Archibald said:i'll add a question that i've often pondered but never really sought an answer to about gears.
is there a distinct difference between all gears on the different chain rings, or is there some overlap between smallest rear cog on smaller CR and the largest rear cog on a larger CR?
Yes, there is a lot of overlap. In general, it is better for the chain not to ride in the extremes (i.e., small chainring and smallest two cogs on the casette or large chainring, largest two cogs on the casette. If you look at the chain when it is in these positions, you will see that there is a lot of sideways stress on it. That will cause premature wear of the chain and the cogs.
A typical 10 speed, tripple chainring road bike configuration would have 30, 42, and 52 teeth chainrings, and 12, 13, 14, 15, 16, 17, 19, 21, 23, and 25 teeth on the casette cogs. You can do the math, but the bottom line is that using the 42 teeth chainring would give you gear ratios from 1.68 (easy) to 3.5 (hard). To go lower than 1.68, you would go to the 30 teeth chainring, and use gears 4 (19 teeth - 1.58 ratio) to 1 (25 teeth - 1.20 ratio). To go higher than 3.5, you would use the 52 teeth chainring and gears 8 (14 teeth - 3.71 ratio) through 10 (12 teeth - 4.33 ratio).
If you are in the small chainring, there is nothing wrong with staying there and going to gears 5 or 6 on the casette to avoid double shifting, but the ratios on these combinations would be similar to being in gears 1 and 2 while you are in the middle chainring. Similarly, if you are already in the large chainring, there is nothing wrong with going down to gears 4 through 7 on the casette, but these combinations would be similar to being in gears 7 through 10 while you are in the middle chainring.
To better visualize the effects of the various combinations, set up a spread sheet with the number of teeth on each casette cog going down and the number of teeth on each chainring going across, then fill in each cell by dividing the number of teeth on the chainring by the number of teeth on the casette. The result is the number of revolutions of the wheel for each revolution of the pedal. The smaller the number, the easier (more torque, less speed). The higher the number, the harder (less torque, more speed). You will see where the overlaps are for your configuration.