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The combination of 3 chainrings and an 8-sprocket cogset does not result in 24 usable gear ratios.
Consider a derailleur-equipped bicycle with 3 chainrings and an 8-sprocket cogset:
The more common configurations have specific names which are usually related to the relative step sizes between the front chainrings and the rear cogset.
A cogset works with a rear derailleur as part of the drivetrain to provide multiple gear ratios to the rider.
On a bicycle, the cogset or cluster is the set of multiple rear sprockets that attaches to the hub on the rear wheel.
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.
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.
Cage length determines the total capacity of the derailleur, that is the size difference between the largest and smallest chainrings, and the size difference between the largest and smallest sprockets on the cogset added together.
With derailleur equipped bicycles, the external width of the chain also matters, because chains must not be too wide for the cogset or they will rub on the next larger sprocket or too narrow that they might fall between two sprockets.
The cogset (freewheel or cassette) of a rear wheel and disc brake rotors, if installed, takes up width on the hub, and so the flanges may not be located symmetrically about the center plane of the hub or the bike.
The SRAM DualDrive system uses a standard 8 or 9-speed cogset mounted on a three-speed internally geared hub, offering a similar gear range to a bicycle with a cogset and triple chainrings.
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.
