Given 3 chain-rings on the front crank and seven on the rear, the number of gears is theoretically 21. However, it is usually unneccessary to use the large chain ring on the front at the same time as the large one at the back, as the chain length may be a restriction.

Hi rcm mech,

The front changer is usually a coarse shifter and the rear is the fine adjustment.

So theoretically you can start in lowest gear on smallest front ring and largest back sprocket.

Then move through the gears from A1 to C9 assuming 3 by 9 gearing. There will inevitably be some overlap but this can help the gear changing to avoid large jumps at critical moments.

Good Luck

Sleepy

... and of course you want to avoid using gears where the "crossing" angle is large, such as the far right sprocket at the front and the far left sprocket at the rear.

Most have both front and rear shifters. The idea of multiple gears is simply to provide a wide range of ratios so that an optimum cadence (pedal rpm) can be maintained. In the extreme cases, a wide range of gears provides a low that is low enough that you never have to get off and push on a steep hill.

"Track bikes" which are made for flat tracks, do not need multiple gears because they don't have to deal with hills. For them, multiple gears just ad unnecessary weight.

You can think of the crank sprocket rings (front shifter) as the mechanical analog of the range selector (rear end shifter) on trucks. Use to the front shifter is very much dependent on both topography differences traversed during any on riding session/trek, combined with riding style of a particular rider. It is usually the case, with 3-sprocket front shifters, that one of the three is seldom or never used by the typical rider--seen another way, addition of the third front ring can command a price much more than its cost in terms of new-bike shelf appeal (some might say ego appeal) at the point of sale.

The rear sprockets, then, become as the transmission (the principal gear box) on the truck...used primarily, once "up-to-rear-sprocket-count-number" range has been selected, for increasing/decreasing speed while maintaining cadence (as previously mentioned).

Let me offer a concrete example how the front (range) and rear (speeds) shifters might be used in practical circumstances.

If your bike trek covered, say, a path along which numerous comparatively small hillocks were traversed, but otherwise the terrain was relatively flat (think of sine wave curve or clipped sine wave curve), you might find it easiest to make few or no (rear) gear shifts, relying primarily of range (front) shifts to maintain satisfactory course momentum.

If, on the other hand, you bike tour would take you from India's interior, north to Himalayan foot hills and on to mountainous terrain, you are surely likely to need the use of at least two (of three) range (front ring) selections....and all of the gear (rear ring) selections. Reliance only upon range shifting as in the earlier example would of a certainty present you with such leverage changes that peddling would become very arduous if not impossible.