Formula for actual # of usable gears

I have 21 "advertized" gears (3-front, 7-reqar). With my seventeen inch
chain stays that reduce chainflex, combined with the half step granny
configuration I have 17 useable and different, evenly spaced gear ratios
(18, if you count the one redundant ratio shared by the granny and
middle rings).

How do you figure that into your theory?

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Mike A Schwab wrote:
...
And in actuality, I like to figure, for my Sun Bicycles EZ-1 with a
triple chainring and 3*7 SRAM rear wheel, that I don't actually have
63 gears. I start by considering the internal hub and chainring are
in the middle. I can change the cassette up and down over 7 gears,
about 10% difference each. If I hit the limits, I can change the
chain ring, for a 20% change or 2 gears on the cassette. If I am at
top speed, using the hub overdrive adds more resistance and ends up
slowing me down. If I am climbing, I can use the underdrive for about
a 25% drop in effort, about 2 more gears. If I rush to stop without
downshift, I will use the under drive to get started and downshift the
derailers and go back to hub direct drive.

So even though I have a hugh number of gears, the hub just gives me a
25% lower range in gear ratios. I think a more accurate calculation
would be to count the # of cogs (7), + 4 additional gears for the two
additional chainrings, + 2 for the hub underdrive.

With 52/42/30T chain wheels, an 11-28T 7-speed cassette and a SRAM
Spectro 3x7 hub on a RANS Tailwind, I have about [1] 22 distinct ratios
and 41 practical duplicates. However, the 3x7 hub adds 4 very useful
ratios, extending both the high and low end gearing.

[1] About, since it is a judgment call on how close the ratios have to
be to be considered functional duplicates.

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