prime number cogs?

Donald Gillies said:

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

On 3 Mar 2005 20:14:13 -0800, "wle" <[email hidden]>

Quoted message said:

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.

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

On Thu, 03 Mar 2005 12:18:44 -0800, Diablo Scott <[email hidden]>

Quoted message 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.

It's okay, some of us got it.

Ron

but i mean, he still doesn;t say why those gears would run smoother and
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.

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

In article <[email hidden]>,

wle said:

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...

_ Booker C. Bense

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Booker C. Bense said:

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

In article <[email hidden]>,

wle said:

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

[email hidden said:

"]On 3 Mar 2005 20:14:13 -0800, "wle" <[email hidden]>

Quoted message said:

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.

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

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.

Werehatrack said:

Quoted message 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...

Maybe Jobst is boycotting this thread because of
how many times "cog" was used to mean "gear".
See http://tinyurl.com/3v3ug

Tom Ace

Quoted message said:

the chain ring tooth counts should be prime numbers,
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

meb said:

Quoted message said:

On 3 Mar 2005 20:14:13 -0800, "wle" <[email hidden]>

Quoted message said:

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.

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

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.

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

On 4 Mar 2005 06:31:41 -0800, "wle" <[email hidden]>

Quoted message said:

but i mean, he still doesn;t say why those gears would run smoother and
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.

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

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'.

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.

"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>.