Bicycles/Maintenance and Repair/Gear-changing Dimensions

Introduction
This page intends to document the various standards that are in use by manufacturers for bicycle gear-shifting. The parts that are most likely to be of interest are the measurements of cogsets, the cable pull of shifters, and the shift ratios of derailleurs. In addition, notes on the mixing of gear from different manufacturers is also of interest to those who intend to improvise.

The Shift Equation
In all indexed shifting there is a fundamental shifting equation that applies to the gear-changing process. For convenience, it is repeated here.

'''The product of cable pull and the derailleur's shift ratio (reciprocal of actuation ratio) equals the transverse distance moved by the derailleur cage across the cogs. For useful shifting the distance shifted must equal the center to center cog spacing (pitch)'''.


 * $$\begin{align}

\textrm{Center To Center Cog Spacing Or Pitch} &= \textrm{Cable Pull}   & \times & & \textrm{Derailleur Shift Ratio} \\ &= \textrm{Cog Thickness} & +     & & \textrm{Spacer Thickness} \end{align}$$

Cog Pitch
The center to center spacing between adjacent cogs of a cluster is called the pitch.  It is usual for the pitch to be uniform across a cog-set whether it is arranged in a freewheel or in a cassette. Other uses of the term pitch refer to the distance between teeth on the cogs and the distance between links of the chain that engage them. Chains have an unambiguous pitch of 0.5 inches on bicycles, so this term can be used here safely to refer to center to center cog spacing.

The pitch is made up of the thickness of a cog plus the thickness of a spacer.  Cogs are sometimes increased in thickness to accommodate the increased stresses applied to them, and in these cases the spacers are reduced in thickness to maintain a uniform pitch.

The pitch is reduced for increasing numbers of cogs. There are disadvantages in setting the chain-line of a bicycle far from the wheel's center, so at some stage as the number of cogs is increased, they must be fitted closer together - hence the reduced pitch.

The pitch of all modern seven-speed cog-sets is invariably five millimeters.  This is true for all manufacturers of seven-speed cog-sets, and such consistency is unusual in cog standards. In most other sizes, manufacturers have used their own standards, so that it is usual to have different pitch dimensions even for the same size of cassette. Table 1 lists the pitch of some commonly available cog-sets as well as various other dimensions:

Cog-set Stack Width
The overall width of a uniform cog-set can be calculated:
 * $$\begin{align}

\textrm{Stack Width}    &= & \textrm{n} \times \textrm{Cog Thickness} & &+ & & (\textrm{n} - 1) \times \textrm{Spacer Thickness}& \\ \textrm{Max Chain Width} &= &                  \textrm{Cog Thickness} & &+ & & 2                \times \textrm{Spacer Thickness}& \\ \end{align}$$ Where n is the number of cogs.

The stack widths for various uniform cog-sets are given in Table 1. When cog-sets are assembled with parts from different sources the stack width is often built out with additional spacers to allow the fitting of cogs onto the freehub. At times it is difficult to reconcile the widths of large cassettes with the known available space on the hub; this is usually because some cogs of the cluster are designed to overhang the normal fittings.

* In cases where the available freehub space is less than the stack width, mainly for large cogsets, some cogs have been specially designed to overhang the stack.

Rear Shift Ratios
Actuation ratio is given as the ratio of an input change to an output effect, and the shift ratio is its reciprocal. In the specific case of bicycle derailleurs, the shift ratio is the distance that the cage travels across the cogs divided by the cable pull to achieve it. In other words shift ratio is the cog-pitch divided by the cable pull.

The SRAM and Shimano manufacturers make use of approximate gain ratios as short-codes that identify the family for compatibility of their products. They refer to them as either 2:1 (for Shimano compatible products) or 1:1 (for SRAM's own products). These terms in fact refer to families with shift ratios of 1.7 (one-point-seven) and 1.1 (one-point-one) respectively, so they do not depict the exact shift or actuation ratios. When SRAM makes a product for Shimano compatibility it uses the 2:1 keyword to identify it as such.

Shifter Cable Pull
The rear shift data listed in these tables is the same for both MTB (mountain bike) rear shifting, and road bike, (drop-handlebars and racers) rear shifting. For front shifting, (section still needs completion, and data is almost non-existent), the cable pull often is different between the two types of bike. For example, Shimano shifters have different cable pulls for their MTB and road series bikes.

Mixing Rear Drive Components
At times it is of interest to know whether or not the components of other than the host manufacturer will work well for indexed shifting. Table 4 brings together the data of Tables 1, 2, and 3 to generate the derailleur shifts that would result from the mixing of components. By relating these shifts to the known pitches of the available cog-sets, it is possible to gauge the likelihood of success or failure. Follow the examples that follow the table to understand how it is used.

Tables 1 and 4 give the means to predict whether or not rear-gear shifting will work with various combinations of shifters, derailleurs, and cogs. Because of the size limitations and difficulty in modifying freewheels, these tables refer in the main to CASSETTES. The emphasis here is on closeness of pitch, and other practical factors might still need to be considered.

The pitch of common cog-sets is given in one table and the derailleur shift data is given in another. The shift data is divided into four main categories:
 * GREEN Colors:These show the resultant derailleur shift in millimeters when the shifter, derailleur, and cogs of one manufacturer are used together.  This is the ideal situation.   For example, the Shimano 10-speed shifter with a cable pull of 2.3mm is applied to a Shimano derailleur with a shift ratio of 1.7, resulting in a shift (2.3mm x 1.7) of 3.91mm.   Allowing for the precision of the available data this fits the Shimano 10-speed cog-set pitch of 3.95mm well, and the shifting is considered to be ideal.
 * YELLOW Colors:These give the resultant derailleur shift in millimeters when other than the ideal combination is used, and are characterized by having an intact set of cogs, but unused positions on the shifter when the modification is complete.(But see Campagnolo 'old and new').     The pitch that is produced works well enough with the alternative cog-set.   For example, the Campagnolo 10-speed shifter with a cable pull of 2.8mm is applied to a Shimano derailleur with a shift ratio of 1.7, resulting in a shift (2.8mm x 1.7) of 4.76mm.   Allowing for the precision of the available data this fits the Shimano 8-speed cog-set pitch of 4.80mm well.   That is to say, the Campagnolo 10-speed shifter could be used with the Shimano derailleur provided that there was an 8-speed Shimano cog-set installed.   The other two positions on the shifter would remain unused, excluded by adjusting the limit stops of the derailleur.
 * RED Colors:These give the resultant derailleur shift in millimeters when other than the ideal combination is used, and although the shifter range will be correct, they need some cogs to be left off the cassette assembly.   The pitch that is produced works well enough with the specified cog-set.   For example, the Campagnolo 8-speed shifter with a cable pull of 3.5mm is applied to a SRAM (1.0) derailleur with a shift ratio of 1.1, resulting in a shift (3.5mm x 1.1) of 3.85mm.   Allowing for the precision of the available data this fits the Shimano S10 cog-set pitch of 3.95mm well.   That is to say, the cog-set can be assembled using eight of the Shimano 10-speed cogs and seven of its spacers.
 * OTHER Shift Data: Data other than those with green, yellow, or red coloring would not index correctly.  That said, there are some other Shimano combinations that can be applied to a Shimano 7-speed freehub.   The set can be extended to eight cogs if S9 cogs form the cassette, and a 9-speed shifter and chain are used.  Similar results can be obtained for nine cogs on a 7-speed freehub if S10 is used for the assembly, and a 10-speed shifter and chain are used.   In each of these two cases the unused positions on the shifters are blocked by the adjustment of the derailleurs' limit stops.

7 August 2011

SRAM Rear Shifter Families (2:1 or 1:1)
The SRAM manufacturer makes two families of gear shifters. The families differ too greatly to be interchanged in rear-shifting. One is Shimano compatible (called 2:1) and one is not; (called 1:1). The 1:1 shifters are designed for SRAM's own (native) 1:1 rear derailleur family, and can also be used with modified numbers of shifts, for their front derailleurs and the front derailleurs of Shimano. See the compatibility details for rear shifting in table 5.

FRONT SHIFTING TABLES
The following table is intended for data collection. If it is successful it will form a useful collaborative effort in writing. As the heading shows it is for Shimano road front shifting, not because of any preference for their products but because they have different cable-pull standards for their front road shifters, compared to their MTB front shifters, and the matter is poorly documented. It might be of interest to know that Shimano's rear shifter cable pulls are the same for road and MTB of a given speed, except for 10 speed. The Dyna-Sys mark denotes the different 10 speed MTB cable pull. Dyna-Sys rear derailleurs can only be used with Dyna-Sys shifters for 10 speed, or SRAM 9 speed MTB shifters for 9 speed.

Interested parties should please add data using a full set of measurements taken from the same well-working, drop-handlebar, road bicycle. In this way it is hoped that data comparable to that available for rear-shifting can be tabulated. If readers are uncomfortable about entering data into the table directly, please just place the data in the discussion text (see page top, and don't forget to save), and an editor will complete the entries or straighten out the table as necessary.

Front Shift Ratios
The notion of shift ratio, the ratio of cable pull to the distance that the derailleur moves across the chain-rings is primarily of interest for indexed shifting, as opposed to friction shifting. Regrettably, manufacturers give no more information for front shifting than they do for rear shifting, and user data is scarce. The few facts that are available are these.
 * SRAM Front Derailleurs:  The native SRAM shift ratio for its front and rear gear is in fact about 1.1, as opposed to the 1:1 family's implied unity.   In general,  SRAM shifters that are made for the 1:1 family can be used with native SRAM front and rear derailleurs, provided of course that they have the correct number of speeds.
 * Shimano Front Derailleurs:  Shimano makes use of indexed front shifting.   The Shimano shift ratio for front derailleurs is close to that of SRAM's 1:1 family, ie, unity or 1.1, (one-point-one).   Note that this differs considerably from their rear derailleur ratios of 1.7.   Although this fact is not specified by Shimano, because SRAM advertises 1:1 shifters for their rear shifting as being suitable for Shimano's front derailleurs, the assumed shift ratio of unity seems reasonable.   Shimano's front shifters however, differ for road and MTB use; a discussion at CTC on Front Shifting implies that an MTB pulls 9.75mm of cable for a front shift whereas a road shifter pulls only 6.75mm; some 3mm less than the MTB.
 * Campagnolo Front Shifters:  No information as yet.

An excessive cable pull on a two-chainring bike might still work if it is recalled that the limit stops of the front derailleur can be brought in to restrict any excessive cage travel. In this way the shifting is not really indexed, and perhaps a bit heavy, but might function just the same. Attempting the same thing with three chain-rings is unlikely to work well. For this, indexed shifting is much preferred.

Shifter Cable Pull
The rear shifter cable pull is not the same for each gear shift. Since the rear derailleur swings in an arc, the shifts to lower gears (bigger cogs) will require more and more cable pull to move the derailleur the same amount. The figures given above for cable pull are an average over the range of gears. For example an average cable pull of 3.1mm per shift may range from 3.6mm in the lowest gear shift to about 2.5mm for the highest gear shift.

CHAIN EXTERNAL WIDTHS
05 speed - 7.8mm (all brands) 06 speed - 7.8mm (all brands) 07 speed - 7.3mm (all brands)

Regina 8 speed = 7.2mm wide (Extra Super Racing)

KMC 8 speed = 7.2mm wide KMC 9 speed = 6.6mm wide KMC 10 speed = 5.88mm wide

SACHS/SEDIS (std) 7/8 speed = 7.3mm SACHS/SEDIS (pro) 8 speed = 6.99mm wide (for MAVIC & recommended alternative for Campagnolo)

Shimano IG 8 speed = 7.1mm wide Shimano HG 8 speed = 7.4mm wide (CN-7401) Shimano HG 9 speed = 6.6mm wide Shimano HG 10 speed = 6.2mm wide (Narrow) Shimano HG 10 speed = 5.88mm wide (Narrow, Directional) Shimano HG 11 speed = 5.62mm wide (Shimano Dura-Ace)

SRAM 8 speed = 7.02mm wide SRAM 9 speed = 6.9mm wide SRAM 10 speed = 5.88mm wide SRAM 11 speed = 5.62mm wide SRAM 12 speed = 5.25mm wide

Rohloff 8 speed = 7.1mm wide Rohloff 9 speed = 6.8mm wide

Campy 8 speed = 6.85mm wide (Contax Chain CN-CA68S) Campy 9 speed = 6.8mm wide Campy 10 speed = 6.2mm wide (C10 - pre 2006) [also stated 6.1mm wide?] Campy 10 speed = 5.88mm wide (Ultra Narrow - post 2006) Campy 11 speed = 5.5mm (Campagnolo CN-RE500 'Ultralink')