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 ratio is fixed, 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; cadence above 100 rpm becomes less effective after short bursts, as during a sprint.
Measuring gear ratios
Methods There are at least four different methods 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 (many online gear calculators have these factors built in for various popular hub gears). Gear inches = Diameter of drive wheel in inches × (number of teeth in front chainring / number of teeth in rear sprocket). Normally rounded to nearest whole number. Metres of development = Circumference of drive wheel in metres × (number of teeth in front chainring / number of teeth in rear sprocket). Gain ratio = (Radius of drive wheel/length of pedal crank) × (number of teeth in front chainring / number of teeth in rear sprocket). Measure radius and length in same units.
Both metres of development and gain ratios are normally rounded to one decimal place.
Gear inches corresponds to the diameter (in inches) of the main wheel of an old-fashioned penny-farthing bicycle with equivalent gearing. Metres of development corresponds to the distance (in metres) traveled by the bicycle for one rotation of the pedals. Gain ratio is the ratio between the distance travelled by the bicycle and the distance travelled by a pedal, and is a pure number, independent of any units of measurement.
Front/rear gear measurement uses two numbers (e.g. 53/19) where the first is the number of teeth in the front chainring and the second is the number of teeth in the rear sprocket. Without doing some arithmetic, it is not immediately obvious that 53/19 and 39/14 represent effectively the same gear ratio.
Examples The following table provides some comparison of the various methods of measuring gears (the particular numbers are for bicycles with 170 mm cranks, 700C wheels, and 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 Gearinches Metredevelopment Gainratio 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 10.0 9.4 53/11 22.3 36 29.7 47.8 37.1 59.7 44.5 72 High 100 8.0 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 Very low 20 1.6 1.5 32/42 3.5 5.6 4.7 7.6 5.9 9.5 7.1 11.4
Single speed bicycles
A single-speed bicycle is a type of bicycle with a single gear ratio and a freewheel mechanism. 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, and bicycles designed for track racing.
Fixed-gear road bicycles and fixed-gear mountain bicycles are also usually single speed in that they typically do not have any gear ratio adjustment. However, fixed gear bicycles do 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 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).
Relative gearing As far as a cyclist's legs are concerned, when changing gears, the relative difference between two gears is more important than the absolute difference between gears. This relative change, from a lower gear to a higher gear, is normally expressed as a percentage, and is independent of what system is used to measure the gears. Cycling tends to feel more comfortable if nearly all gear changes have more or less the same percentage difference. For example, a change from a 13-tooth sprocket to a 15-tooth sprocket (15.4%) feels very similar to a change from a 20-tooth sprocket to a 23-tooth sprocket (15%), even though the latter has a larger absolute difference.
To achieve such consistent relative differences the absolute gear ratios should be in logarithmic progression; 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%; such big steps require a very substantial change in pedalling speed and often feel excessive. A step of 7% corresponds to a 1-tooth change from a 14-tooth sprocket to a 15-tooth sprocket, while a step of 15% corresponds to a 2-tooth change from a 13-tooth sprocket to a 15-tooth sprocket.
By contrast, car engines deliver power over a much larger range of speeds than cyclists' legs do, so relative differences of 30% or more are common for car gearboxes.
Usable gears On a bicycle with only one gear change mechanism (e.g. rear hub only or rear derailleur only), the number of possible gear ratios is the same as the number of usable gear ratios, which is also the same as the number of distinct gear ratios.
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.