Also, I believe the likelihood of vibrations to be exponential as speed increases. Surely increasing the speed from 80 to 100 would have a greater likelihood of creating problems than increasing the speed from 40 to 50 would, even though they are both a 25% increase. Or you could frame it as miles per hour and not a percentage. I'd expect a greater chance of problems in the 80 to 100 scenario than I would in a 40 to 60 scenario, both increases of 20 mph. I feel like I know in my heart that vibrations as a result of centripetal/centrifugal force increase exponentially as speed increases but wanted to see if I could figure it out with math. I'm way too dumb to know how to actually do this math so I used an online calculator. I used 3" as the diameter, this is an educated guess as the majority of the diameter of the drive shaft in question would be 2" but the ends, the yokes, which account for around half the net weight of the shaft are closer to 3.5" diameter. So I averaged it and called it 3". I then ran the formula based on 1 ounce at 2,800 rpm and again at 2,940 rpm, 5% faster. The results were 45.72 Newtons of force at 2,800 rpm and 50.6 Newtons at 2,940. This is a 10.2% increase in centripetal force. So the increase in force, percentage wise, is more than double the increase in speed. Interestingly though if I halve the numbers and do the 5% speed increase calculations I still come up with about a 10.2% increase in force. This doesn't support my exponential increase theory. However, the force does appear to increase at a disproportionate ratio to rpm. I don't think it is as simple as 5% faster only means 5% more vibrations. Also, lets remember that the vibrations are always there, it is a matter of amplitude and intensity. The crossover point at which the intensity and amplitude become a problem is both highly subjective and highly dependent on a ton of other factors (luck). There are certainly lots of lengthy threads dedicated to "vibrations after re-gear". It obviously opens up a can of worms. And one person's anecdote of "I run X and Y" with no problems doesn't nullify another persons "I run X and Y and I have a horrible vibration".
I'll double down on saying that there is a ton of nuance with these things and there is not a one size fits all answer to a question like "what gear ratio should I be running?". Subjectivity plays a huge role too.
Someone smarter than me feel free to figure out the math pertaining to rates of increased speed and how they relate to rates of increased vibrations. Here's the force calculator I used.
http://hyperphysics.phy-astr.gsu.ed...Centripetal force = mass x velocity2 / radius
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