| T.R | Title | User | Personal
Name | Date | Lines |
|---|
| 920.1 | Mathematics of developing gear progressions | SMURF::BINDER | And the quarterback is *toast*! | Fri Nov 11 1988 11:45 | 120 |
| This reply discusses the mathematics of developing near-ideal gearing
progressions. As with the base note, it deals only with double-
chainring setups. I don't see progressions as applying to triples.
To develop a progression, you need to know these things:
1. Desired high gear
2. Desired low gear
3. Wheel size
4. Number of gears
5. Progression type
6. Size of at least one cog or chainring
From 1 and 2, you can figure the ratio between them.
From 4 and 5, you can calculate the number of half steps (intervals)
between low and high. You need this number so you can make each gear
step be a uniform percentage above the one below it. (That doesn't mean
the same number of gear inches - a change from 50 to 54 isn't the same
as a change from 90 to 94. What you are looking for is changes that
will entail the same amount of change in pedaling effort.)
If your progression is an Apline, then you will have "missing" gears at
the two interval points indicated by "M" in this sketch:
Big cog ... Small cog
Big ring M X X X X X Alpine
Small ring X X X X X M progression
You still need to know where they *would* be if they were there, or your
gears won't come out even.
To develop this uniform percentage, you take the nth root of the ratio
between high and low. For this purpose, "n" is the number of intervals.
A 10-speed Alpine has 11 intervals. If your gear range is from 40 to
100, the ratio is 1:2.5, and the 11th root is 1.087... This difference
value is the interval root. Your second gear (for an Alpine, this is a
"missing" gear) should be 1.087... times your first, or 43.5. Your third
gear (for an Alpine, the second "real" gear) would be 47.3. Of course,
because cogs and chainrings don't exist to get those exact gears, you
have to compromise and take the next best thing.
How do you arrive at that magical "next best thing"? Since gearing is a
function of wheel size and cog size, we bring those two factors into the
equation. In my list of needed information, I said you need to know the
size of at least one cog. It could be any cog or chainring, but you'd
like to give yourself the best possible chance of getting sprockets with
integral numbers of teeth, so you pick the one that will give you this
chance. That's the small cog, because the percentage difference between
two sizes of sprocket gets smaller as you work upward, and there's more
likelihood that a real sprocket will be close to the ideal. For the
10-speed 40-100 Alpine I'm developing here, I'll use a 14-tooth cog.
Using the wheel size and the desired 100-inch gear, you can calculate
the size of your large chainring:
gear X cog_size 100 X 14
big_ring = --------------- = -------- = 51.85
wheel 27
We have a 52-tooth chainring, which gives us a 100.3-inch gear. Now, in
order to get the most accurate numbers, use the integer size, 52, for
the next step.
To develop the size of the small chainring, figure how many intervals
it is less than the big ring. For a 1-1/2 step progression, the
difference between rings is 3 intervals. Here is the formula:
big_ring 52
small_ring = ----------------------------- = ------ = 40.501
no_of_half_steps 3
interval_root 1.087
This gives us a 41-tooth chainring.
Now for the cog sizes. Each cog is two intervals larger than the
preceding one. Here's the formula:
2
new_cog = old_cog X interval_root
For the progression I'm building here, the resulting cogs are:
14 (The one we started with)
16.538 = 17
19.536 = 20
23.077 = 23
27.261 = 27
And our resulting gearing looks like this:
| Chainrings
Cogs | 52 41
------+-------------
14 | 100.3 79.1
17 | 82.6 65.1
20 | 70.2 55.3
23 | 61.0 48.1
27 | 52.0 41.0
40 50 60 70 80 90 100 110
52 | | X |X X | X | X |
+---------+---------+---------+---------+---------+---------+---------+
41 |X X | X | X | X| | | |
This display is the actual typeout from a C program I wrote yesterday to
do all this math for me. (I worked the math out about 10 years ago - my
own bikes have had progressions designed this way since then.) It also
checks illegal cog sizes and allows you to diddle cogs in case the
mathematically closest cogs don't work out as well as perhaps having two
cogs one tooth "off" might do. ANYONE INTERESTED IN THE PROGRAM, PLEASE
SEND ME EMAIL. DO *NOT* REPLY TO THIS NOTE ASKING FOR IT!
- Dick
|
| 920.2 | The Lazy Man's Guide to Gearing | CESARE::JOHNSON | Tutto sbagliato; tutto da rifare. | Fri Nov 11 1988 14:10 | 36 |
| I've always liked gear combinations like the Alpine on paper, but have
failed to use them properly on the road. Basically, I'm lazy: I want
to spend my time riding, not thinking about how to move both levers so
I reach the next higher or lower gear. My approach (for general use)
is to select gears that will give me predictable, usable shifts one
lever at a time. This means that the front derailleur becomes my "big
quantum" shift (uphill/downhill, headwind/tailwind), while the rear is
"small quantum" (adjusting within upper or lower ranges). I think Dick
would call this the "crossover" pattern.
Anyway, here overlap doesn't matter at all. What matters is to make
the change in effort between each gear as uniform as possible. You do
this by selecting gears that are further apart in size as they get
larger. Near the top of the range (15-14-13) there's only a one-tooth
difference. Near the bottom (22-19-17-16 or 24-21-19-17) it becomes
progressively greater. For this reason, I don't like the popular
(23-21-19-17-15-13) block: it bunches the ratios too closely together
at the bottom of the range, and too far apart at the top.
The effect of this is to make shifting a thought-free process. I always
know what the increase or decrease in effort will be if I shift one way
or the other. No surprises, just the gear I expected.
Dick also mentioned that racing bikes can't get away with big ring/big
cog, or small ring/small cog gearing. That further reduces the appeal
of Alpine gears in these cases.
There's one final advantage to the "crossover" approach: you don't have
to write a program to do gearing math!
MATT
PS - Of course, for racing, the best method is to ride the course
and choose the ratios you plan to use for each section, whatever
they happen to be....
|
| 920.3 | It's all too much for me. | BANZAI::FISHER | BMB Finisher | Fri Nov 11 1988 14:33 | 3 |
| If this keeps up I'm going to switch to a fixed gear.
ed
|
| 920.4 | Right on about crossovers | SMURF::BINDER | And the quarterback is *toast*! | Fri Nov 11 1988 14:55 | 32 |
| Re: .2
> My approach (for general use) is to select gears that will give me
> predictable, usable shifts one lever at a time. This means that the
> front derailleur becomes my "big quantum" shift (uphill/downhill,
> headwind/tailwind), while the rear is "small quantum" (adjusting
> within upper or lower ranges). I think Dick would call this the
> "crossover" pattern.
Yup, that's a crossover. And your laziness isn't unusual - much of the
time, I use my half-step as a five-speed, staying on one chainring. I
go to the other chainring as needed for fine-tuning the gearing for a
given bit of road.
> Anyway, here overlap doesn't matter at all. What matters is to make
> the change in effort between each gear as uniform as possible. You do
> this by selecting gears that are further apart in size as they get
> larger. Near the top of the range (15-14-13) there's only a one-tooth
> difference. Near the bottom (22-19-17-16 or 24-21-19-17) it becomes
> progressively greater.
You're right about this uniformity. This choice of increasingly greater
differences between cogs is a natural result of using the math I laid
out in .1 - running my program for a 12-speed half-step from 40 to 100
yields cogs of 14, 17, 20, 23, 27, and 32 teeth.
> There's one final advantage to the "crossover" approach: you don't
> have to write a program to do gearing math!
Of course you don't. But then you miss all the fun of it!
- Dick
|
| 920.5 | see 164.2 | NAC::LANDRY | | Fri Nov 11 1988 14:58 | 3 |
| Also see note 164.2 for a discussion of half-step vs. crossover
vs. Alpine.
|
| 920.6 | 48 x 19 or 50 x 21 ? | MENTOR::REG | a little risc averse | Mon Nov 14 1988 09:45 | 2 |
| re .3 Yo Ed !
|
| 920.7 | Simple Table Needed | AIMHI::JSMITH | Bikes Spoke_n Here | Mon Dec 05 1988 15:03 | 6 |
| What ever happened to the simple little table that had
the frewheel size on one axis and the chainwheel size
on the other with all of the gear inches listed for each ?
Does anyone have a copy they could post here as a quick
reference chart ?
Jerry
|
| 920.8 | for those averse to 11th roots... | JULIE::CORENZWIT | Everybody remember where we parked. | Fri Dec 16 1988 08:05 | 3 |
| A spreadsheet can do wonders for the trial-and-error approach.
Julie
|
| 920.9 | Solution to root aversion | SMURF::BINDER | And the quarterback is *toast*! | Fri Dec 16 1988 11:24 | 19 |
| Re: .8
> A spreadsheet can do wonders for the trial-and-error approach.
True. In fact, the first practical implementation I made of my gearing
program was a VisiCalc spreadsheet. The top half of the sheet was for
putting in the information about your current setup, and the bottom was
for calculating a new setup using the math I'd worked out. I got *real*
sick of piddling with that 40-column Apple ][+ toy spreadsheet...
Anyway, for those people who are averse to 11th (or 13th, or...) roots,
my program is available. If you're on a VMS system, copy this file:
SMURF::USERD:[BINDER.FUN]GEARS.EXE
If you're on an ULTRIX system, send me mail and I'll figure out how to
get a copy to you.
- Dick
|
| 920.10 | A fool and his money or brilliant idea? | VERVE::BUCHANAN | Bat | Thu Nov 09 1989 13:24 | 94 |
| This is an idea that I've been toying with for awhile. Comments would be
appreciated.
I'm thinking of converting my road bike over to a triple. I'm comfortable with
it for the most part but there are some hills around that I just have to admit
that I can't handle. So what I would like is to basically keep racing style
gearing but have a bail-out gear for long climbs of 10% or greater.
I current set-up is Dura-Ace (42-53) x (13-15-17-19-21-23-26). This gives me a
low gear of about 44 and a high of 110. Because I wanted the low gear I am
forced to use a (fairly) wide range in the back where all the steps are either
2 or 3 teeth. It charts out as follows:
42 53
13 xxxxx 110.08
15 75.60 95.40
17 66.71 84.18
19 59.68 75.32
21 54.00 68.14
23 49.30 62.22
26 43.62 xxxxx
1 1
3 4 5 6 7 8 9 0 1
5678901234567890123456789012345678901234567890123456789012345678901234567890123
x x x x x x
x x x x x x
One gearing the strikes my fancy is (28-40-50) x (13-14-15-16-18-20-22). It
would give me a low of 34 (over 20% lower than a 44) and a high of 104. And
since it is almost a straight block each jump is closer. Other slight
modifications to the rear cluster also look pretty good. (12-21) gives a low of
36 and a high of 113 or (13-21). My first choice charts out as follows:
28 40 50
13 xxxxx 83.08 103.85
14 xxxxx 77.14 96.43
15 50.40 72.00 90.00
16 47.25 67.50 84.38
18 42.00 60.00 75.00
20 37.80 54.00 xxxxx
22 34.37 49.09 xxxxx
1 1
3 4 5 6 7 8 9 0 1
12345678901234567890123456789012345678901234567890123456789012345678901234567890123
x x x x x
x x x x x x x
x x x x x
==========================
most used
I find that I spend most of my time riding in the range of 60 to 85 and this
has 7 gears in that range, with 5 on one chain ring.
A Dura-Ace rear derailluer is supposed to be able to wrap 26 teeth. If I throw
out two gears at each extreme as shown then I have a 25 tooth difference so I
won't need a new derailluer and shift levers. Actually I would even be willing
to throw out three gears on the small chain ring.
Oh by the way, my bike shop assures me that all of the cogs are available, even
the 40 tooth chain ring. They also claim that a short wheel base racing frame
will work, they just put a triple on a Kestrel that week. They also said that
some men used triples in a couple stages in the Giro and Longo used one in the
Alps in the Tour.
It sounds good to me. I get the bail-out low that I want, plus tighter gearing
in the upper and middle range. The only thing holding me back is that once the
decision is made it's final. And it won't be cheap. I would need the
following parts:
Crank set - Deore or Deore XT plus one additional chain ring since
Shimano doesn't make a 40.
Bottom Bracket - to get the longer spindle.
Some new cogs - I would use my current freewheel.
Front derailluer - my current derailluer can't handle the 28-50 range.
Chain.
These parts plus labor will run in the neighborhood of $200.
|
| 920.11 | | WLDWST::POLLARD | | Thu Nov 09 1989 19:11 | 10 |
| Hi Mike,
You climb just fine now. How often to you do Redwood Gulch
anyway? If you want a tougher looking rear cluster, why not just use
a 39 inner ring? It is a lot cheaper than a new crank, and it
looks maaaahvelous compared to a triple. Besides, I think that
there is a law against putting a triple on a Guerciotti.
If you really want the triple, tell me before you sell off
the double and the front changer. I might be able to use `em.
|
| 920.12 | A 39 is much cheaper (another happy customer) | CESARE::JOHNSON | Matt Johnson, DTN 871-7473 | Fri Nov 10 1989 06:56 | 4 |
| I agree with -.1. At least try a 39 before going to the triple
with 2/3 unusable gears.
MATT
|
| 920.13 | How about a 39? | TPWEST::SHROYER | | Fri Nov 10 1989 11:54 | 26 |
| <<< Note 920.11 by WLDWST::POLLARD >>>
> Hi Mike,
>
> You climb just fine now. How often to you do Redwood Gulch
> anyway? If you want a tougher looking rear cluster, why not just use
> a 39 inner ring? It is a lot cheaper than a new crank, and it
> looks maaaahvelous compared to a triple. Besides, I think that
> there is a law against putting a triple on a Guerciotti.
John,
I disagree with you on a few points. First, Mike doesn't climb all
that well! He is getting older every day and is even out looking to buy a
large RV to replace his weekend rides.
Secondly, although he doesn't do Redwood often, we are doing Moody at
lunch today.
Finally, the law against tripple chain rings only applies to the Fuso
and the Peter Mooney.
As for a more serious note, I really like my 53/39 with a
13-14-15-17-19-21-24. The 39-24 comes in handy on grades of 10-20% like
Redwood, Tunitas or Hicks. It may be worth trying. It is an easy change and
would be much cheaper than the tripple option.
|
| 920.14 | Or I could lose some weight... | VERVE::BUCHANAN | Bat | Fri Nov 10 1989 13:07 | 18 |
| Putting a triple on a Guerciotti may sound like sacrilege but it's nothing
compared to when my wife suggested I put a BABY SEAT on the back after my first
kid was born!
How often do I do Redwood Gulch? Never and that's the problem. I haven't
climbed that road in about 3 years. (Redwood Gulch is a road that AVERAGES
about 15% for nearly 2 miles).
I think that a 42x26 is about the same as a 39x24. As I said this gearing is
good for 95% of the time. It's just every once in a while there is that hill
that just kicks my ass! I've tentively committed to doing the Marklevile Death
Ride next year and maybe I'm spooked by the stories I've heard. [The Death
Ride is a ride in the Sierra Nevada Mountains near Lake Tahoe that cover 1, 3
or 5 mountain passes each at an altitude of 8 - 10K feet above sea level. The
full 5 pass ride is 150 miles with some pretty wicked climbs I'm told.]
Yes I'm a wimp, but I'm also a cheap wimp. So I'll likely stick with what I've
got. But next bike....
|
| 920.15 | This is what's got me spooked | VERVE::BUCHANAN | Bat | Fri Nov 10 1989 16:57 | 39 |
| Thanks to John Bingham who sent this to me. The artical listed 4 other rides,
all in the Pacific Northwest.
The Death Ride --
The Tour of the California Alps
Okay, it's not in the Northwest, but this ride epitomizes
the concept. You couldn't come up with a tougher scenario
for a cyclist.
Held outside of South Lake Tahoe, the ride begins at 5000
feet above sea level. Oxygen is already a scarce resource,
and there is no where to go but up. The course has five
mountain passes, with a total elevation gain of 15,000 feet.
Grades are relentless, averaging 6 percent, with long
stretches of 8-15 percent. Temperatures are in the 90
degree range and there is little shade. But there is the
wind. It never seems to be at your back and it can gust up
to 25 mph. Many riders discover how slow they can go
without falling over.
The 156 mile course is picturesque, but most finishers
remember only a white line on the side of the road. The
Death Ride centers on the town of Markleeville and goes over
Ebbetts Pass (elev. 8730'), Carson Pass (8573'), Luther Pass
(7740') and both sides of Monitor Pass (8314'). Ebbetts
Pass, arguably the toughest, is last. With its countless
switchbacks, this hill toys with your mind. Those who
reach the top are rewarded with the coveted "Death Ride" pin
and a 20 mile ride back to the finish in Markleeville.
The ride is held in July and entrants are limited to 1500,
so enter early. Contact the Alpine County Chamber of
Commerce, (916)694-2475.
|
| 920.16 | More Friendly Advice | WLDWST::POLLARD | | Fri Nov 10 1989 20:04 | 13 |
| Mike,
I'm sold. Now, tell me how I get a 39 on a Nuovo Record crank
and an old Superbe (Campy bolt pattern again.) Maybe you should
get the triple so that I can get your Dura-Ace at a good price.
That's it! Think about how much you NEEEEED that triple, all shiny
and new! You DESERVE it. You haven't had new equipment for far
too long a time. Like the ad says: "Just Do It."
Looking out for your best interests,
John
|
| 920.17 | more gearing chatter | ARTIE::ALVIDREZ | | Fri Apr 16 1993 16:20 | 61 |
| I've been corresponding with Mike "Bat" Buchanan about gearing ratios. I just
purchased a Bridgestone RB-1 now that comes with 8-speed Ultegra. I decided
against the STI for personal reasons.
Any comments on the following gearings are appreciated.
-----------------------------------------------------------------------------
Here's why I think a 53X41 combination will work best for me:
Right now I have a 53X39 with 13-14-15-16-17-19-21-23 in back. I think you
have the same set-up:
53 39
13 110.08 81.00
14 102.21 75.21
15 95.40 70.20
16 89.44 65.81
17 84.18 61.94
19 75.32 55.42
21 68.14 50.14
23 62.22 45.78
40 50 60 70 80 90 100 110
5678901234567890123456789012345678901234567890123456789012345678901234567890123
| | | | | | | |
| | | | | | | |
Notice there is a jump of nearly nine inches between 53X17 and 53X19. There
might be a time when a 53X17 will be too much mashing and I'll need to spin
more, but a 53X19 will be too much spinning. I can't use the lower chain ring
gears either, as you can see. I need to have a gear somewhere between 53X17
and 53X19 going into a headwind at the end of a long ride (like Davis or ???).
If I spin at an efficient rate, I should be going 20-21 MPH.
If I had a 53X41, and swap out the 23-tooth with a 24-tooth cog, here is
what I get:
53 41
13 110.08 85.15
14 102.21 79.07 <----- this is the gear I need
15 95.40 73.80
16 89.44 69.19
17 84.18 65.12
19 75.32 58.26
21 68.14 52.71
24 59.63 46.13
40 50 60 70 80 90 100 110
5678901234567890123456789012345678901234567890123456789012345678901234567890123
| | | | | | | |
| | | | | | | |
^
|
here is where I'll use it ------+
This looks better. The 41X24 combination should get me up any hill as long
as I'm in shape. Now, the only problem is finding out if there is such a
beast as a 41-inch chainring. I'll try Wheelsmith and see what they say.
AAA
|
| 920.18 | "Bat" Buchanan's reply | ARTIE::ALVIDREZ | | Fri Apr 16 1993 16:22 | 26 |
|
I've never heard of a 41 but I could be wrong. My current gearing is the same
as yours except I've already put he 24 tooth cog on.
One thing that you should keep in mind when you're looking at you chart is how
many shifts it will take to get from one gear to the next. For instance in
your ideal setup to get from the 84 (53x17) to the 79 (41x14) requires 4
shifts, the chain ring in front plus 17 to 16 to 15 to 14 in back. Not bad if
you have STI! With down tube shifter going in that direction isn't too bad
since you can down shift the front derailleur with you right hand so you can do
the whole thing at once. But going the opposite way requires you to change
hands and do it in two separate shifts.
In general I don't like the big gap between a 53 and 39, the old days of 42, 52
were better, but the trade off is you need a wider range in back. I guess the
only perfect solution is a racing triple!
Just for kicks try a 42,53 x 13-24 or 26. You can obviously get a 42.
A 42 would change your 79 into an 81, still between 75 and 84 but not so close
to the middle.
Another possibility is 43, which I had once, although I haven't seen since.
43,53 x 13-26 would still give a fairly low gear (44.65) and would give you TWO
gears (a 77.4 and an 82.9) in your gap, it would also reduce the number of rear
shifts when you shift up front.
|
| 920.19 | | NOVA::FISHER | DEC Rdb/Dinosaur | Fri Apr 16 1993 16:40 | 4 |
| you can't upshift a downtube shifter with your right hand?
hmmmmm,
ed
|
| 920.20 | I've seen them.... | MYOSPY::D_SWEENEY | | Wed Apr 21 1993 14:54 | 8 |
|
They make a 41 tooth chainwheel. In fact I think I have one at home.
I used it when I raced my BMX bike indoors or on real sandy tracks, the
only thing I'm not sure about is if it will match up with a chain on a
road bike. For some reason I think they might be diffrent widths on the
tooth spacing on the chain wheels?? Might be worth checking out however...
Dan
|