Bicycle gearing is the aspect of a bicycle drivetrain that determines the relation between the cadence, the rate at which the rider pedals, and the rate at which the drive wheel turns.
On some bicycles there is only one gear and, therefore, the gear ratioisfixed, but most modern bicycles have multiple gears and thus multiple gear ratios. A shifting mechanism allows selection of the appropriate gear ratio 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 speed range, or cadence. Gearing can be optimized to use this narrow range as efficiently as possible. As in other types of transmissions, the gear ratio is closely related to the mechanical advantage of the drivetrain of the bicycle. On single-speed bicycles and multi-speed bicycles using derailleur gears, the gear ratio depends on the ratio of the number of teeth on the crankset to the number of teeth on the rear sprocket (cogset). For bicycles equipped with hub gears, the gear ratio also depends on the internal planetary gears within the hub. For a shaft-driven bicycle the gear ratio depends on the bevel gears used at each end of the shaft.
For a bicycle to travel at the same speed, using a lower gear (larger mechanical advantage) requires the rider to pedal at a faster cadence, but with less force. Conversely, a higher gear (smaller mechanical advantage) provides a higher speed for a given cadence, but requires the rider to exert greater force or stand while pedalling. Different cyclists may have different preferences for cadence, riding position, and pedalling force. Prolonged exertion of too much force in too high a gear at too low a cadence can increase the chance of knee damage;[1] cadence above 100 rpm becomes less effective after short bursts, as during a sprint.[1]
There are at least four different methods[2] for measuring gear ratios: gear inches, metres of development (roll-out), gain ratio, and quoting the number of teeth on the front and rear sprockets respectively. 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 regardless of drive wheel diameter; the numbers produced by different methods are not comparable, but for each method the larger the number the higher the gear. The third method, gain ratio, also takes the length of the crankarm into account, which can vary from bike to bike. The fourth method uses two numbers and is only useful in comparing bicycles with the same drive wheel diameter. In the case of road bikes, this is usually around 670 mm. A 700c "standard" wheel has a 622 mm rim diameter. The final wheel diameter depends on the specific tire but will be approximately 622 mm plus twice the tire width.
Front/rear measurement 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 precisely: 0.0798, or exactly: 0.0254 · π).
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 [3] (many online gear calculators have these factors built in for various popular hub gears).
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 25 mm tyres). Speeds for several cadences in revolutions per minute are also given. On each row the relative values for gear inches, metres of development, gain ratio, and speed are more or less correct, while the front/rear values are the nearest approximation which can be made using typical chainring and cogset sizes. Note that bicycles intended for racing may have a lowest gear of around 45 gear inches (3.6 meters), or 35 gear inches (2.8 meters) 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
00010.0
9.4
53/11
22.3
36
29.7
47.8
37.1
59.7
44.5
72
High
100
00008.0
7.5
53/14
18
29
24
38.6
30
48.3
36
57.9
Medium
070
00005.6
5.2
53/19 or 39/14
12.5
20
16.6
26.7
21
33.6
25
40
Low
040
00003.2
3.0
34/23
07.2
11.6
09.6
15.4
11.9
19.2
14.3
23
Very low
020
00001.6
1.5
32/42
03.5
05.6
04.7
07.6
05.9
09.5
07.1
11.4
Asingle-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. 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, unicycles, bicycles designed 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.[dubious – discuss]
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 use. 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 (bike shoes permitting).
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.[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 gears. Cycling 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 similar to a change from a 20-tooth sprocket to a 23-tooth sprocket (15%), even though the latter has a larger absolute difference.
To achieve such consistent relative differences the absolute gear ratios should be in logarithmic progression; 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 speed. 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%;[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.
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 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.[7] 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 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 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.
range
transmission
usable
gears
mean
step
180%
3-speed hub gears
03
34.2%
250%
5-speed hub gears
05
25.7%
300%
7-speed hub gears
07
20.1%
307%
8-speed hub gears
08
17.4%
327%
typical 1 chainring derailleur setup (1×10, 11-36)
10
14.1%
327%
road 1 chainring derailleur setup (1×11, 11-36)
11
12.6%
380%
NuVinci continuously variable transmission
continuous
none
409%
11-speed hub gears
11
15.1%
420%
mountain 1 chainring derailleur setup (1×11, 10-42)
11
15.4%
428%
road 2 chainring derailleur setup (2×10, 50-34 × 11-32)
13
12.9%
441%
road 3 chainring derailleur setup (3×10, 52/39/30 × 11-28)
15
11.2%
500%
extreme 1 chainring derailleur setup (1×12, 10-50)
12
15.8%
518%
mountain 2 chainring derailleur setup (2×10, 38-24 × 11-36)
14
13.5%
526%
Rohloff Speedhub 14-speed hub gear
14
13.6%
630%
Mountain 2×11 derailleur setup (24/36 × 10-42)[8]
14
15.2%
636%
18-speed bottom bracket gearbox[9]
18
11.5%
655%
mountain 3 chainring derailleur setup (3×10, 44-33-22 × 11-36)
16
13.3%
698%
touring 3 chainring derailleur setup (3×10, 48-34-20 × 11-32)
15
14.9%
Gear ranges of almost 700% can be achieved on derailleur setups, though this may result in some rather large steps between gears or some awkward gear changes. However, through the careful choice of chainrings and rear cogsets, e.g. 3 chainrings 48-34-20 and a 10-speed cassette 11–32, one can achieve an extremely wide range of gears that are still well spaced. This sort of setup has proven useful on a multitude of bicycles such as cargo bikes, touring bikes and tandems. Even higher gear ranges can be achieved by using a 2-speed bottom bracket hub gear in conjunction with suitable derailleurs.
There are two main types of gear change mechanisms, known as derailleurs and hub gears. Both systems have advantages and disadvantages, and which is preferable depends 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 gearing is so called because all the sprockets involved are readily visible. There may be up to 4 chainrings[10] attached to the crankset and pedals, and typically between 5 and 12 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 shifter 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 also has 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[11] which are usually related to the relative step sizes between the front chainrings and the rear cogset.
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.
Advantages of this arrangement include:
One disadvantage is that the overlapping gear ranges result in a lot of duplication or near-duplication of gear ratios.
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 speed, 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.
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 lowest 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 Shimano 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.
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.
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.[12] 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.[11] The small chainring (granny gear) is a bailout for handling steeper hills, but it requires some anticipation in order to use it effectively.
Internal 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 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 2 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.
Current systems have gears incorporated in the cranksetorbottom bracket. Patents for such systems appeared as early as 1890.[13] The Schlumpf Mountain Drive and Speed Drive have been available since 2001.[14] Some systems 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 protruding 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 gearbox model, offering an evenly spaced 636% range. This gearbox is actuated by traditional twist shifter and uses two cables for gear changing. The Pinion system is well suited for mountain bicycles due to its wide range and low gravity center suitable for full-suspension bikes, but it is still somewhat heavier than derailleur-based drivetrain.[15]
It is sometimes possible to combine a hub gear with deraileur gears. There are several commercially available possibilities:
There have been, and still are, some quite different methods of selecting a different gear ratio:
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.
Factors besides gearing which affect performance include rolling resistance and air resistance:
Human factors can also be significant. Rohloff argues[19] 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.
An encyclopedic overview can be found in Chapter 9 of "Bicycling Science"[20] 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[19] 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.
Derailleur type mechanisms of a typical mid-range product (of the sort used by serious amateurs) achieve between 88% and 99% mechanical efficiency at 100 W. In derailleur mechanisms the highest efficiency is achieved by the larger sprockets. Efficiency generally decreases with smaller sprocket and chainring sizes.[21] 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)[22] that testing on three derailleur systems (from 4 to 27 gears) and eight gear hub transmissions (from 3 to 14 gears), performed with 80 W, 150 W, 200 W inputs, gave results as follows:
Transmission type
Average efficiency at 150 W
Derailleurs
93–95%
3-speed gear hubs
92–95%
7- and 14-speed gear hubs
89–91%
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 W will drive a typical bicycle at 20 miles per hour (32 km/h), while athletes can achieve 400 W, at which point efficiencies "approaching 98%" are claimed.[23]
At a more typical 150 W, hub-gears tend to be around 2% less efficient than a derailleur system assuming that both systems are well maintained.[24]
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.
Crankset: Sugino Aero Mighty Tour Forged Alloy Triple 28-45-50. Freewheel: Atom Helicomatic 6-spd 13-28 (13/14/17/20/24/28)
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