Sheldon Brown wrote:

Quoth Frank Krygowski:

The key is that on a log plot, equal percent changes show up as equal
distances between points.

If you felt that each gear change should have the same effect (say,
reducing your gear ratio by 5%) then you could plot different cog
combinations until you achieved equal spacing on a log plot. If you
felt you wanted greater spacing in the low gears and finer spacing in
the high gears, you could verify that as well.

If you plotted things on a linear scale, or just looked at the number
of gear inches, you might think shifting from a 100 inch gear to a 95
inch gear would feel the same as shifting from a 30 inch to a 25
inch. But in practice, the former is a fine adjustment, the latter is
a pretty big jump.


That would be true if we cycled in a vacuum, opposed by linear
frictional resistances only.

However, the non-linearity of air resistance cancels this out to a
considerable extent.

See: http://sheldonbrown.com/gear-theory.html#progression

Sheldon "Pear Shaped" Brown

This may sound like a quibble, but: my descriptions of "fine
adjustment" and "pretty big jump" are correct. The adjustments are as I
describe them, 5% in one case, 17% in the other. What the person is
adjusting _for_ is another matter.

I'm aware, of course, of the variation in air resistance with speed.
That's the reason for the "If" beginning my paragraph above, and the
reason for my saying "If you felt you wanted greater spacing in the low
gears and finer spacing in the high gears, you could verify that as
well." It's perfectly logical to prefer the latter.

My intent is not to act as a proponent for either scheme. My intent is
to point out why log graph paper is a useful tool when designing either
scheme.

--
Frank Krygowski [To reply, remove rodent and vegetable dot com.
Substitute cc dot ysu dot
edu]