prime number cogs?
wle
know have some bogus information, i won;t name them.
one thing i wondered about though.
it said that rear cogs with a prime number of teeth,
like 11, 13, 17, etc,
'run smoother and last longer'.
reason given was that the cog
teeth do not regularly 'line up'
with the chain ring teeth.
this doesn;t make sense to me.
it might if they were meshed gears like a car transmission.
but the chain separates the 2 gears, so what difference could
it possibly make?
even if they were the same size, the same 2 teeth would be constantly
in sync with each other but so what?
they don;t touch, how could it matter?
even if the chain had some even
multiple number of links,
say the cog was 15 teeth and the chain had 7*15=105 links,
it would be in sync with the chain, but again, so what?
wle.
Diablo Scott
> i have been reading some bike books recently that i
> know have some bogus information, i won;t name them.
>
> one thing i wondered about though.
>
> it said that rear cogs with a prime number of teeth,
> like 11, 13, 17, etc,
> 'run smoother and last longer'.
That explains why my 24 and 27 always start skipping way before my 11 is
worn out.
--
My bike blog:
http://diabloscott.blogspot.com/
Werehatrack
said:
[snip]
>even if the chain had some even
>multiple number of links,
The roller count is what would matter in the chain IMO, and the number
of rollers will always be an even number unless one of what I have
heard called an "AC/DC" extender link is employed, and those are
beyond rare for a derailleur chain. However, the whole thing's based
on what I have to say looks like a pretty flimsy concept. I do not
think this issue needs to be taken seriously, even on a fixed-gear
setup.
>say the cog was 15 teeth and the chain had 7*15=105 links,
>it would be in sync with the chain, but again, so what?
The idea was to ensure cyclic complete recirculation of the chain so
that every roller would hit every tooth and thereby regularize the
wear. What I have heard, however, is that even on a fixed-gear setup,
it's not at all critical. On a der setup, it's essentially
irrelevant; the random reset of the relationships during gear changes
will keep it from being an issue if it every really was one.
My opinion: Don't worry about it.
--
My email address is antispammed; pull WEEDS if replying via e-mail.
Typoes are not a bug, they're a feature.
Words processed in a facility that contains nuts.
Werehatrack
<N0SPAMdi...@terra.es> may have said:
>wle wrote:
>
>> i have been reading some bike books recently that i
>> know have some bogus information, i won;t name them.
>>
>> one thing i wondered about though.
>>
>> it said that rear cogs with a prime number of teeth,
>> like 11, 13, 17, etc,
>> 'run smoother and last longer'.
>
>
>That explains why my 24 and 27 always start skipping way before my 11 is
>worn out.
I would bet that you ride in the 24 and 27 a lot more than the 11.
wle
wle.
russell...@yahoo.com
Diablo Scott wrote:
> wle wrote:
>
> > i have been reading some bike books recently that i
> > know have some bogus information, i won;t name them.
> >
> > one thing i wondered about though.
> >
> > it said that rear cogs with a prime number of teeth,
> > like 11, 13, 17, etc,
> > 'run smoother and last longer'.
>
>
> That explains why my 24 and 27 always start skipping way before my 11
is
> worn out.
But my 17 cog wears out before my 13 cog. And both are prime number
cogs. And my 19 cog wears out before my 13, but not before my 17 cog.
All are prime cogs. And the 23 cog wears out about as frequently as
the 13 cog, long after the 17 and 19 wear out. All prime cogs. There
must be some other principle involved besides merely being a prime cog.
Maybe having a "3" in it like 13 and 23 or being a multiple of "3"
like 24 and 27. Yes that must be it. And I bet if I counted the links
on my chain, it would be a multiple of "3" or have 103 or 113 links. I
would also add it might be the number of prime cogs you have on the
cassette, but I have four prime cogs (13, 17, 19, 23) on my cassette so
this might not be relevant. But it should be studied nonetheless.
I wonder if Mr. Brandt could come up with the engineering formula to
explain this prime cog wearing out theory and the number "3".
Tom Ace
wle wrote:
> i have been reading some bike books recently that i
> know have some bogus information, i won;t name them.
Please name the one that has the claim about prime
tooth counts. I'd like to know who said that.
Tom Ace
Benjamin Lewis
> But my 17 cog wears out before my 13 cog. And both are prime number
> cogs. And my 19 cog wears out before my 13, but not before my 17 cog.
> All are prime cogs. And the 23 cog wears out about as frequently as
> the 13 cog, long after the 17 and 19 wear out. All prime cogs. There
> must be some other principle involved besides merely being a prime cog.
If primeness mattered at all, I would think it would just have to be
relatively prime with the number of links in the chain. This ensures that
each link gets exactly one turn with each cog on the wheel before the cycle
repeats (why this would make a difference I have no idea, but I can't think
of *any* explanation for the primeness of a cog making a difference).
I suspect, possibly, that how much you use a particular cog wheel just
might have something to do with it too :)
--
Benjamin Lewis
I regret to say that we of the FBI are powerless to act in cases of
oral-genital intimacy, unless it has in some way obstructed interstate
commerce. -- J. Edgar Hoover
Greg Berchin
>>But my 17 cog wears out before my 13 cog. And both are prime number
>>cogs. And my 19 cog wears out before my 13, but not before my 17 cog.
>>All are prime cogs. And the 23 cog wears out about as frequently as
>>the 13 cog, long after the 17 and 19 wear out. All prime cogs.
You must express the numbers in binary, since there are two
rollers per link:
17 = 10001
13 = 01101
19 = 10011
23 = 10111
Obviously the 17 wears out first, because it has the fewest "1"
bits, and they're separated by a huge gap of three "0" bits. The
19 wears out next, because there is a gap of two "0" bits between
the "1" bits. The 13 and the 23 are about the same, because they
only have a gap of one "0" bit between the "1" bits.
:-)
Greg
Diablo Scott
So a 31 tooth cog would last virutally forever since it's both prime and
written in binary as 11111. But you'll never see one because then there
would be no market for replacements. It's all about the money.
Greg Berchin
<N0SPAMdi...@terra.es> wrote:
>>So a 31 tooth cog would last virutally forever since it's both prime and
>>written in binary as 11111. But you'll never see one because then there
>>would be no market for replacements. It's all about the money.
And a 32 tooth cog, with that long string of zeroes, would be
utterly useless.
Greg
Larry Coon
> But my 17 cog wears out before my 13 cog. And both are prime number
> cogs. And my 19 cog wears out before my 13, but not before my 17 cog.
> All are prime cogs. And the 23 cog wears out about as frequently as
> the 13 cog, long after the 17 and 19 wear out. All prime cogs. There
> must be some other principle involved besides merely being a prime cog.
Some cogs have better feng shui.
Larry Coon
University of California
Werehatrack
>I wonder if Mr. Brandt could come up with the engineering formula to
>explain this prime cog wearing out theory and the number "3".
He's apparently got better things to do.
Maybe it has something to do with the way that the numeral 3 looks
like a worn-out sprocket's teeth...
Donald Gillies
>i have been reading some bike books recently that i
>know have some bogus information, i won;t name them.
>one thing i wondered about though.
>it said that rear cogs with a prime number of teeth, like 11, 13, 17,
>etc, 'run smoother and last longer'.
>reason given was that the cog teeth do not regularly 'line up' with
>the chain ring teeth.
Clearly fallacious, all we need to know is that the lcm of (cog teeth,
front crankset teeth) is suitably large. It is not essential for the
lcm to be absolutely as large as possible. In other words, you can
certainly use composite-number rear cogs as long as the prime factors
of your front cogs and prime factors of your rear cogs are
sufficiently different as to form nearly disjoint sets.
For example 42 x 26, the only shared factor is 2, so the lcm is 2x
away from optimal.
Am I clear?
- Don Gillies
San Diego, CA
Drew Eckhardt
wle <w...@mailinator.com> wrote:
>it said that rear cogs with a prime number of teeth,
>like 11, 13, 17, etc,
>'run smoother and last longer'.
With 30-40-50 x 13-14-15-16-17-18-19-21 my 18 and 16 wore out first.
I wasn't too surprised since 50 x 18 and 40 x 16 were my favorite
combinations.
The big ring went first.
--
<a href="http://www.poohsticks.org/drew/">Home Page</a>
In 1913 the inflation adjusted (in 2003 dollars) exemption for single people
was $54,567, married couples' exemption $72,756, the next $363,783 was taxed
at 1%, and earnings over $9,094,578 were taxed at the top rate of 7%.
Donald Gillies
>So a 31 tooth cog would last virutally forever since it's both prime and
>written in binary as 11111. But you'll never see one because then there
>would be no market for replacements. It's all about the money.
Ahah! This explains why the schwinn paramount P-15 had a 31T rear
cog, and why replacements are impossible to find. I bet Suntour knew
about the excessive longevity of 31T freewheels and quietly retired
these freewheels right away, expecting that the existing 31T cogs
would last forever.
I personally prefer a high gear of 63T x 31T. I'm not re-using teeth
combos until I've gone over a kilometer in this gear. Of course, I
have to remember not to shift gears for the entire kilometer, but
that's a small price to pay ...
Benjamin Lewis
> "wle" <w...@mailinator.com> writes:
>
>> it said that rear cogs with a prime number of teeth, like 11, 13, 17,
>> etc, 'run smoother and last longer'.
>
>> reason given was that the cog teeth do not regularly 'line up' with
>> the chain ring teeth.
>
> Clearly fallacious, all we need to know is that the lcm of (cog teeth,
> front crankset teeth) is suitably large. It is not essential for the
> lcm to be absolutely as large as possible. In other words, you can
> certainly use composite-number rear cogs as long as the prime factors
> of your front cogs and prime factors of your rear cogs are
> sufficiently different as to form nearly disjoint sets.
>
> For example 42 x 26, the only shared factor is 2, so the lcm is 2x
> away from optimal.
>
> Am I clear?
What does the front chainring have to do with it? You should be looking at
the number of links in the chain, not the number of teeth in the chainring.
As I said before, if you don't want a given tooth to "regularly line up"
with a given chain link, the number of links in the chain and the number of
teeth in the cog wheel should be relatively prime to each other.
Of course, back here in reality, this isn't going to make any
difference. :)
Nick Payne
numbered days...
"wle" <w...@mailinator.com> wrote in message
news:1109880759....@l41g2000cwc.googlegroups.com...
wle
rob van der plas, "bicycle technology", p 150, 1991, 3rd printin 1995,
bicycle books..
i found some other doubtful statements in it too but don;t want to plow
through it again to find them.
wle.
wle
with.
he says the chain ring tooth counts should be prime numbers,
and all the cogs should be prime.
no reference to the chain.
or 'prime with respect to each other'.
as if any real bike ever did this in practice.
what was he thinking?
wle.
carl...@comcast.net
wrote:
Dear WLE,
Presumably a front triple 53x41x37 attached to a seven-cog
rear 11-13-17-19-23-29-31?
For mountains, perhaps 53x37x31 and 13-17-19-23-29-31-37?
I bet that Sheldon could whip them up.
Carl Fogel
Mark Janeba
> Ahah! This explains why the schwinn paramount P-15 had a 31T rear
> cog, and why replacements are impossible to find. I bet Suntour knew
> about the excessive longevity of 31T freewheels and quietly retired
> these freewheels right away, expecting that the existing 31T cogs
> would last forever.
Nah, SunTour knew this so well, (perhaps because they knew 31 was not
only prime but a Mersenne prime), that they never even made a 31T cog -
that was Shimano (early Dura-Ace 5sp IIRC) and perhaps the Italians or
French.
The real secret is to have a cog whose number of teeth is a PERFECT
number [1], like 28 (the only lower perfect number is 6, which is tricky
for cogs, but we're working on the technology). SunTour DID make a 28T
cog, it was very popular. Despite the close relationship between
PERFECT cogs and MERSENNE cogs, some sort of exclusionary principle
didn't allow both to appear in the same product line.
It's a popular misconception that SunTour/Maeda named their "PERFECT"
freewheels because they thought the word sounded good, when it was
really top-secret numerology. There were rumors that their secret
MERSENNE line of freewheels was coming out of prototype testing when the
company went under. It's all in the code - 888 - if you can decode it.
[1] A perfect number equals the sum of its divisors (excluding itself),
e.g. 6=1+2+3 28=1+2+4+7+14.
Diophantus
RonSonic
wrote:
>wle wrote:
>
>> i have been reading some bike books recently that i
>> know have some bogus information, i won;t name them.
>>
>> one thing i wondered about though.
>>
>> it said that rear cogs with a prime number of teeth,
>> like 11, 13, 17, etc,
>> 'run smoother and last longer'.
>
>
>That explains why my 24 and 27 always start skipping way before my 11 is
>worn out.
It's okay, some of us got it.
Ron
wle
last longer.
that was what i meant, why did he say that?
[you of course realize that 31 tooth is totally weird between 29 and
37?]
wle.
Booker C. Bense
In article <1109909653.8...@z14g2000cwz.googlegroups.com>,
_ Well, if the front chainrings were relatively prime, then
you would have no exact gear duplicates. However, in practice
this is meaningless as there will still be gears that are
within a few percentage of each other.
_ Sounds like too much beer and math...
_ Booker C. Bense
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russell...@yahoo.com
Ooh, Ooh, Ooh. I need to expand on my number of prime cogs in the
cassette theory. After considerable analysis and studying of the
standard cassettes produced by Campagnolo and Shimano, I have created
the Prime Squared Theory (PS2). This theory requires a prime number of
prime cogs in a cassette to achieve the greatest rate of wear.
Prime*Prime=~Wear
1. The Shimano cassettes with the most prime cogs are 11-23 9 and 10
speed cassettes with 5 prime cogs each (11,13,17,19,23). The
Campagnolo cassettes with the most prime cogs are 11-23 and 13-29 10
speed cassettes (11,13,17,19,23) and (13,17,19,23,29).
2. Based on various theoretical work, and the principles in my new
Prime Squared Theory (PS2), I conclude the Shimano 9 speed 11-23
cassette will have the greatest number of cogs that will not wear out
in a reasonable time period.
3. To maximize cassette longevity, you should select cassettes with a
prime number of prime cogs. Select only cassettes containing 1, 2, 3,
or 5 prime cogs.
4. As an added corollary, its best to use cassettes with a total prime
number of cogs. 5 or 7 cogs. Then apply the Prime Squared Theory
(PS2).
RonSonic
<bbense+rec.bicycl...@telemark.slac.stanford.edu> wrote:
>-----BEGIN PGP SIGNED MESSAGE-----
>
>In article <1109909653.8...@z14g2000cwz.googlegroups.com>,
>wle <w...@mailinator.com> wrote:
>>actually what he said makes even less sense than what i said to begin
>>with.
>>
>>he says the chain ring tooth counts should be prime numbers,
>> and all the cogs should be prime.
>>
>>no reference to the chain.
>>
>>or 'prime with respect to each other'.
>>
>>as if any real bike ever did this in practice.
>>
>>what was he thinking?
>>
>
>_ Well, if the front chainrings were relatively prime, then
>you would have no exact gear duplicates. However, in practice
>this is meaningless as there will still be gears that are
>within a few percentage of each other.
>
>_ Sounds like too much beer and math...
"Beer and math?"
Don't drink and derive?
Ron
meb
Nah, 29 and 31 are too close together to be of benefit to the rider for
low ratios. Besides you gotta come down the hill. Spread them low
ratios out 11
-13-17-19-23-31-41 with a 63x47x31. I think we'll need to come up with
a new groupo set of ders for this Ultraprime drivetrain. These ratios
probably would make a lot of sense on a tadpole trike.
--
meb
Tom Ace
> >I wonder if Mr. Brandt could come up with the engineering formula to
> >explain this prime cog wearing out theory and the number "3".
>
> He's apparently got better things to do.
>
> Maybe it has something to do with the way that the numeral 3 looks
> like a worn-out sprocket's teeth...
Maybe Jobst is boycotting this thread because of
how many times "cog" was used to mean "gear".
See http://tinyurl.com/3v3ug
Tom Ace
LioNiNoiL_a t_Y a h 0 0_d 0 t_c 0 m
> and all the cogs should be prime.
I seem to recall an extrememly-rare old SunTour Perfect Prime Mover
drivetrain consisting of a 13-17-23-29-37 freewheel, a 53-41 crankset,
and a 113-link chain, reputed to be very durable. The general
unavailability of the special five-prong freewheel remover led to its
early demise, however.
--
"It is the sad fate of simple, elegant logic
that it always stumbles over unforeseen
mathematical contingencies." -- J.W.R. Kern
carl...@comcast.net
Dear Meb,
The benefit of the rider?
This thread is not concerned with riders, who are merely a
bicycle's way of obtaining maintenance and improved parts.
S. Butler
carl...@comcast.net
wrote:
Dear WLE,
To be serious for a moment, he said it because he failed to
see the practical objections to his silly notion.
For example, think of the sculpted teeth on brand-new chain
rings and rear cogs. The visible tooth variety does help
shifting, but no one complains of "roughness" after the
shifting as shorter and higher teeth engage the chain.
And as Werehatrack has pointed out, being afraid of
"matching" front and rear gear teeth in some intricate
pattern through the chain is nonsense, since the chain will
re-engage randomly at both ends as we shift up and down.
A 53-tooth chain ring will last slightly longer than a
52-tooth chain ring, but prime numbers have nothing to do
with it. The larger gear spreads the load out over almost 2%
more teeth, and the chain arrives at a slightly gentler
angle.
But chain rings last so long that no one cares about this
trifling advantage.
Carl Fogel
Zog The Undeniable
> i have been reading some bike books recently that i
> know have some bogus information, i won;t name them.
>
> one thing i wondered about though.
>
> it said that rear cogs with a prime number of teeth,
> like 11, 13, 17, etc,
> 'run smoother and last longer'.
>
> reason given was that the cog
> teeth do not regularly 'line up'
> with the chain ring teeth.
>
> this doesn;t make sense to me.
>
> it might if they were meshed gears like a car transmission.
>
> but the chain separates the 2 gears, so what difference could
> it possibly make?
>
> even if they were the same size, the same 2 teeth would be constantly
> in sync with each other but so what?
>
> they don;t touch, how could it matter?
>
> even if the chain had some even
> multiple number of links,
> say the cog was 15 teeth and the chain had 7*15=105 links,
> it would be in sync with the chain, but again, so what?
I can see the theory. If the # of chainring teeth is directly divisible
by the # sprocket teeth (e.g. a 48T and a 16T), your power stroke will
always affect the same sprocket teeth. Prime-numbered chainrings
eliminate this risk, but of course prime-numbered sprockets don't
becayse they're always the quotient in that particular calculation.
However, this is completely negated by the frequent skipping of the
chain in a derailleur system, and only applies to fixed, singlespeed or
hub geared bikes.
It's also not ideal to have the number of links in a fixed, singlespeed
or hub geared chain exactly divisible by the number of teeth on the
chainring, for the same reason. Unfortunately most track bikes with
normal length chainstays and a 48T chainring (very common as OEM
equipment) will want 96 links of chain with a wide range of useful
sprockets, e.g. 15T-18T.
Every time you remove and refit the chain you alter its location
relative to the sprocket and chainring, so regular chain cleaning is to
be encouraged if your bike has this unfortunate coincidence of teeth
and/or chain.
Leo Lichtman
"Zog The Undeniable" wrote: (clip)your power stroke will always affect the
same sprocket teeth. Prime-numbered chainrings eliminate this risk, (clip)
^^^^^^^^^^^^^
Only in the very lowest ratios on a mountain bike do the chainrings and rear
cogs approach this condition. Normally, the cogs make a full revolution or
more per power stroke.
What you need to do is make the chainrings prime to the number of pedals
<G>.