The Dancing Chain, by Frank Berto
 

John McGraw wrote:

I'd use log
log paper to day to know where my cross over redundant gears are, if I
could find the graph paper. Any suggestions on where to find it would
be deeply appreciated. John

Google "Graph paper software" and you'll find several programs that will
print the stuff out.

But these days, when I want to do a gear chart, I use a spreadsheet
package. Depending what you need, you may find it better to set up an
extra column containing the logarithm of the gear inches, but simply
plotting the gear inches on a logarithmic axis may be fine.

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

Frank Krygowski wrote in message ...
John McGraw wrote:

I'd use log
log paper to day to know where my cross over redundant gears are, if I
could find the graph paper. Any suggestions on where to find it would
be deeply appreciated. John

Google "Graph paper software" and you'll find several programs that will
print the stuff out.

But these days, when I want to do a gear chart, I use a spreadsheet
package. Depending what you need, you may find it better to set up an
extra column containing the logarithm of the gear inches, but simply
plotting the gear inches on a logarithmic axis may be fine.

okay, i don't understand the origianl need for log plots of gear
inches. i've seen how the spacing of gears on a single chainring for a
typical bike is somewhat logarithmic.

perhaps you'd want the gears across the entire range to be lined up on
the log plot as a magical ideal, but that seems pretty arbitrary.

i don't see how a log plot helps you elimintate duplicate gears in a
way that you couldn't do on a linear plot, or even by simply
eyeballing the gear chart.

-Amit

Amit wrote:


okay, i don't understand the origianl need for log plots of gear
inches. i've seen how the spacing of gears on a single chainring for a
typical bike is somewhat logarithmic.

perhaps you'd want the gears across the entire range to be lined up on
the log plot as a magical ideal, but that seems pretty arbitrary.

i don't see how a log plot helps you elimintate duplicate gears in a
way that you couldn't do on a linear plot, or even by simply
eyeballing the gear chart.

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.

Of course, many people rode far, fast and long without giving this a
thought. It all depended on how much you were into the technology and
the numbers.

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

Frank Krygowski wrote:
Amit wrote:


okay, i don't understand the origianl need for log plots of gear
inches. i've seen how the spacing of gears on a single chainring
for a
typical bike is somewhat logarithmic.

perhaps you'd want the gears across the entire range to be lined up
on
the log plot as a magical ideal, but that seems pretty arbitrary.

i don't see how a log plot helps you elimintate duplicate gears in
a
way that you couldn't do on a linear plot, or even by simply
eyeballing the gear chart.

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.

Of course, many people rode far, fast and long without giving this a
thought. It all depended on how much you were into the technology
and
the numbers.

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

It's not as important today as 20+ more years ago, when 5 or 6 speeds
were all that were available. It's also not at all difficult to do if
log paper is used. What I was saying is that it's still a good way look
at ones gearing. So far spread sheets baffle me. They sure don't look
like any math I've ever done. Also my peculiar mind has to see or
imagine seeing something in order to understand it. Words just float
around in empty space.
Happy Holidays, John

Amit wrote:

Frank Krygowski wrote in message ...
John McGraw wrote:

I'd use log
log paper to day to know where my cross over redundant gears are, if I
could find the graph paper. Any suggestions on where to find it would
be deeply appreciated. John

Google "Graph paper software" and you'll find several programs that will
print the stuff out.

But these days, when I want to do a gear chart, I use a spreadsheet
package. Depending what you need, you may find it better to set up an
extra column containing the logarithm of the gear inches, but simply
plotting the gear inches on a logarithmic axis may be fine.

okay, i don't understand the origianl need for log plots of gear
inches. i've seen how the spacing of gears on a single chainring for a
typical bike is somewhat logarithmic.

When changing gears, the difference your legs feel is a "percent change
difference"; so the problem by definition is a geometric sequence. A geometric
sequence, which is exponential, of course becomes linear when transformed by the
log function. This is where the utility of log-paper comes in, although I've
never bothered myself.

perhaps you'd want the gears across the entire range to be lined up on
the log plot as a magical ideal, but that seems pretty arbitrary.

Well sort of--it isn't a law, nor is it exactly acheivable with only rational
fractions available. But the rule of thumb is to determine what increments feel
good (for example, I choose 6 gStep 9% as desirable), and try to approximate
from that specification. Once that is determined, synthesis starts from
there--although we are obviously constrained by what actual hardware is
available.

Some folks do choose to intentionally distort this rule by "stretching the
lows," for example. That is, they figure they only need to "bail out" on a rare
basis, and don't wish to sacrifice step size. As the number of speeds increases,
obviously there are less trade offs.

i don't see how a log plot helps you elimintate duplicate gears in a
way that you couldn't do on a linear plot, or even by simply
eyeballing the gear chart.

There is no presumption to eliminate duplicates, except for certain designs.
Obviously the so-called "half-step" *requires* interleaving (half-steps are
rarely used anymore). For the so-called "crossover," the point is to actually
have a duplicate available. IOW, the same percentage step is available whether
you cross to other ring, or change only the back. Nowadays, a lot of the
duplicate gear concern is awash with 9sp and 10sp cassettes. It just doesn't
matter for the most part. (Funny how 9&10sp cassettes have helped obsolete
log-paper. Whodda thunk?)

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
+------------------------------------------+
| The lower your gear, the more of your |
| riding time will be spent going uphill. |
+------------------------------------------+
Harris Cyclery, West Newton, Massachusetts
Phone 617-244-9772 FAX 617-244-1041
http://harriscyclery.com
Hard-to-find parts shipped Worldwide
http://captainbike.com http://sheldonbrown.com

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]

Sheldon Brown wrote:


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.


Why do you presume the speed changed (or anything else)?

Sheldon Brown wrote:

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

Hmmm. Within that same page, I disagree with much of the stuff you've
written in this topic:
http://sheldonbrown.com/gear-theory.html#cadence, but particularly with
this:

"For the cyclist who wants to maximize efficiency, there is a particular
combination of cadence and resistance that will produce the most power
with the least stress on the body. [...] The idea of gears is to select
the gear in which this combination of cadence and resistance is met.
Depending on the wind, grade and surface conditions, your speed may be
faster or slower, but theoretically your legs should always be pushing
against the same resistance, and spinning the cranks at the same cadence."


--
Still a proud member of the reality-based community.

On Tue, 7 Dec 2004 10:36:30 +0100, "Robert Chung"
wrote:

Sheldon Brown wrote:

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

Hmmm. Within that same page, I disagree with much of the stuff you've
written in this topic:
http://sheldonbrown.com/gear-theory.html#cadence, but particularly with
this:

"For the cyclist who wants to maximize efficiency, there is a particular
combination of cadence and resistance that will produce the most power
with the least stress on the body. [...] The idea of gears is to select
the gear in which this combination of cadence and resistance is met.
Depending on the wind, grade and surface conditions, your speed may be
faster or slower, but theoretically your legs should always be pushing
against the same resistance, and spinning the cranks at the same cadence."

And I disagree with you, so? it might be helpful if you explained
what/why you disagree with the above.
It makes sense to me.


Life is Good!
Jeff