prime number cogs?

wle said:

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/

On 3 Mar 2005 12:12:39 -0800, "wle" <[email hidden]> may have
said:

[snip]

Quoted message said:

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.

Quoted message said:

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.

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On Thu, 03 Mar 2005 12:18:44 -0800, Diablo Scott

may have said:

wle said:

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.

--
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.

well, yes, if it were true, i am saying it can;t be true.

wle.

Diablo Scott said:

wle said:

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

Quoted message said:

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".

wle said:

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

Quoted message said:

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

Quoted message said:

Quoted message said:

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

Greg Berchin said:

Quoted message said:

Quoted message said:

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

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.

--
My bike blog:
http://diabloscott.blogspot.com/

Diablo Scott said:

Quoted message said:

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

Quoted message said:

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

In article <[email hidden]>,

wle said:

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.
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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%.

wle said:

i have been reading some bike books recently that i
know have some bogus information, i won;t name them.

Quoted message said:

one thing i wondered about though.

Quoted message said:

it said that rear cogs with a prime number of teeth, like 11, 13, 17,
etc, 'run smoother and last longer'.

Quoted message said:

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

may have said:

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...

--
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.

Diablo Scott said:

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 ...

- Don Gillies
San Diego, CA

Donald Gillies said:

wle said:

it said that rear cogs with a prime number of teeth, like 11, 13, 17,
etc, 'run smoother and last longer'.

Quoted message said:

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. 🙂

--
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

And there was the mathematician who would only sleep with his wife on prime
numbered days...

"wle" <[email hidden]> wrote in message
news:[email hidden]...

Quoted message said:

it said that rear cogs with a prime number of teeth,
like 11, 13, 17, etc,
'run smoother and last longer'.

ok.

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.

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?

wle.