors which affect bicycle performanceBicycle performance

A bicycle's performance, in both biological and mechanical terms, is extraordinarily efficient. In terms of the amount of energy a person must expend to travel a given distance, investigators have calculated it to be the most efficient self-powered means of transportation...

include rolling resistance and air resistance:

- Rolling resistanceRolling resistanceRolling resistance, sometimes called rolling friction or rolling drag, is the resistance that occurs when a round object such as a ball or tire rolls on a flat surface, in steady velocity straight line motion. It is caused mainly by the deformation of the object, the deformation of the surface, or...

can vary by a factor of 10 or more depending on the type of tireBicycle tireA bicycle tire is a tire that fits on the wheel of a bicycle, unicycle, tricycle, quadracycle, bicycle trailer, or trailer bike. They may also be used on wheelchairs and handcycles, especially for racing...

, the diameter of the tire, the width of the tire, and the tire pressure. - Air resistance increases greatly as speed increases and is the most significant factor at speeds above 10 to 12 miles per hour (the drag force increases in proportion to the square of the speed, thus the power required to overcome it increases in proportion to the cube of the speed).

Human factors can also be significant. Rohloff demonstrates that overall efficiency can be improved in some cases by using a slightly less efficient gear ratio when this leads to greater human efficiency (in converting food to pedal power) because a more effective pedalling speed is being used.

### Overview

An encyclopedic overview can be found in Chapter 9 of "Bicycling Science" which covers both theory and experimental results. Some details extracted from these and other experiments are provided in the next subsection, with references to the original reports.Factors which have been shown to affect the drive-train efficiency include the type of transmission system (chain, shaft, belt), the type of gearing system (fixed, derailleur, hub, infinitely variable), the size of the sprockets used, the magnitude of the input power, the pedalling speed, and how rusty the chain is. For a particular gearing system, different gear ratios generally have different efficiencies.

Some experiments have used an electric motor to drive the shaft to which the pedals are attached, while others have used averages of a number of actual cyclists. It is not clear how the steady power delivered by a motor compares with the cyclic power provided by pedals. Rohloff argues that the constant motor power should match the peak pedal power rather than the average (which is half the peak).

There is little independent information available relating to the efficiency of belt drives and infinitely variable gear systems; even the manufacturers/suppliers appear reluctant to provide any numbers.

### Details

Derailleur type mechanisms of a typical mid-range product (of the sort used by serious amateurs) achieve between 88% and 99% mechanical efficiencyMechanical efficiency

Mechanical efficiency measures the effectiveness of a machine in transforming the energy and power that is input to the device into an output force and movement...

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.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.

## See also

- BicycleBicycleA bicycle, also known as a bike, pushbike or cycle, is a human-powered, pedal-driven, single-track vehicle, having two wheels attached to a frame, one behind the other. A person who rides a bicycle is called a cyclist, or bicyclist....
- Bicycle drivetrain systemsBicycle drivetrain systemsBicycle drivetrain systems are used to transmit power on bicycles, tricycles, quadracycles, unicycles, or other human-powered vehicles from the riders to the drive wheels. Most also include some type of a mechanism to convert speed and torque via gear ratios....
- CadenceCadence (cycling)
- Cogset
- CranksetCranksetThe crankset or chainset , is the component of a bicycle drivetrain that converts the reciprocating motion of the rider's legs into rotational motion used to drive the chain, which in turn drives the rear wheel...
- Derailleur gearsDerailleur gears
- Gear inchesGear inchesGear inches is a system that assigns numerical measurements to bicycle gear ratios, to indicate how low or high a gear is.Gear inches has no current physical significance; it corresponds to the diameter in inches of the main wheel of an old-fashioned penny-farthing bicycle with equivalent gearing...
- Hub gearHub gear
- NuVinci
- Recumbent bicycleRecumbent bicycleA recumbent bicycle is a bicycle that places the rider in a laid-back reclining position. Most recumbent riders choose this type of design for ergonomic reasons; the rider's weight is distributed comfortably over a larger area, supported by back and buttocks...

## External links

About bicycle gearing:Online gear ratio calculators: