The “balance factor” is at best a compromise, and partially suppresses vibration at some RPM and power/vacuum levels.
Classifying the connecting rod’s upper and lower halves as “reciprocating” or “rotating” is not completely accurate. The rod’s pin eye does reciprocate, but the rod’s absolute upper end (including the material closing the top of the eye), and the rod beam between the pin eye and the crankshaft’s rod journal follow different and more complex paths. The rod’s big end does rotate, but only the imaginary line marking the contact with the crankshaft’s rod journal is “pure” rotation, the rod’s big end actually oscillates as well.
Mathematical-based formula using only conventional factors will never predict accurately how well a given engine will run, even at a given RPM, because the dynamic forces aren’t limited to reciprocating vs. rotating weight. The forces acting on the rod + crank-pin (mass inertia) are not only the reciprocating weight (as listed above), but also the forces present in the cylinder and combustion chamber above the piston.
No formula is “correct”, some just come closer than others, by the “empirical” method - they’ve been tried + adjusted by experiment.
The bottom line is that the physics and mathematics involved in how the engine operates are far too complex to make a formula-based balance factor any more than a reasonable compromise.
Some people still think that the balance factor is something other than a way of recording what you found to work by trial and error. All I have to say to them is let’s put your method to the test. Here’s two sets of data and you tell me what balance factors will work and I will tell you how far off you are using my crank balancing software (which agrees with real life experience in these two cases):
piston assembly 122 grams
wrist pin 24 gm
con rod 133 gm
weight at the small end of con rod that statically balances the crank: 52 gm
top RPM 10,200
test case #2
piston assembly 66 grams
wrist pin 10 gm
con rod 85 gm
weight at the small end of con rod that statically balances the crank: 23 gm
top RPM 8,400
Sean responded and gave me a balance factor of .187 for the first one and .143 for the second one.
Look at this graphic which shows these two test cases on the left and what their balance would look like on the right if they were balanced using the balance factor. I can tell you from riding my bikes that what the graph says and what I experience are nearly exactly the same. The AX100 graph has 100% balance (where it crosses the zero line) a bit higher than I prefer now but that was back when I had the program set to balance it that way. At top RPM anything within 50 of the zero line is not felt hardly at all on a small engine. I think the main flaw using a balance factor is that there is no way to scale it for top RPM. I’m sure I could figure that all out but I’m not going to because I’ve already expended a lot of brain power getting this calculator to work just right. Any way the results here speak for themselves. Using balance factor is as hit and miss as throwing a dart trying to hit the bullseye. It’s just no good.
To read about my crank balancing spreadsheet go to www.dragonfly75.com/moto/crankbalance.html