bicycle gearing - wikipedia, the free encyclopedia.pdf

7/28/2019 Bicycle gearing - Wikipedia, the free encyclopedia.pdf

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6/18/12 1:icycle gearing - Wikipedia, the free encyclopedia

Page 1ttp://en.wikipedia.org/wiki/Bicycle_gearing

A bicycle with a hub gear.

Shimano XT rear derailleur on a

mountain bike

Bicycle gearingFrom Wikipedia, the free encyclopedia

Bicycle gearing is the aspect of bicycle transmission that determines

he relation between the cadence, the rate at which the rider pedals, and

he rate at which the drive wheel turns.

On some bicycles, there is only one gear and the gear ratio is fixed.

Many contemporary bicycles have multiple gears and thus multiple gear

atios. A shifting mechanism allows selection of the appropriate gear

atio for efficiency or comfort under the prevailing circumstances: for

example, 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. Different gear ratios and gear ranges are

appropriate for different people and styles of cycling.

A cyclist's legs produce power optimally within a narrow pedalling

peed range. Gearing is optimized to use this narrow range as best as

possible. As in other types of transmissions, the gear ratio is closely

elated to the mechanical advantage of the drivetrain of the bicycle. On

ingle-speed bicycles and multi-speed bicycles using derailleur gears,

he gear ratio depends on the ratio of the number of teeth on the

hainring 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

he 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

hance of knee damage;[1] cadence above 100 rpm becomes less

effective after short bursts, as during a sprint. [1]

Contents

1 Measuring gear ratios1.1 Methods1.2 Examples1.3 Gear ratio calculators
http://en.wikipedia.org/wiki/File:Shimano_xt_rear_derailleur.jpghttp://en.wikipedia.org/wiki/File:Rohloff-nabe.jpghttp://en.wikipedia.org/wiki/File:Rohloff-nabe.jpghttp://en.wikipedia.org/wiki/Bicycle_gearing#Exampleshttp://en.wikipedia.org/wiki/Bicycle_gearing#Exampleshttp://en.wikipedia.org/wiki/Bicycle_gearing#Methodshttp://en.wikipedia.org/wiki/Bicycle_gearing#Measuring_gear_ratioshttp://en.wikipedia.org/wiki/File:Shimano_xt_rear_derailleur.jpghttp://en.wikipedia.org/wiki/File:Shimano_xt_rear_derailleur.jpghttp://en.wikipedia.org/wiki/File:Shimano_xt_rear_derailleur.jpghttp://en.wikipedia.org/wiki/Hub_gearhttp://en.wikipedia.org/wiki/File:Shimano_xt_rear_derailleur.jpghttp://en.wikipedia.org/wiki/File:Shimano_xt_rear_derailleur.jpghttp://en.wikipedia.org/wiki/Single-speed_bicyclehttp://en.wikipedia.org/wiki/Derailleur_gearshttp://en.wikipedia.org/wiki/File:Shimano_xt_rear_derailleur.jpghttp://en.wikipedia.org/wiki/Transmission_(mechanics)http://en.wikipedia.org/wiki/Gear_ratiohttp://en.wikipedia.org/wiki/File:Shimano_xt_rear_derailleur.jpghttp://en.wikipedia.org/wiki/Cadence_(cycling)http://en.wikipedia.org/wiki/List_of_gear_nomenclature#Gear_rangehttp://en.wikipedia.org/wiki/File:Rohloff-nabe.jpghttp://en.wikipedia.org/wiki/File:Rohloff-nabe.jpghttp://en.wikipedia.org/wiki/File:Rohloff-nabe.jpghttp://en.wikipedia.org/wiki/File:Rohloff-nabe.jpghttp://en.wikipedia.org/wiki/File:Rohloff-nabe.jpghttp://en.wikipedia.org/wiki/File:Rohloff-nabe.jpghttp://en.wikipedia.org/wiki/File:Rohloff-nabe.jpghttp://en.wikipedia.org/wiki/Cadence_(cycling)http://en.wikipedia.org/wiki/Cadence_(cycling)http://en.wikipedia.org/wiki/File:Rohloff-nabe.jpghttp://en.wikipedia.org/wiki/Bicycle_gearing#Gear_ratio_calculatorshttp://en.wikipedia.org/wiki/Bicycle_gearing#Exampleshttp://en.wikipedia.org/wiki/Bicycle_gearing#Methodshttp://en.wikipedia.org/wiki/Bicycle_gearing#Measuring_gear_ratioshttp://en.wikipedia.org/wiki/Bicycle_gearing#cite_note-Pevelka-0http://en.wikipedia.org/wiki/Bicycle_gearing#cite_note-Pevelka-0http://en.wikipedia.org/wiki/Cadence_(cycling)http://en.wikipedia.org/wiki/Shaft-driven_bicyclehttp://en.wikipedia.org/wiki/Planetary_gearhttp://en.wikipedia.org/wiki/Hub_gearhttp://en.wikipedia.org/wiki/Derailleur_gearshttp://en.wikipedia.org/wiki/Single-speed_bicyclehttp://en.wikipedia.org/wiki/Mechanical_advantagehttp://en.wikipedia.org/wiki/Gear_ratiohttp://en.wikipedia.org/wiki/Transmission_(mechanics)http://en.wikipedia.org/wiki/Cadence_(cycling)http://en.wikipedia.org/wiki/List_of_gear_nomenclature#Gear_rangehttp://en.wikipedia.org/wiki/Cadence_(cycling)http://en.wikipedia.org/wiki/Shimanohttp://en.wikipedia.org/wiki/File:Shimano_xt_rear_derailleur.jpghttp://en.wikipedia.org/wiki/Hub_gearhttp://en.wikipedia.org/wiki/File:Rohloff-nabe.jpg


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2 Single speed bicycles3 General considerations

3.1 Relative gearing3.2 Usable gears3.3 Gearing range

4 Types of gear change mechanisms4.1 External (derailleur)

4.1.1 Crossover gearing4.1.2 Multi-range gearing4.1.3 Alpine gearing4.1.4 Half-step gearing4.1.5 Half-step plus granny gearing

4.2 Internal (hub)4.3 Internal (bottom bracket)4.4 Internal and external combined4.5 Others

5 Efficiency5.1 Aside

5.2 Overview5.3 Details

6 See also7 References8 External links

Measuring gear ratios

Methods

There are at least four different methods[2] for measuring gear ratios: gear inches, metres of development (r

out), gain ratio, and front/rear (racing-style). The first three methods result in each possible gear ratio being

epresented 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 chainring and a rear sprock

Gear inches and metres of development also take the size of the rear wheel into account. Gain ratio gfurther 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 ofdevelopment, 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

urther factor is needed to allow for any other selected hub gear ratio [3] (many online gear calculators have
http://en.wikipedia.org/wiki/Bicycle_gearing#cite_note-2http://en.wikipedia.org/wiki/Bicycle_wheelhttp://en.wikipedia.org/wiki/Gear_inches#Gain_ratiohttp://en.wikipedia.org/wiki/Gear_inches#Calculating_metres_of_developmenthttp://en.wikipedia.org/wiki/Gear_incheshttp://en.wikipedia.org/wiki/Bicycle_gearing#cite_note-1http://en.wikipedia.org/wiki/Bicycle_gearing#External_linkshttp://en.wikipedia.org/wiki/Bicycle_gearing#Referenceshttp://en.wikipedia.org/wiki/Bicycle_gearing#See_alsohttp://en.wikipedia.org/wiki/Bicycle_gearing#Detailshttp://en.wikipedia.org/wiki/Bicycle_gearing#Overviewhttp://en.wikipedia.org/wiki/Bicycle_gearing#Asidehttp://en.wikipedia.org/wiki/Bicycle_gearing#Efficiencyhttp://en.wikipedia.org/wiki/Bicycle_gearing#Othershttp://en.wikipedia.org/wiki/Bicycle_gearing#Internal_and_external_combinedhttp://en.wikipedia.org/wiki/Bicycle_gearing#Internal_.28bottom_bracket.29http://en.wikipedia.org/wiki/Bicycle_gearing#Internal_.28hub.29http://en.wikipedia.org/wiki/Bicycle_gearing#Half-step_plus_granny_gearinghttp://en.wikipedia.org/wiki/Bicycle_gearing#Half-step_gearinghttp://en.wikipedia.org/wiki/Bicycle_gearing#Alpine_gearinghttp://en.wikipedia.org/wiki/Bicycle_gearing#Multi-range_gearinghttp://en.wikipedia.org/wiki/Bicycle_gearing#Crossover_gearinghttp://en.wikipedia.org/wiki/Bicycle_gearing#External_.28derailleur.29http://en.wikipedia.org/wiki/Bicycle_gearing#Types_of_gear_change_mechanismshttp://en.wikipedia.org/wiki/Bicycle_gearing#Gearing_rangehttp://en.wikipedia.org/wiki/Bicycle_gearing#Usable_gearshttp://en.wikipedia.org/wiki/Bicycle_gearing#Relative_gearinghttp://en.wikipedia.org/wiki/Bicycle_gearing#General_considerationshttp://en.wikipedia.org/wiki/Bicycle_gearing#Single_speed_bicycles


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hese factors built in for various popular hub gears).

Gear inches = Diameter of drive wheel in inches (number of teeth in front chainring / number of tein rear sprocket).Normally rounded to nearest whole number.Metres of development = Circumference of drive wheel in metres (number of teeth in front chainr/ 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 metretraveled by the bicycle for one rotation of the pedals. Gain ratio is the ratio between the distancetravelled by the bicycle and the distance travelled by a pedal, and is a pure number, independent of anunits of measurement.

Front/rear gear measurement uses two numbers (e.g. 53/19) where the first is the number of teeth in th

front chainring and the second is the number of teeth in the rear sprocket. Without doing somearithmetic, 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

evolutions per minute are also given. On each row the relative values for gear inches, metres of developme

gain ratio, and speed are more or less correct, while the front/rear values are the nearest approximation whic

an be made using typical chainring and cogset sizes. Note that bicycles intended for racing may have a low

gear of around 45 gear inches (or 35 if fitted with a compact crankset).

GearGear

inchesMetre

developmentGainratio

Front/rear

60 rpm 80 rpm 100 rpm 120 rpm

mph km/h mph km/h mph km/h mph km/h

Veryhigh

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 5.253/19 or39/14

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

Verylow

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
http://en.wikipedia.org/wiki/Bicycle_gearing#External_linkshttp://en.wikipedia.org/wiki/Cadence_(cycling)http://en.wikipedia.org/wiki/Penny-farthinghttp://en.wikipedia.org/wiki/Drive_wheel


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Single-speed mountain bike

measurement methods.

Caution: if a calculator does not have any option for specifying tire size (or wheel size including tire) then

numbers it produces are suspect - variations in tire size can lead to results differing by as much as 10%

hroughout 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 spacedratios, duplicate gears are obvious.Cater for both major types of gear-change mechanism (or even combinations thereof): derailleur andhub.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 s

of the back wheel, and the size of the tires. The wheel size, rim diameter, and tire size can usually be foundembossed on the side of a tire. If gain ratios are to be calculated you also need to know the length of the pe

ranks in millimetres (crank lengths are normally some multiple of 2.5 mm). If the bicycle has a hub gear th

details of this mechanism are also needed (make and model is enough for some calculators). Some calculato

equire the effective (wheel+tire) diameter; this can be determined as the rim diameter plus twice the tire si

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 inch

Single speed bicycles

Main article: Single-speed bicycle

A single-speed bicycle is a type of bicycle with a single gear

atio. These bicycles are without derailleur gears, hub gearing or

other methods for varying the gear ratio of the bicycle. Adult

ingle-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

ype bicycles, classic commuter bicycles, unicycles, bicyclesdesigned for track racing, fixed-gear road bicycles, 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.
http://en.wikipedia.org/wiki/Fixed-gear_bicyclehttp://en.wikipedia.org/wiki/Mountain_bicyclehttp://en.wikipedia.org/wiki/Road_bicyclehttp://en.wikipedia.org/wiki/Track_bicyclehttp://en.wikipedia.org/wiki/Unicyclehttp://en.wikipedia.org/wiki/Bicycle_commutinghttp://en.wikipedia.org/wiki/Cruiser_bicyclehttp://en.wikipedia.org/wiki/BMXhttp://en.wikipedia.org/wiki/Hub_gearhttp://en.wikipedia.org/wiki/Derailleur_gearshttp://en.wikipedia.org/wiki/Single-speed_bicyclehttp://en.wikipedia.org/wiki/File:Singlespeed-mountainbike.jpg


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General considerations

The gearing supplied by the manufacturer on a new bicycle is selected to be useful to the majority of peopl

Some cyclists choose to fine-tune the gearing to better suit their strength, level of fitness, and expected usag

When buying from specialist cycle shops, it may be less expensive to get the gears altered before delivery

ather 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 lo

peed. Balancing a bicycle becomes more difficult at lower speeds. For example, a bottom gear around 16 g

nches gives an effective speed of perhaps 3 miles/hour (5 km/hour) or less, at which point it might be quick

o walk.

Relative gearing

As far as a cyclist's legs are concerned, when changing gears, the relative difference between two gears is m

mportant than the absolute difference between gears.[4] 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 gearCycling tends to feel more comfortable if nearly all gear changes have more or less the same percentage

difference.[5] For example, a change from a 13-tooth sprocket to a 15-tooth sprocket (15.4%) feels very

imilar to a change from a 20-tooth sprocket to a 23-tooth sprocket (15%), even though the latter has a larg

absolute difference.

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

most off-the-shelf cogsets do this with small absolute differences between the smaller sprockets and

ncreasingly larger absolute differences as the sprockets get larger. Because sprockets must have a (relative

mall) 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 stepsvarying between 12.5% and 16.7%. The epicyclic gears used within hub gears have more scope for varying

number of teeth than do derailleur sprockets, so it may be possible to get much closer to the ideal of consis

elative 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 speed. Mountain bikes a

hybrid bikes often have gears with a moderate relative difference of around 15%; this allows for a much larg

gear range while having an acceptable step between gears. 3-speed hub gears may have a relative difference

ome 33% to 37%;[5] such big steps require a very substantial change in pedalling speed and often feel

excessive.[6] 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
http://en.wikipedia.org/wiki/Transmission_(mechanics)http://en.wikipedia.org/wiki/Sprockethttp://en.wikipedia.org/wiki/Bicycle_gearing#cite_note-5http://en.wikipedia.org/wiki/Bicycle_gearing#cite_note-Hub_Gear-4http://en.wikipedia.org/wiki/Cadence_(cycling)http://en.wikipedia.org/wiki/Rohloff_Speedhubhttp://en.wikipedia.org/wiki/Logarithmhttp://en.wikipedia.org/wiki/Bicycle_gearing#cite_note-Hub_Gear-4http://en.wikipedia.org/wiki/Bicycle_gearing#cite_note-3http://en.wikipedia.org/wiki/Bicycle_and_motorcycle_dynamics#Balancehttp://en.wikipedia.org/wiki/Cogset


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On a bicycle with only one gear change mechanism (e.g. rear hub only or rear derailleur only), the number

possible gear ratios is the same as the number ofusable gear ratios, which is also the same as the numbe

distinct gear ratios.

On a bicycle with more than one gear change mechanism (e.g. front and rear derailleur), these three number

an be quite different, depending on the relative gearing steps of the various mechanisms. The number of ge

or 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 ofpossible gear ratios is 24 (=38, this is the number usually quoted in advertisements)the number ofusable gear ratios is 22;the number ofdistinct 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 rprocket) result in a very diagonal chain alignment which is inefficient and causes excessive chain wear.[7]

Due to the overlap, there will usually be some duplicates or near-duplicates, so that there might only be 16

8 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 deraille

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 m

popular ratio is duplicated then it may be feasible to extend the life of the gear set by using different version

of this popular ratio.

Gearing range

The gearing range indicates the difference between bottom gear and top gear, and provides some measure o

he range of conditions (high speed versus steep hills) with which the gears can cope; the strength, experienc

and fitness level of the cyclist are also significant. A range of 300% or 3:1 means that for the same pedallin

peed 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 to

gear.

The overlapping ranges with derailleur gears mean that 24 or 27 speed derailleur gears may only have the sa

otal gear range as a (much more expensive) Rohloff 14-speed hub gear. Internal hub geared bikes typicallyhave a more restricted gear range than comparable derailleur-equipped bikes, and have fewer ratios within t

ange.

The approximate gear ranges which follow are merely indicative of typical gearing setups, and will vary

omewhat from bicycle to bicycle.

180% 3-speed hub gears
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Bicycle rear wheel

showing front and rear

derailleurs, and rear

cogset

250% 5-speed hub gears300% 7-speed hub gears350% 8-speed hub gears; derailleur with 2 chainrings; continuously variable transmission530% derailleur with 3 chainrings; 14-speed hub gear

636% 18-speed bottom bracket gearbox[8]

Gear ranges around 600% can be achieved on derailleur setups by careful choice of (non-standard) chainrin

and rear cogsets, but this may result in some rather large steps between gears or some awkward gear changee.g. 3 chainrings 22-32-44 and 9-speed cogset 12-36. Somewhat higher gear ranges can be achieved either b

using larger steps between gears or by using a 2-speed bottom bracket hub gear in conjunction with a suitab

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

ange.

Types of gear change mechanisms

There are two main types of gear change mechanisms, known as derailleurs and hub gears. These two system

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 us

with chain drive transmissions, so bicycles with belt drive or shaft drive transmissions must either be single

peed or use hub gears.

External (derailleur)

Main article: Derailleur gears

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

s operated remotely by a Bowden cable attached to a shifter mounted on the down

ube, handlebar stem, or handlebar. A shifter may be a single lever, or a pair of

evers, or a twist grip; some shifters may be incorporated with brake levers into a

ingle unit. When a rider operates the shifter while pedalling, the change in cable

ension 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

hain between rear sprockets it also has some spring-mounted jockey wheelswhich 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 runnin

at an angle. The use of two derailleurs generally results in some duplicate or near duplicate gear ratios, so th

he number of distinct gear ratios is typically around two-thirds of the number of advertised gear ratios. The

more common configurations have specific names [9] which are usually related to the relative step sizes
http://en.wikipedia.org/wiki/Bicycle_gearing#cite_note-Gear_Theory-8http://en.wikipedia.org/wiki/Twistgriphttp://en.wikipedia.org/wiki/Shifter_(bicycle_part)http://en.wikipedia.org/wiki/Cogsethttp://en.wikipedia.org/wiki/Derailleur_gearshttp://en.wikipedia.org/wiki/Hub_gears#Disadvantageshttp://en.wikipedia.org/wiki/Hub_gears#Advantageshttp://en.wikipedia.org/wiki/Hub_gearhttp://en.wikipedia.org/wiki/Derailleur_gearshttp://en.wikipedia.org/wiki/Bicycle_gearing#cite_note-7http://en.wikipedia.org/wiki/Cogsethttp://en.wikipedia.org/wiki/Derailleur_gearshttp://en.wikipedia.org/wiki/File:2010_Cervelo_RS_02.jpg


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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

tep 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.

Advantages of this arrangement include:

A wide range of gears may be available suitable for touring and for off-road riding.There is seldom any need to change both front and rear derailleurs simultaneously so it is generallymore suitable for casual or inexperienced cyclists.

One disadvantage is that there is that the overlapping gear ranges result in a lot of duplication or near-

duplication of gear ratios.

Multi-range gearing

This style is commonly found on racing bicycles with two chainrings. The relative step on the chainrings (sa

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 speed, but any chan

of chainring must be accompanied by a simultaneous change of 3 or 4 sprockets on the cogset if the goal is

witch 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 n

owest gear. In the 1960s the term was used by salespeople to refer to then current 10-speed bicycles (2

hainrings, 5-sprocket cogset), without any regard to its original meaning. The nearest current equivalent to

he original meaning can be found in the Shimano Megarange cogsets, where most of the sprockets have

oughly 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 abo

half the relative step on the cogset (say 20%). This was used in the mid-20th century when front derailleurs

ould only handle a small step between chainrings and when rear cogsets only had a small number of

prockets, e.g. chainrings 44-48 and cogset 14-17-20-24-28. The effect is to provide two interlaced gear ran

without any duplication. However to step sequentially through the gear ratios requires a simultaneous front

ear shift on every other gear change.
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Half-step plus granny gearing

This style is not available off the shelf. There are three chainrings with half-step differences between the la

wo 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

ear derailleur and occasional fine tuning using the two large chainrings.[9] The small chainring (granny gea

s a bailout for handling steeper hills, but it requires some anticipation in order to use it effectively.

Internal (hub)

Main article: Hub gear

nternal gearing is so called because all the gears involved are hidden within a wheel hub. Hub gears work

using internal planetary, or epicyclic, gearing which alters the speed of the hub casing and wheel relative to

peed of the drive sprocket. They have just a single chainring and a single rear sprocket, almost always wit

traight chain path between the two. Hub gears are available with between 3 and 14 speeds; weight and pric

end to increase with the number of gears. All the advertised speeds are available as distinct gear ratios

ontrolled by a single shifter (except for some early 5-speed models which used two shifters). Hub gearing ioften used for bicycles intended for city-riding and commuting.

Internal (bottom bracket)

Current systems have a 2-speed hub gear incorporated in the crankset or bottom bracket. Patents for such

ystems appeared as early as 1890.[10] The Schlumpf Mountain Drive and Speed Drive have been available

ince 2001 [11] and offer direct drive plus one of three variants (reduction 1:2.5, increase 1.65:1, and increa

2.5:1). Changing gears is accomplished by using your foot to tap a button protuding on each side of the bott

bracket spindle. The effect is that of having a bicycle with twin chainrings with a massive difference in size

Pinion GmbH introduced in 2010 an 18 speed model, offering an evenly spaced 636% range.[12]

Internal and external combined

t is sometimes possible to combine a hub gear with deraileur gears.

There are several commercially available possibilities:

One standard option for the Brompton folding bicycle is to use a3-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 ofhalf-step gearing. Some Brompton suppliers offer a 2-speedchainring 'Mountain Drive' as well, which results in 12 distinctgear ratios with a range exceeding 5:1; in this case, the changefrom 6th to 7th gear involves changing all three sets of gearssimultaneously.The SRAM DualDrive system uses a standard 8 or 9-speedcogset mounted on a three-speed internally geared hub, offering a
http://en.wikipedia.org/wiki/Brompton_Bicyclehttp://en.wikipedia.org/wiki/Bicycle_gearing#cite_note-Pinion-11http://en.wikipedia.org/wiki/Bottom_brackethttp://en.wikipedia.org/wiki/Bicycle_gearing#cite_note-10http://en.wikipedia.org/wiki/Bicycle_gearing#cite_note-Berto-9http://en.wikipedia.org/wiki/Bottom_brackethttp://en.wikipedia.org/wiki/Cranksethttp://en.wikipedia.org/wiki/Epicyclic_gearinghttp://en.wikipedia.org/wiki/Hub_gearhttp://en.wikipedia.org/wiki/Bicycle_gearing#cite_note-Gear_Theory-8http://en.wikipedia.org/wiki/File:SRAM_Dual_Drive.jpg


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SRAM Dual Drive combination

derailleur gears and hub gear

similar gear range to a bicycle with a cogset and triple chainrings.Less common is the use of a double or triple chainring inconjunction with an internally geared hub, extending the gearrange 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 r

derailleurs, giving a very wide-ranging drivetrain at the expense of weight and complexity of operatiothere are a total of three sets of gears. This approach may be suitable for recumbent trikes, where verylow gears can be used without balance issues, and the aerodynamic position allows higher gears thannormal.

Others

There have been, and still are, some quite different methods of selecting a different gear ratio:

Retro-direct drivetrains used on some early 20th century bicycles have been resurrected by bicyclehobbyists. These have two possible gear ratios but no gear lever; the operator simply pedals forward fone gear and backward for the other. The chain path is quite complicated, since it effectively has to dfigure of eight as well as follow the normal chain path.Flip-flop hubs have a double-sided rear wheel with a (different sized) sprocket on each side. To changear: stop, remove the rear wheel, flip it over, replace the wheel, adjust chain tension, resume cyclingCurrent double sided wheels typically have a fixed sprocket on one side and a freewheel sprocket on other.

Prior to 1937 this was the only permitted form of gear changing on the Tour de France.[13] Competitocould have 2 sprockets on each side of the rear wheel, but still had to stop to manually move the chaifrom one sprocket to the other and adjust the position of the rear wheel so as to maintain the correct

chain tension.

Continuously variable transmissions are a relatively new development in bicycles (though not a newidea). Mechanisms like the NuVinci gearing system use balls connected to two disks by static frictionchanging the point of contact changes the gear ratio.Automatic transmissions have been demonstrated and marketed for both derailleur and hub gearmechanisms, often accompanied by a warning to disengage auto-shifting if standing on the pedals. Thhave met with limited market success.

Efficiency

The numbers in this section apply to the efficiency of the drive-train, including means of transmission and a

gearing system. In this context efficiency is concerned with how much power is delivered to the wheel

ompared with how much power is put into the pedals. For a well-maintained transmission system, efficien

s generally between 86% and 99%, as detailed below.

Aside
http://en.wikipedia.org/wiki/NuVinci_Continuously_Variable_Transmissionhttp://en.wikipedia.org/wiki/Continuously_variable_transmissionhttp://en.wikipedia.org/wiki/Bicycle_gearing#cite_note-12http://en.wikipedia.org/wiki/Flip-flop_hubhttp://en.wikipedia.org/wiki/Retro-directhttp://en.wikipedia.org/wiki/Hub_gearhttp://en.wikipedia.org/wiki/Derailleur_gearshttp://en.wikipedia.org/wiki/File:SRAM_Dual_Drive.jpg


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Other very significant factors which affect bicycle performance include rolling resistance and air resistance

Rolling resistance can vary by a factor of 10 or more depending on the type of tire, the diameter of th

tire, the width of the tire, and the tire pressure.[14]

Air resistance increases greatly as speed increases and is the most significant factor at speeds above 1to 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).[15]

Human factors can also be significant. Rohloff demonstrates[16] that overall efficiency can be improved in

ome cases by using a slightly less efficient gear ratio when this leads to greater human efficiency (in

onverting 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" [17] which covers both theory a

experimental results. Some details extracted from these and other experiments are provided in the next

ubsection, 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

prockets 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 oth

have used averages of a number of actual cyclists. It is not clear how the steady power delivered by a moto

ompares with the cyclic power provided by pedals. Rohloff argues[16] that the constant motor power shoul

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 variab

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 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

mall-ring to small-sprocket. This cross-chaining also results in increased wear because of the lateraldeflection of the chain.

Chester Kyle and Frank Berto reported in "Human Power" 52 (Summer 2001) [19] that testing on three

derailleur systems (from 4 to 27 gears) and eight gear hub transmissions (from 3 to 14 gears), performed wi

80W, 150W, 200W inputs, gave results as follows:

Transmission Type Efficiency (%)
http://en.wikipedia.org/wiki/Bicycle_gearing#cite_note-18http://en.wikipedia.org/wiki/Bicycle_gearing#cite_note-whitt-17http://en.wikipedia.org/wiki/Mechanical_efficiencyhttp://en.wikipedia.org/wiki/Bicycle_gearing#cite_note-Rohloff1-15http://en.wikipedia.org/wiki/Bicycle_gearing#cite_note-Wilson-16http://en.wikipedia.org/wiki/Bicycle_gearing#cite_note-Rohloff1-15http://en.wikipedia.org/wiki/Bicycle_gearing#cite_note-14http://en.wikipedia.org/wiki/Aerodynamic_draghttp://en.wikipedia.org/wiki/Bicycle_gearing#cite_note-13http://en.wikipedia.org/wiki/Bicycle_tirehttp://en.wikipedia.org/wiki/Rolling_resistancehttp://en.wikipedia.org/wiki/Bicycle_performance


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Derailleurs 87-97

Gear Hubs 86-95

Efficiency testing of bicycle gearing systems is complicated by a number of factors - in particular, all system

end to be better at higher power rates. 200 Watts will drive a typical bicycle at 20 mph, while top cyclists c

achieve 400W, at which point one hub-gear manufacturer (Rohloff) claims 98% efficiency.[20]

At a more typical 150W, hub-gears tend to be around 2% less efficient than a well-lubricated derailleur.[21

See also

BicycleBicycle drivetrain systemsCadenceCogsetCrankset

Derailleur gearsGear inchesHub gearNuVinciRecumbent bicycle

References

1. ^ ab Ed Pavelka (1999).Bicycling magazine's training techniques for cyclists: greater power, faster

(http://books.google.com/books?

id=LDmxGcjoCaYC&pg=PA4&lpg=PA4&dq=dangers+of+pushing+too+big+a+gear&source=bl&ots=eOjt2ni4Ml&=KLzUfCVPRTRZXIPYCRzAZr4cZw&hl=en&ei=9ivTTZi2G4GctweXg4SxCg&sa=X&oi=book_result&ct=result

snum=6&ved=0CEAQ6AEwBQ#v=onepage&q&f=false) . Rodale Press. pp. 45. http://books.google.com/books?

id=LDmxGcjoCaYC&pg=PA4&lpg=PA4&dq=dangers+of+pushing+too+big+a+gear&source=bl&ots=eOjt2ni4Ml&

=KLzUfCVPRTRZXIPYCRzAZr4cZw&hl=en&ei=9ivTTZi2G4GctweXg4SxCg&sa=X&oi=book_result&ct=result

snum=6&ved=0CEAQ6AEwBQ#v=onepage&q&f=false. "There are lots of cyclists who have suffered debilitating

trauma from pushing too big a gear....benefits of spinning begin to disappear above 100 rpm."

2. ^ "Gain Ratios; a new way to think about bicycle gears" (http://www.adventurecycling.org/resources/gainratios.pdf

http://www.adventurecycling.org/resources/gainratios.pdf. Retrieved 2011-05-25.

3. ^ "Cyclists Touring Club: internal gear ratios" (http://www.ctc.org.uk/DesktopDefault.aspx?TabID=4005) .

http://www.ctc.org.uk/DesktopDefault.aspx?TabID=4005. Retrieved 2011-06-29.

4. ^ "Cycling Cadence and Bicycle Gearing" (http://www.kenkifer.com/bikepages/touring/gears.htm) .http://www.kenkifer.com/bikepages/touring/gears.htm. Retrieved 2011-07-18.

5. ^ ab "Internal Gear Hub Review" (http://hubstripping.wordpress.com/internal-gear-hub-review/) .

http://hubstripping.wordpress.com/internal-gear-hub-review/. Retrieved 2011-07-20.

6. ^ "What Kind Of Drive The Cyclist Needs"

(http://www.rohloff.de/en/technology/speedhub/gear_shift_comparison/index.html) .

http://www.rohloff.de/en/technology/speedhub/gear_shift_comparison/index.html. Retrieved 2011-07-20.

7. ^ "Derailleur Gears: A practical guide to their use and operation." (http://www.southcoastbikes.co.uk/articles.asp?

article=Gears) . http://www.southcoastbikes.co.uk/articles.asp?article=Gears. Retrieved 2011-06-27.
http://www.southcoastbikes.co.uk/articles.asp?article=Gearshttp://www.southcoastbikes.co.uk/articles.asp?article=Gearshttp://en.wikipedia.org/wiki/Bicycle_gearing#cite_ref-6http://www.rohloff.de/en/technology/speedhub/gear_shift_comparison/index.htmlhttp://www.rohloff.de/en/technology/speedhub/gear_shift_comparison/index.htmlhttp://en.wikipedia.org/wiki/Bicycle_gearing#cite_ref-5http://hubstripping.wordpress.com/internal-gear-hub-review/http://hubstripping.wordpress.com/internal-gear-hub-review/http://en.wikipedia.org/wiki/Bicycle_gearing#cite_ref-Hub_Gear_4-1http://en.wikipedia.org/wiki/Bicycle_gearing#cite_ref-Hub_Gear_4-0http://www.kenkifer.com/bikepages/touring/gears.htmhttp://www.kenkifer.com/bikepages/touring/gears.htmhttp://en.wikipedia.org/wiki/Bicycle_gearing#cite_ref-3http://www.ctc.org.uk/DesktopDefault.aspx?TabID=4005http://www.ctc.org.uk/DesktopDefault.aspx?TabID=4005http://en.wikipedia.org/wiki/Bicycle_gearing#cite_ref-2http://www.adventurecycling.org/resources/gainratios.pdfhttp://www.adventurecycling.org/resources/gainratios.pdfhttp://en.wikipedia.org/wiki/Bicycle_gearing#cite_ref-1http://books.google.com/books?id=LDmxGcjoCaYC&pg=PA4&lpg=PA4&dq=dangers+of+pushing+too+big+a+gear&source=bl&ots=eOjt2ni4Ml&sig=KLzUfCVPRTRZXIPYCRzAZr4cZw&hl=en&ei=9ivTTZi2G4GctweXg4SxCg&sa=X&oi=book_result&ct=result&resnum=6&ved=0CEAQ6AEwBQ#v=onepage&q&f=falsehttp://en.wikipedia.org/wiki/Rodale_Presshttp://books.google.com/books?id=LDmxGcjoCaYC&pg=PA4&lpg=PA4&dq=dangers+of+pushing+too+big+a+gear&source=bl&ots=eOjt2ni4Ml&sig=KLzUfCVPRTRZXIPYCRzAZr4cZw&hl=en&ei=9ivTTZi2G4GctweXg4SxCg&sa=X&oi=book_result&ct=result&resnum=6&ved=0CEAQ6AEwBQ#v=onepage&q&f=falsehttp://en.wikipedia.org/wiki/Bicycle_gearing#cite_ref-Pevelka_0-1http://en.wikipedia.org/wiki/Bicycle_gearing#cite_ref-Pevelka_0-0http://en.wikipedia.org/wiki/Recumbent_bicyclehttp://en.wikipedia.org/wiki/NuVincihttp://en.wikipedia.org/wiki/Hub_gearhttp://en.wikipedia.org/wiki/Gear_incheshttp://en.wikipedia.org/wiki/Derailleur_gearshttp://en.wikipedia.org/wiki/Cranksethttp://en.wikipedia.org/wiki/Cogsethttp://en.wikipedia.org/wiki/Cadence_(cycling)http://en.wikipedia.org/wiki/Bicycle_drivetrain_systemshttp://en.wikipedia.org/wiki/Bicyclehttp://en.wikipedia.org/wiki/Bicycle_gearing#cite_note-20http://en.wikipedia.org/wiki/Bicycle_gearing#cite_note-19http://en.wikipedia.org/wiki/Rohloff


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8. ^ Mike Levy (Aug 30, 2011). "Pinion 18 speed Gearbox - Eurobike 2011" (http://www.pinkbike.com/news/Pinion

Gearbox-Eurobike-2011.html) . PinkBike.com. http://www.pinkbike.com/news/Pinion-Gearbox-Eurobike-2011.htm

Retrieved 2011-09-12.

9. ^ ab "Gear Theory for Bicyclists" (http://www.sheldonbrown.com/gear-theory.html) .

http://www.sheldonbrown.com/gear-theory.html. Retrieved 2011-06-20.

10. ^ Berto, Frank (2010). The Dancing Chain (Third ed.). Van der Plas Publications. pp. 3947. ISBN 978-1-892495

4.

11. ^ Peter Eland (Monday 12 Aug 2002). "Schlumpf announces new High Speed Drive"

(http://www.velovision.com/showStory.php?storynum=402) . Velo Vision. http://www.velovision.com/showStory.p

storynum=402. Retrieved 2011-05-17.

12. ^ "Pinion P1.18" (http://pinion.eu/discover-pinion/pinion-p1-18/) . Pinion GmbH. http://pinion.eu/discover-

pinion/pinion-p1-18/.

13. ^ "1937 Tour de France" (http://bikeraceinfo.com/tdf/tdf1937.html) . http://bikeraceinfo.com/tdf/tdf1937.html.


14. ^ "Rolling Resistance of Bike Tires" (http://www.terrymorse.com/bike/rolres.html) .

http://www.terrymorse.com/bike/rolres.html. Retrieved 2011-07-20.

15. ^ "Bicycle efficiency and power -- or, why bikes have gears" (http://users.frii.com/katana/biketext.html) .

http://users.frii.com/katana/biketext.html. Retrieved 2011-07-20.

16. ^ ab "Efficiency measurement of bicycle transmission"

(http://www.rohloff.de/en/technology/speedhub/efficiency_measurement/) .

http://www.rohloff.de/en/technology/speedhub/efficiency_measurement/. Retrieved 2011-07-22.

17. ^ Wilson, David G.; J Papadopuolos (2004).Bicycling Science (Third ed.). Massachusetts Institute of Technology.

pp. 311352. ISBN 0-262-73154-1.

18. ^ Whitt, Frank R.; David G. Wilson (1982).Bicycling Science (Second edition ed.). Massachusetts Institute of

Technology. pp. 277300. ISBN 0-262-23111-5.

19. ^ "The mechanical efficiency of bicycle derailleur and hub-gear transmissions"

(http://www.ihpva.org/HParchive/PDF/hp52-2001.pdf) . http://www.ihpva.org/HParchive/PDF/hp52-2001.pdf.


20. ^ "Efficiency Measurements of Bicycle Transmissions" (http://www.ihpva.eu/HParchive/PDF/hp55/hp55p11-15.pd

Bernhard Rohloff and Peter Greb (translated by Thomas Siemann) 2004. Rohloff's testing "at 400 watts, double w

we did and found efficiencies approaching 98%".21. ^ "Efficiency Measurements of Bicycle Transmissions" (http://www.ihpva.eu/HParchive/PDF/hp55/hp55p11-15.pd

Bernhard Rohloff and Peter Greb (translated by Thomas Siemann) 2004. "In our article we therefore concluded tha

hub gears are about 2% less efficient that derailleur transmissions under typical field conditions. We see no reason

change that conclusion.".

External links

About bicycle gearing:

Cycling glossary, links to articles (http://www.sheldonbrown.com/glossary.html)Gearing 101 (http://www.cyclingsite.com/lists_articles/gearing_101.htm)

Online gear ratio calculators:

Calculate your gear ratios, as numbers and percentages (http://www.sheldonbrown.com/gears/)Calculate your gear ratios, as numbers and graphs (http://home.earthlink.net/~mike.sherman/shift.htmCalculate gear ratios, speed and cadence with spreadsheet option (http://www.machars.net/bikecalc.ht
http://www.machars.net/bikecalc.htmhttp://home.earthlink.net/~mike.sherman/shift.htmlhttp://www.sheldonbrown.com/gears/http://www.cyclingsite.com/lists_articles/gearing_101.htmhttp://www.sheldonbrown.com/glossary.htmlhttp://www.ihpva.eu/HParchive/PDF/hp55/hp55p11-15.pdfhttp://en.wikipedia.org/wiki/Bicycle_gearing#cite_ref-20http://www.ihpva.eu/HParchive/PDF/hp55/hp55p11-15.pdfhttp://en.wikipedia.org/wiki/Bicycle_gearing#cite_ref-19http://www.ihpva.org/HParchive/PDF/hp52-2001.pdfhttp://www.ihpva.org/HParchive/PDF/hp52-2001.pdfhttp://en.wikipedia.org/wiki/Bicycle_gearing#cite_ref-18http://en.wikipedia.org/wiki/Special:BookSources/0-262-23111-5http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Bicycle_gearing#cite_ref-whitt_17-0http://en.wikipedia.org/wiki/Special:BookSources/0-262-73154-1http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Bicycle_gearing#cite_ref-Wilson_16-0http://www.rohloff.de/en/technology/speedhub/efficiency_measurement/http://www.rohloff.de/en/technology/speedhub/efficiency_measurement/http://en.wikipedia.org/wiki/Bicycle_gearing#cite_ref-Rohloff1_15-1http://en.wikipedia.org/wiki/Bicycle_gearing#cite_ref-Rohloff1_15-0http://users.frii.com/katana/biketext.htmlhttp://users.frii.com/katana/biketext.htmlhttp://en.wikipedia.org/wiki/Bicycle_gearing#cite_ref-14http://www.terrymorse.com/bike/rolres.htmlhttp://www.terrymorse.com/bike/rolres.htmlhttp://en.wikipedia.org/wiki/Bicycle_gearing#cite_ref-13http://bikeraceinfo.com/tdf/tdf1937.htmlhttp://bikeraceinfo.com/tdf/tdf1937.htmlhttp://en.wikipedia.org/wiki/Bicycle_gearing#cite_ref-12http://pinion.eu/discover-pinion/pinion-p1-18/http://pinion.eu/discover-pinion/pinion-p1-18/http://en.wikipedia.org/wiki/Bicycle_gearing#cite_ref-Pinion_11-0http://www.velovision.com/showStory.php?storynum=402http://www.velovision.com/showStory.php?storynum=402http://en.wikipedia.org/wiki/Bicycle_gearing#cite_ref-10http://en.wikipedia.org/wiki/Special:BookSources/978-1-892495-59-4http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Bicycle_gearing#cite_ref-Berto_9-0http://www.sheldonbrown.com/gear-theory.htmlhttp://www.sheldonbrown.com/gear-theory.htmlhttp://en.wikipedia.org/wiki/Bicycle_gearing#cite_ref-Gear_Theory_8-1http://en.wikipedia.org/wiki/Bicycle_gearing#cite_ref-Gear_Theory_8-0http://www.pinkbike.com/news/Pinion-Gearbox-Eurobike-2011.htmlhttp://www.pinkbike.com/news/Pinion-Gearbox-Eurobike-2011.htmlhttp://en.wikipedia.org/wiki/Bicycle_gearing#cite_ref-7


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