Changing gearing -- front vs rear

Kabara, Richard M. richard.kabara at
Mon Jun 23 14:54:27 PDT 2008

Architeuthis dux, whooooh, we are on two different wavelengths here, I was
talking about wear...looks like you are using the sprocket/pin counts to
find the source of the vibration??? That's a far-out theory...

Two different (but related) issues:
1) Wear: the "numerology" wear effect is real in *gears*, but as I stated,
it is unlikely the "numerology" is affecting Jim's chain and sprocket wear
issue, even if he had a 90 link chain, which obviously he doesn't.

2) Vibration:
The chain 'hop' I described COULD be the source of the vibration at 41 mph,
since the vibration happens in any gear at that 41 mph. We can do the math
to get the hop frequency (14X the c/s sprocket rotation speed) then put a
bunch of accelerometers and an oscilloscope on Jim's bike to test it out...

I don't have the actual rear tire diameter here, so let's estimate 25"

41 mile/hour  X  63360 in/mile  X   1/3600 hour/second  X  1/(PI(25)) rev/in
=  9.2 rev/s

So the rear wheel rotates 9.2 rev/s at 41 mph (wow, that sounds high? Is my
math correct?)

The c/s sprocket rotates 44/14  X  9.2 rev/s  =  28.9 rev/s  = 28.9 Hz for a
1E (once per rev) excitation

Since the chain hop happens 14 times per c/s sprocket rotation (14E), the
frequency would be ~400 Hz. Well, that sounds way too high for Jim's
estimate of 20 Hz, so it's probably not his vibration excitation  :-(

As with many vib issues, there are many potential excitation sources, when
an excitation frequency matches up with a resonant mode of a component like
the engine cases, frame, metal panel, etc it will result in a vibration that
Jim can hear and feel at 41 mph. 

When he switched back to a 15 tooth, the vibration disappeared. The rear
wheel is still going 41 mph, but the counter/shaft is turning slightly


Architeuthis dux wrote:
Chain/sprocket numerology is a hotly debated topic on one of my other 
lists.. I'm a skeptic, but lets run some numbers...

F:14  = 2                 * 7
R:44  = 2 * 2                 * 11
C:108 = 2 * 2 * 3 * 3 * 3

Same F/C every 7 * 2 * 3 * 3 * 3 = 378
among these is theoretically the 15:44 with a 108-link chain, although I 
think other factors like maintenance and cleanliness would almost always 
outweigh this numerology silliness unless you were to pick some sort of 
really pathologically terrible combination.)

Jim, what was the approximate frequency of your resonance?  And what 
gear were you in?


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