Double Step Gearing Possibilites

Doug Goncz <[email hidden]> wrote:
: users.aol.comDoubleStepGearingPossibilites.aviOpen ↗

404 cat. or aol's hometown equivalent.
--
david reuteler [email hidden]

David Reuteler <[email hidden]> wrote in message news:<[email hidden]>...

Quoted message said:

Doug Goncz <[email hidden]> wrote:
: users.aol.comDoubleStepGearingPossibilites.aviOpen ↗

404 cat. or aol's hometown equivalent.

Dear Doug and Dave,

The possibilit-

-i-

-es

improve with traditional spelling.

Carl Fogel

Quoted message said:

Quoted message said:

Doug Goncz <[email hidden]> wrote:
: users.aol.comDoubleStepGearingPossibilites.aviOpen ↗

Quoted message said:

David Reuteler <[email hidden]> wrote in message
news:<[email hidden]>...

Quoted message said:

404 cat. or aol's hometown equivalent.

Carl Fogel said:

The possibilit- -i- -es improve with traditional spelling.

I am confused. Carl's recommended address change (I bow to your superior analytical skills) brings
up a teeny little series of green lines on a white background grid with red dots that dance around
What is it supposed to mean?

Is it some kind of animated gear charrt?

--
Andrew Muzi www.yellowjersey.org Open every day since 1 April, 1971

Quoted post said:

Originally posted by A Muzi

BDoug Goncz said:

Quoted message said:

: users.aol.comDoubleStepGearingPossibilites.aviOpen ↗

Quoted message said:

David Reuteler <[email hidden]> wrote in message
news:<[email hidden]>...

Quoted message said:

404 cat. or aol's hometown equivalent.

Carl Fogel said:

The possibilit- -i- -es improve with traditional spelling.

I am confused. Carl's recommended address change (I bow to your superior analytical skills) brings
up a teeny little series of green lines on a white background grid with red dots that dance around
What is it supposed to mean?

Is it some kind of animated gear charrt?

--
Andrew Muzi www.yellowjersey.org Open every day since 1 April, 1971 [/B]

Dear Andrew,

If you fool around with the view (compact, perhaps)
on a Windows Media Player, you can get a graph that
looks vaguely sensible. (Our video card settings may
not be up to whatever the task is.)

An F and and R suggest front and rear gearing, with
each followed by numbers for typical teeth that change
rapidly. Meanwhile the little red dots jiggle a bit down
on a wide green graph.

I can't make heads or tails out of it, but perhaps
there's more concealed by my video settings or
maybe a more knowledgeable bicyclist would see
the point.

Carl Fogel

Dear Andrew and Carl,

users.aol.comDoubleStepGearingPossibilities.aviOpen ↗

(Copy, Paste, Go) (it works!)

is 99 frames, now at 2 frames per second. It is designed to use the position cursor to drag left and
right to select individual frames. I'm sorry, the first attempt was as I was rushing out the door to
salt my mother's driveway.

The patterns are generated thus:

Assume a top cog of 11. Assume a bottom cog of 30-34. Generate an evenly spaced cassette of seven
cogs. Determine the step size of the cassette. Pick a low range of 24-27. Pick a middle range that's
two steps above the low. Pick a high range that's two steps above the middle. Vary both by a couple
of chainwheel teeth.

Analyze each front/rear combination this way:

Using logarithms, compare each gear to it's nearest integer gear. Zero out the extreme positions
like 52/34 an 24/11, six positions in all. Call this M. Create matrix J stepping the middle range
over ONE, not two, and the high range TWO, not four. This puts the gears in opposition as you see
them on the graph. So when you go up one on the graph, you're going up one in gear sequence. That
is, pressing once on both index shifters at the same time in the same direction moves you one gear.
Create D, the display matrix, with gear numbers like 1, 11, and 9.025, as J is laid out. 21 gears,
10 duplicates, 11 distinct gears.

Analyze J: for the lower two chainwheels, subtract the upper from the lower to form W. Remember
these are already variances from integer gear positions, so this represents how accurately each
double shifted step of one gear is made. That's 5 pairs, I think. Also square the number obtained
forming Q. Do the same for the pairings in the upper two chainwheels.

Slop it all together this way: the mean of M, which represents how closely even spacing is
maintained, time the standard deviation of W, which represents how evenly the double lever shifts
are distributed, times the mean of Q, which represents how accurately the double level shifts come
to being one gear each. This is C, the rating.

Do this for every cassette and chainwheel combination in the limited area of search. Sort on C.
Display the first 99 so that first gear, second chainwheel is right about second gear, first
chainwheel. This takes 13 coordinates. All zeroed out combination go to one, so they don't take any
space on the graph.

The first combination in the latest upload has a range of 670% and near perfect spacing. As you'll
see by running the video, they only get worse from there, but each has its own character. Like some
have excellent spacing which is somewhat off of integer perfection in the low range. If you are
pushing hard, it might be good to have a predictable step there.

This gearing is not for racers. The step between two gears is like a huge change in rpm and pedal
force. This setup is designed to keep you pedaling up the steepest hill and down the other side. I
have another worksheet modeling my ultracapacitor and motor/generator combination. This lets you
store energy pedaling down hill, and use it on ascent. Currently the simulations are not
encouraging.

However this gearing is of use for automatic shifting. The shifter need only warn of impending up
and down shifts, avoid the forbidden combinations, and shift, producing a predictable lurch. The
way I see it, you're only in one gear on long hills. Most of the time, terrain changes, and
you're shifting.

I have developed a lockout to prevent the forbidden gears from being reached, and a PCB with buzzer
that beeps when you go to the extreme second chainwheel positions, and next to extreme first and
third chainwheel positions, so you can back off. I'm working to change the troublesome PCB contacts
to analog slide pots with trim pots and digitizers and comparaters to do the same job, regardless of
your indexer spacing.

I selected 24-25-51 and 11-13-16-19-23-28-34, and as you can see that's not number one. But I've
purchased the cassetes, cogs, and chainwheel. I could send the 51s back for 52s and I would have
this setup. I purchased on the basis of a much less sophisticated graph.

Now that you know the story, enjoy the video!

Sorry I had to dash on that first post.

My physics project at NVCC: Google Groups, then "dgoncz" and some of: ultracapacitor bicycle
fluorescent flywheel inverter

Doug Goncz said:

users.aol.comDoubleStepGearingPossibilities.aviOpen ↗

(Copy, Paste, Go) (it works!)

is 99 frames, now at 2 frames per second. It is designed to use the position cursor to drag left
and right to select individual frames. I'm sorry, the first attempt was as I was rushing out the
door to salt my mother's driveway.

The patterns are generated thus:

Assume a top cog of 11. Assume a bottom cog of 30-34. Generate an evenly spaced cassette of seven
cogs. Determine the step size of the cassette. Pick a low range of 24-27. Pick a middle range
that's two steps above the low. Pick a high range that's two steps above the middle. Vary both by
a couple of chainwheel teeth.

Analyze each front/rear combination this way:

Using logarithms, compare each gear to it's nearest integer gear. Zero out the extreme positions
like 52/34 an 24/11, six positions in all. Call this M. Create matrix J stepping the middle range
over ONE, not two, and the high range TWO, not four. This puts the gears in opposition as you see
them on the graph. So when you go up one on the graph, you're going up one in gear sequence. That
is, pressing once on both index shifters at the same time in the same direction moves you one
gear. Create D, the display matrix, with gear numbers like 1, 11, and 9.025, as J is laid out. 21
gears, 10 duplicates, 11 distinct gears.

Analyze J: for the lower two chainwheels, subtract the upper from the lower to form W. Remember
these are already variances from integer gear positions, so this represents how accurately each
double shifted step of one gear is made. That's 5 pairs, I think. Also square the number obtained
forming Q. Do the same for the pairings in the upper two chainwheels.

Slop it all together this way: the mean of M, which represents how closely even spacing is
maintained, time the standard deviation of W, which represents how evenly the double lever shifts
are distributed, times the mean of Q, which represents how accurately the double level shifts come
to being one gear each. This is C, the rating.

Do this for every cassette and chainwheel combination in the limited area of search. Sort on C.
Display the first 99 so that first gear, second chainwheel is right about second gear, first
chainwheel. This takes 13 coordinates. All zeroed out combination go to one, so they don't take
any space on the graph.

The first combination in the latest upload has a range of 670% and near perfect spacing.

I think your idea of what constitutes "perfect" spacing is fundamentally flawed.

Since drag varies in a non linear fashion with speed, the steps should be smaller at the higher end
of the range. The example you give has a humungous 23% jump in the middle of the fast cruising
range, the 16-13 jump. This is exactly the part of the gear range that _should_ be closest. There
will be lots of road/wind conditions where the 16 is too low, but the 13 is too high.

I think the stock Shimano 11 - 13 - 15 - 18 - 21 - 24 - 34 is just about optimal for the range,
given the limitation to 7 sprockets. It may look funny on paper, but I'll bet that if you were to
spend some time actually riding with each of these setups, you'd wind up preferring the Shimano
arrangement.

I go into these concepts in more detail at:

sheldonbrown.comgear theoryOpen ↗

Sheldon "GIGO" Brown +--------------------------------------------------+
| I'm crazy about the music of Leos Janacek, | especially the Msa Glagolskaya and Sinfonietta |
| sheldonbrown.commusic.htmlOpen ↗ |
+--------------------------------------------------+ Harris Cyclery, West Newton, Massachusetts
Phone 617-244-9772 FAX 617-244-1041 harriscyclery.comharriscyclery.comOpen ↗ Hard-to-find parts shipped Worldwide
captainbike.comcaptainbike.comOpen ↗ sheldonbrown.comsheldonbrown.comOpen ↗

[email hidden] ( Doug Goncz ) wrote in message news:<[email hidden]>...

Dear Doug,

The curious with dialup connections should be warned that the download is 1.6mb for an animated
graph whose point still seems to be better hidden than its original URL.

Possibly your explanation below reveals something, but frankly the position changes of the red dots
on the unlabelled graph resemble minor road vibration.

In a hundred words or fewer, what's the point?

Curiously,

Carl Fogel

Quoted message said:

Dear Andrew and Carl,

users.aol.comDoubleStepGearingPossibilities.aviOpen ↗

(Copy, Paste, Go) (it works!)

is 99 frames, now at 2 frames per second. It is designed to use the position cursor to drag left
and right to select individual frames. I'm sorry, the first attempt was as I was rushing out the
door to salt my mother's driveway.

The patterns are generated thus:

Assume a top cog of 11. Assume a bottom cog of 30-34. Generate an evenly spaced cassette of seven
cogs. Determine the step size of the cassette. Pick a low range of 24-27. Pick a middle range
that's two steps above the low. Pick a high range that's two steps above the middle. Vary both by
a couple of chainwheel teeth.

Analyze each front/rear combination this way:

Using logarithms, compare each gear to it's nearest integer gear. Zero out the extreme positions
like 52/34 an 24/11, six positions in all. Call this M. Create matrix J stepping the middle range
over ONE, not two, and the high range TWO, not four. This puts the gears in opposition as you see
them on the graph. So when you go up one on the graph, you're going up one in gear sequence. That
is, pressing once on both index shifters at the same time in the same direction moves you one
gear. Create D, the display matrix, with gear numbers like 1, 11, and 9.025, as J is laid out. 21
gears, 10 duplicates, 11 distinct gears.

Analyze J: for the lower two chainwheels, subtract the upper from the lower to form W. Remember
these are already variances from integer gear positions, so this represents how accurately each
double shifted step of one gear is made. That's 5 pairs, I think. Also square the number obtained
forming Q. Do the same for the pairings in the upper two chainwheels.

Slop it all together this way: the mean of M, which represents how closely even spacing is
maintained, time the standard deviation of W, which represents how evenly the double lever shifts
are distributed, times the mean of Q, which represents how accurately the double level shifts come
to being one gear each. This is C, the rating.

Do this for every cassette and chainwheel combination in the limited area of search. Sort on C.
Display the first 99 so that first gear, second chainwheel is right about second gear, first
chainwheel. This takes 13 coordinates. All zeroed out combination go to one, so they don't take
any space on the graph.

The first combination in the latest upload has a range of 670% and near perfect spacing. As you'll
see by running the video, they only get worse from there, but each has its own character. Like
some have excellent spacing which is somewhat off of integer perfection in the low range. If you
are pushing hard, it might be good to have a predictable step there.

This gearing is not for racers. The step between two gears is like a huge change in rpm and pedal
force. This setup is designed to keep you pedaling up the steepest hill and down the other side. I
have another worksheet modeling my ultracapacitor and motor/generator combination. This lets you
store energy pedaling down hill, and use it on ascent. Currently the simulations are not
encouraging.

However this gearing is of use for automatic shifting. The shifter need only warn of impending up
and down shifts, avoid the forbidden combinations, and shift, producing a predictable lurch. The
way I see it, you're only in one gear on long hills. Most of the time, terrain changes, and you're
shifting.

I have developed a lockout to prevent the forbidden gears from being reached, and a PCB with
buzzer that beeps when you go to the extreme second chainwheel positions, and next to extreme
first and third chainwheel positions, so you can back off. I'm working to change the troublesome
PCB contacts to analog slide pots with trim pots and digitizers and comparaters to do the same
job, regardless of your indexer spacing.

I selected 24-25-51 and 11-13-16-19-23-28-34, and as you can see that's not number one. But I've
purchased the cassetes, cogs, and chainwheel. I could send the 51s back for 52s and I would have
this setup. I purchased on the basis of a much less sophisticated graph.

Now that you know the story, enjoy the video!

Sorry I had to dash on that first post.

My physics project at NVCC: Google Groups, then "dgoncz" and some of: ultracapacitor bicycle
fluorescent flywheel inverter

Quoted post said:

Originally posted by Sheldon Brown

BDoug Goncz said:

users.aol.comDoubleStepGearingPossibilities.aviOpen ↗

(Copy, Paste, Go) (it works!)

is 99 frames, now at 2 frames per second. It is designed to use the position cursor to drag left
and right to select individual frames. I'm sorry, the first attempt was as I was rushing out the
door to salt my mother's driveway.

The patterns are generated thus:

Assume a top cog of 11. Assume a bottom cog of 30-34. Generate an evenly spaced cassette of seven
cogs. Determine the step size of the cassette. Pick a low range of 24-27. Pick a middle range
that's two steps above the low. Pick a high range that's two steps above the middle. Vary both by
a couple of chainwheel teeth.

Analyze each front/rear combination this way:

Using logarithms, compare each gear to it's nearest integer gear. Zero out the extreme positions
like 52/34 an 24/11, six positions in all. Call this M. Create matrix J stepping the middle range
over ONE, not two, and the high range TWO, not four. This puts the gears in opposition as you see
them on the graph. So when you go up one on the graph, you're going up one in gear sequence. That
is, pressing once on both index shifters at the same time in the same direction moves you one
gear. Create D, the display matrix, with gear numbers like 1, 11, and 9.025, as J is laid out. 21
gears, 10 duplicates, 11 distinct gears.

Analyze J: for the lower two chainwheels, subtract the upper from the lower to form W. Remember
these are already variances from integer gear positions, so this represents how accurately each
double shifted step of one gear is made. That's 5 pairs, I think. Also square the number obtained
forming Q. Do the same for the pairings in the upper two chainwheels.

Slop it all together this way: the mean of M, which represents how closely even spacing is
maintained, time the standard deviation of W, which represents how evenly the double lever shifts
are distributed, times the mean of Q, which represents how accurately the double level shifts come
to being one gear each. This is C, the rating.

Do this for every cassette and chainwheel combination in the limited area of search. Sort on C.
Display the first 99 so that first gear, second chainwheel is right about second gear, first
chainwheel. This takes 13 coordinates. All zeroed out combination go to one, so they don't take
any space on the graph.

The first combination in the latest upload has a range of 670% and near perfect spacing.

I think your idea of what constitutes "perfect" spacing is fundamentally flawed.

Since drag varies in a non linear fashion with speed, the steps should be smaller at the higher end
of the range. The example you give has a humungous 23% jump in the middle of the fast cruising
range, the 16-13 jump. This is exactly the part of the gear range that _should_ be closest. There
will be lots of road/wind conditions where the 16 is too low, but the 13 is too high.

I think the stock Shimano 11 - 13 - 15 - 18 - 21 - 24 - 34 is just about optimal for the range,
given the limitation to 7 sprockets. It may look funny on paper, but I'll bet that if you were to
spend some time actually riding with each of these setups, you'd wind up preferring the Shimano
arrangement.

I go into these concepts in more detail at:

sheldonbrown.comgear theoryOpen ↗

Sheldon "GIGO" Brown +--------------------------------------------------+
| I'm crazy about the music of Leos Janacek, | especially the Msa Glagolskaya and Sinfonietta |
| sheldonbrown.commusic.htmlOpen ↗ |
+--------------------------------------------------+ Harris Cyclery, West Newton, Massachusetts
Phone 617-244-9772 FAX 617-244-1041 harriscyclery.comharriscyclery.comOpen ↗ Hard-to-find parts shipped Worldwide
captainbike.comcaptainbike.comOpen ↗ sheldonbrown.comsheldonbrown.comOpen ↗ [/B]

The non linear drag relationship Sheldon spoke of is due aerodynamic drag.

I prefer even closer ratios at high end than Shimano since in addition to the nonlinear drag issues, I’m spending more time with the high ratios.

I also believe Shimano optimized their standard cassette combinations for doubles rather than triple rings, resulting in lots of ratio replication with triples.

The 12T is my level ground no wind cruise gear while in the high of my dual drive.
Here’s some nice combinations I’ve come up with:

For dual drive or triples of: 72/53/39 on 406s or 53/39/29 on 700C: cassettes comprised of:
11/12/13/14/20/28/34 minimal ratio repetition with broadest range- made from 3 cassettes
11/12/13/14/24/28/32 ab(11-14) +F(24-32)minimal ratio repetition made from only 2 cassettes, but that 14-24 jump is the downside
11/12/13/14/17/26/34 ab+Megarange (26,34) w 17Tab separated from matched sprockets.

Those were developed for recumbent rather than electric bikes, but above electric speeds, tight ratios would be desirable.

If it weren’t for your automatic shifting project, I’d tighten the ratio difference between the to big chainrings as well and use the granny as an extreme emergency bailout only. Is your shifting microprocessor controlled, mechanical, analog electro-mechanical? If micro, you should still be able to program a non repetitive gear selection step sequence. Otherwise, you might need set up ratio combinations to give a repetitive shift sequence as you step through the gears. Also, I think you’ll find you will you change ratios on downhills because your speed is not constant.

What is your top speed with electric boost? I find on my electric bikes, tight ratios are less critical since the motor supplements enough torque to give you a broad range of acceptable pedal ratios. Above the electric speed, the tight ratios would be desirable.

Are you at the Annandale campus of NVCC? I’m located in Arlington and have come accross fewer than ten electrics in the DC area.

-----BEGIN PGP SIGNED MESSAGE-----

In article said:

I think your idea of what constitutes "perfect" spacing is fundamentally flawed.

Since drag varies in a non linear fashion with speed, the steps should be smaller at the higher end
of the range. The example you give has a humungous 23% jump in the middle of the fast cruising
range, the 16-13 jump. This is exactly the part of the gear range that _should_ be closest. There
will be lots of road/wind conditions where the 16 is too low, but the 13 is too high.

I think the stock Shimano 11 - 13 - 15 - 18 - 21 - 24 - 34 is just about optimal for the range,
given the limitation to 7 sprockets. It may look funny on paper, but I'll bet that if you were to
spend some time actually riding with each of these setups, you'd wind up preferring the Shimano
arrangement.

_ I've been thinking that it would nice to have a 9 speed cassette with a "large" jump at the top
and bottom ends. Maybe's it's just where I ride[1], but I rarely use the top two gears with my big
chainwheel. The idea is to maximize gears in the "useful" range and have a single big gear if you
ever spin out the second gear on the range.

Something like

12-14-15-17-19-21-23-25-32

or even

11-14-15-16-18-20-22-25-32

_ What's the biggest jump in the front that's reasonable?

_ Booker C. Bense

[1]- Or how slow I am....

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Booker C. Bense said:

_ I've been thinking that it would nice to have a 9 speed cassette with a "large" jump at the top
and bottom ends. Maybe's it's just where I ride[1], but I rarely use the top two gears with my big
chainwheel.

That suggests your big chainwheel is probably too big.

Back in the 5-speed days, lotsa bikes had 14-17-20... freewheels, with
52/40 chainrings. Sometimes folks would get rid of the 14 because they never used it, but I believe
that they _might_ have used it if it were accessible.

It is tough to get going fast enough in 52/17 to be able to turn over a
52/1. With an intermediate step to help you accelerate, the 52/14 becomes much more useful.

Quoted message said:

The idea is to maximize gears in the "useful" range and have a single big gear if you ever spin
out the second gear on the range.

Something like

12-14-15-17-19-21-23-25-32

or even

11-14-15-16-18-20-22-25-32

_ What's the biggest jump in the front that's reasonable?

I can envsion situations/terrains where this might be a good thing.

I haven't ridden in California, but my impression of it is that it's mostly either flat or
mountainous.

The area I lived in in France was the opposite, high plateau cut by steep river valleys.

For such situations, tight gearing for fine tuning in flat cruising would be desirable, and a
seriously high gear for descending could be useful even if it had a big jump.

For rolling terrain like my New England area, this would be less satisfactory.

Sheldon "Terrain Matters" Brown +----------------------------------------+
| The art of being wise is the art of | knowing what to overlook. | --William James |
+----------------------------------------+ Harris Cyclery, West Newton, Massachusetts Phone 617-244-
9772 FAX 617-244-1041 harriscyclery.comharriscyclery.comOpen ↗ Hard-to-find parts shipped Worldwide
captainbike.comcaptainbike.comOpen ↗ sheldonbrown.comsheldonbrown.comOpen ↗

Doug Goncz said:

users.aol.comDoubleStepGearingPossibilities.aviOpen ↗ (Copy, Paste, Go)
(it works!) is 99 frames, now at 2 frames per second. It is designed to use the position cursor to
drag left and right to select individual frames. I'm sorry, the first attempt was as I was rushing
out the door to salt my mother's driveway. -snip very complex way to look at gearing-

Quoted message said:

I selected 24-25-51 and 11-13-16-19-23-28-34, and as you can see that's not number one. But I've
purchased the cassetes, cogs, and chainwheel. I could send the 51s back for 52s and I would have
this setup. I purchased on the basis of a much less sophisticated graph.

Now that you know the story, enjoy the video!

Frankly I find analog more useful. Sketch in the radiant diagonal lines through 50, 60, 70, etc
inches on a printed gear chart and you can lay out a reasonable gear set in a minute.

From that you got 11-13-16????

That would lead me to think there is a major problem in your software someplace because that range
isn't very useful.

At any rate, even if your chart were big enough to read, the gear points were moving.
--
Andrew Muzi www.yellowjersey.org Open every day since 1 April, 1971

Sheldon Brown said:

Since drag varies in a non linear fashion with speed, the steps should be smaller at the higher end
of the range.

I still don't buy this. It seems to me that the only question is whether or not, for any given
possible speed, there is a gear available that gives a tolerable cadence; and obviously the range of
cadences needed is minimised by causing the gears' largest step to be as small as possible,
irrespective of where it occurs.
--
David Damerell <[email hidden]> Distortion Field!

I opined:

Quoted message said:

Quoted message said:

Since drag varies in a non linear fashion with speed, the steps should be smaller at the higher
end of the range.

David Damerell demurred:

Quoted message said:

I still don't buy this. It seems to me that the only question is whether or not, for any given
possible speed, there is a gear available that gives a tolerable cadence; and obviously the range
of cadences needed is minimised by causing the gears' largest step to be as small as possible,
irrespective of where it occurs.

A single speed permits a "tolerable" cadence under almost all conditions. Some of us want to spend
most of our riding time at something fairly close to an "optimal" cadence.

For riders who wish to go fast, or to cope with headwinds without being slowed too much, smaller
steps near the top of the range let them get up to higher speeds with less of a struggle.

At the low end of the range, close spacing is much less important. As you start to climb a hill,
your pedaling cadence drops, until you must downshift or stall. There's always a slight loss of
momentum involved in making a shift, and if the jumps are too small, a single jump may not be worth
the loss of momentum involved.

When you get over the top of the hill, and start to accellerate up through the gears, you aren't
facing much resistance as you shift out of your climbing range, and you don't tend to spend much
time in any gear until you're back up to cruising speed, so largish jumps in the low range aren't a
serious detriment either going up or going down. wide low, close high

Sheldon "Pear Shaped" Brown +---------------------------------------+
| The cure for boredom is curiosity. | There is no cure for curiosity. | -- Ellen Parr |
+---------------------------------------+ Harris Cyclery, West Newton, Massachusetts Phone 617-244-
9772 FAX 617-244-1041 harriscyclery.comharriscyclery.comOpen ↗ Hard-to-find parts shipped Worldwide
captainbike.comcaptainbike.comOpen ↗ sheldonbrown.comsheldonbrown.comOpen ↗

Sheldon Brown said:

I opined:

Quoted message said:

Quoted message said:

Since drag varies in a non linear fashion with speed, the steps should be smaller at the higher
end of the range.

David Damerell demurred:

Quoted message said:

I still don't buy this. It seems to me that the only question is whether or not, for any given
possible speed, there is a gear available that gives a tolerable cadence; and obviously the range
of cadences needed is minimised by causing the gears' largest step to be as small as possible,
irrespective of where it occurs.

A single speed permits a "tolerable" cadence under almost all conditions. Some of us want to spend
most of our riding time at something fairly close to an "optimal" cadence.

Well, that's a mere matter of semantics; it remains true that having the smallest largest jump,
IYSWIM, lets one remain closest to that optimal cadence at all speeds.

Quoted message said:

At the low end of the range, close spacing is much less important.

See, this I am less convinced about. Once you have finished the shifts as the hill begins, why is it
any better to have to use a cadence you dislike than it would be while cruising on the flat?
--
David Damerell <[email hidden]> Distortion Field!

In article <[email hidden]>,

David Damerell said:

Sheldon Brown said:

I opined:

Quoted message said:

>Since drag varies in a non linear fashion with speed, the steps should be smaller at the higher
>end of the range.

David Damerell demurred:

Quoted message said:

I still don't buy this. It seems to me that the only question is whether or not, for any given
possible speed, there is a gear available that gives a tolerable cadence; and obviously the
range of cadences needed is minimised by causing the gears' largest step to be as small as
possible, irrespective of where it occurs.

A single speed permits a "tolerable" cadence under almost all conditions. Some of us want to
spend most of our riding time at something fairly close to an "optimal" cadence.

Well, that's a mere matter of semantics; it remains true that having the smallest largest jump,
IYSWIM, lets one remain closest to that optimal cadence at all speeds.

Quoted message said:

At the low end of the range, close spacing is much less important.

See, this I am less convinced about. Once you have finished the shifts as the hill begins, why is
it any better to have to use a cadence you dislike than it would be while cruising on the flat?

The short answer is "I don't know," but it's quite observable that the vast majority of cyclists
(including myself) happily take a cadence hit during climbing.

A partial answer is that at low speed it's so much easier to increase your speed with increased
effort that changes in cadence are not that big a deal: if you start slowing, it's relatively easy
to spin up again. At high speeds, aerodynamics make gaining back lost speed take more effort.

Note that increasing your speed n% in any gear requires an n% increase in cadence. The difference is
that there is much more resistance to n% increases in speed as you go faster than when you are going
slower. Net result is it's easier to make the same percentage change in cadence at low speed than at
high speed.

--
Ryan Cousineau, [email hidden] sfu.ca~rcousineOpen ↗ President, Fabrizio Mazzoleni Fan Club

David Damerell said:

Sheldon Brown said:

I opined:

Quoted message said:

> Since drag varies in a non linear fashion with speed, the steps should be smaller at the higher
> end of the range.

David Damerell demurred:

Quoted message said:

I still don't buy this. It seems to me that the only question is whether or not, for any given
possible speed, there is a gear available that gives a tolerable cadence; and obviously the
range of cadences needed is minimised by causing the gears' largest step to be as small as
possible, irrespective of where it occurs.

A single speed permits a "tolerable" cadence under almost all conditions. Some of us want to
spend most of our riding time at something fairly close to an "optimal" cadence.

Well, that's a mere matter of semantics; it remains true that having the smallest largest jump,
IYSWIM, lets one remain closest to that optimal cadence at all speeds.

Quoted message said:

At the low end of the range, close spacing is much less important.

See, this I am less convinced about. Once you have finished the shifts as the hill begins, why is
it any better to have to use a cadence you dislike than it would be while cruising on the flat?

There is another way of making the cadence likeable: ride at the speed that suits the gear. This is
easier, more comfortable and more natural to do at lower speeds and can be worthwhile for the sake
of having closer gearing elsewhere.

In particular, when climbing and cadence is too high, gravity rapidly pulls and holds you back to a
comfortable cadence after easing up on the pedals. Alternatively, if you do have the power and
energy to spin a higher gear, acceleration is quick (even uphill) if speed is low to start with.

At high steady speed, wind drag is so great that it's difficult to accelerate, yet you can't slow
down quickly either because momentum is high. So speed varies more slowly and slightly therefore
closer gears are required to be comfortable.

However, if you want to climb as fast as possible then it does indeed help to have reasonably close
gears at the bottom end as well - and racers do have.

~PB

Quoted post said:

Originally posted by David Damerell

BSheldon Brown said:

I opined:

Quoted message said:

Quoted message said:

Since drag varies in a non linear fashion with speed, the steps should be smaller at the higher
end of the range.

David Damerell demurred:

Quoted message said:

I still don't buy this. It seems to me that the only question is whether or not, for any given
possible speed, there is a gear available that gives a tolerable cadence; and obviously the range
of cadences needed is minimised by causing the gears' largest step to be as small as possible,
irrespective of where it occurs.

A single speed permits a "tolerable" cadence under almost all conditions. Some of us want to spend
most of our riding time at something fairly close to an "optimal" cadence.

Well, that's a mere matter of semantics; it remains true that having the smallest largest jump,
IYSWIM, lets one remain closest to that optimal cadence at all speeds.

Quoted message said:

At the low end of the range, close spacing is much less important.

See, this I am less convinced about. Once you have finished the shifts as the hill begins, why is it
any better to have to use a cadence you dislike than it would be while cruising on the flat?
--
David Damerell <[email hidden]> Distortion Field! [/B]

At higher gear ratios and higher speeds, power (and force if rider maintains constant cadence) required to crank the pedals is higher than at lower speeds and gear ratios. Consequently, it becomes more critical the rider stay near his peak operating cadence.

At higher speeds the rider is generating more power as shown below:
Work = Force X distance=Power X Time,
Power = Force X distance/ time = Force X velocity

At the higher speeds, the exponential aero drag factor means small changes in bike speed and wind speed and direction effect the pedal resistance more than at slow speeds.

Further, changes in grade effect the power needed to maintain a given speed (although merely linearly unlike the non-linear aero effect) as shown below:

POWERvertical = mgh/time= mass X gravitational constant X VELOCITYvertical =
mass X gravitational constant X VELOCITY X sin (theta) , wherein theta is the angle of the incline.

At higher speed, a further increase in speed needs a greater difference in power than at lower speeds. If spinning away from the peak cadences, you’d overtax your legs more than if spinning proximate the peak cadences.

All these extra resistances and higher rider leg generated power combine to narrow the tolerable optimal operating cadence window and increase the criticality of operating near peak operating cadence if one is traveling at higher speeds- whether going for max power or max endurance. Tightening the ratio differences at high drag resistance speeds, enables the rider to keep his cadence near his peak or preferred cadence when small cadence changes normally result in big changes in power and pedal torque.

At lower speeds low resistance lets the rider adjust his cadence without any undue exertion or strain.

Given limited ratio selections available, better to select tight ratios in the high drag higher speed range than lower speeds, and better to select tight ratios at speeds you travel at a lot.

Sheldon Brown said:

David Damerell demurred:

Quoted message said:

I still don't buy this. It seems to me that the only question is whether or not, for any given
possible speed, there is a gear available that gives a tolerable cadence; and obviously the range
of cadences needed is minimised by causing the gears' largest step to be as small as possible,
irrespective of where it occurs.

A single speed permits a "tolerable" cadence under almost all conditions. Some of us want to spend
most of our riding time at something fairly close to an "optimal" cadence.

I thought about this some more, and I think I see where Sheldon is coming from.

There are two ways to approach this situation. One is to desire a specific cadence and to be
willing to allow the effort to vary to match that cadence; the other is to desire a specific
effort (obviously the available effort varies depending on how you feel that day and how far you
have to go, but at any given point it's a specific amount) and to allow the cadence to vary to
match that effort.

You can't do both; unless the slope and wind conditions are coincidentally just right, either your
cadence or your effort will not be "ideal". However, you probably want to minimise the variation in
whichever you allow to vary.

If you desire a specific cadence, you notice that (as Sheldon points out) the increase in effort
needed for a given speed increase is higher at higher speeds. Hence you want closely spaced high
gears, so as to keep the changes in amount of effort roughly constant as you change up gears - so
that in given conditions you can always ride at your preferred cadence without either pushing too
hard or slacking off too much.

If you want to keep effort constant, you want evenly spaced gears; your speed is determined by the
available effort, and then you just want the cadence not to vary too much; and a wide-spaced gear
anywhere in the range might cause that.

Of course no-one falls entirely into these two camps; but I think it does come down to whether you
are more tolerant of varying cadence or varying effort. In the former case, take evenly spaced
gears; in the latter case, closely spaced high gears.
--
David Damerell <[email hidden]> Kill the tomato!

David Damerell snipped what he was replying to and said:

Quoted message said:

Quoted message said:

I still don't buy this. It seems to me that the only question is whether or not, for any given
possible speed, there is a gear available that gives a tolerable cadence; and obviously the range
of cadences needed is minimised by causing the gears' largest step to be as small as possible,
irrespective of where it occurs.

I replied:

Quoted message said:

Quoted message said:

A single speed permits a "tolerable" cadence under almost all conditions. Some of us want to spend
most of our riding time at something fairly close to an "optimal" cadence.

David

Quoted message said:

I thought about this some more, and I think I see where Sheldon is coming from.

There are two ways to approach this situation. One is to desire a specific cadence and to be
willing to allow the effort to vary to match that cadence; the other is to desire a specific
effort (obviously the available effort varies depending on how you feel that day and how far you
have to go, but at any given point it's a specific amount) and to allow the cadence to vary to
match that effort.

You can't do both; unless the slope and wind conditions are coincidentally just right, either your
cadence or your effort will not be "ideal". However, you probably want to minimise the variation
in whichever you allow to vary.

If you desire a specific cadence, you notice that (as Sheldon points out) the increase in effort
needed for a given speed increase is higher at higher speeds. Hence you want closely spaced high
gears, so as to keep the changes in amount of effort roughly constant as you change up gears - so
that in given conditions you can always ride at your preferred cadence without either pushing too
hard or slacking off too much.

If you want to keep effort constant, you want evenly spaced gears; your speed is determined by the
available effort, and then you just want the cadence not to vary too much; and a wide-spaced gear
anywhere in the range might cause that.

This seems to me to be a "distinction without a difference." Indeed, if a perfect, continuously
variable transmission existed, one would be able to maintain constant effort and cadence under all
slope and wind conditions.

In practice, one has to compromise, but the usual compromises involve adjustments to _both_ cadence
and effort, rather than just one or t'other.

If the jumps are too large in the high cruising range, you cannot necessarily maintain the desired
effort level. There will be situations where the desired effort in one gear will cause you to
accelerate until you spin out of that gear, while the same effort in the next gear up won't be
sufficient to maintain speed, and you'll either have to pedal harder or decelerate.

Sheldon "Geometric Progression" Brown +-------------------------------------------------+
| There is something fascinating about science. | One gets such wholesale returns of conjecture |
| out of such a trifling investment of fact. | --Mark Twain |
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