I think we can dispute the effects of Rg & differentials on pin carry but there is no
dispute as to the physics behind it all.
Rg alone does not give us enough information on a ball's ability to rev up. Neither does differential. They are directly dependent on one another only if we know the MASS of the imbalance.
Of the 2, Rg has a significant influence because it determines the DISTANCE of the core's imbalance from
its axis of rotation. The simplest formula that describes this relationship is:
I (moment of inertia)= mr^2 . where m = mass of the imbalance r= distance of the imbalance from its axis of rotation. This is just one of many formulas that determines
an object's moment of inertia----the most important factor in determining a ball's
resistance to "rev-up". These formulas vary, depending on the shape of the object
(i.e., sphere, cylinder, fixed rod, etc.) in question. The important thing to notice is that in the formula the quantity "r" is squared. This means that any change in a core's center of mass is not linear. This is significant because a change of say, 2.52 in a ball's Rg to
2.47 is not .005 but is .250 (two hundred and fifty thousandths--a full 1/4 inch).
Don't let core design confuse you as to its effects when it come to determining
a ball's moment of inertia. In the end, it's the mass (weight) of the imbalance
and its distance from the PSA (Rg) that count in determining a ball's ability (or inability) to "rev up".
Now when it comes to a ball's ability to flare, this is where differential
does play a big role, because it measures a ball's "wobble" (precession) about the
axis of rotation. Here, an asymmetric core that has asymmetry about all 3 axes
PLUS having a large intermediate differential, will maximize flare , depending on how it's drilled.
So, what does all of this actually signify? It signifies that if you take 2 similar balls
and for example, drill one with 2.52 Rg and the other with 2.47 Rg, The ball with the lower Rg WILL noticeably rev-up much quicker than the one drilled at 2.52 Rg.
On the other hand, doing the same with 2 dissimilar balls will not necessarily
produce the same moment of inertia (again, the most important quantity in determining a ball's ability to rev-up) even though they might both have the same Rg. The reason for this is that we simply don't know the mass of the imbalanced force . Differential alone doesn't tell us this quantity either.
For these reasons, I was never very fond of ball manufacturers' use of "Rg" alone, in trying to describe a ball's "rev capabilities". Some balls with an Rg of 2.50 will
rev faster (or slower) than another ball with 2.50 Rg but with a different mass that the first ball.
Also, when it comes to bowling ball dynamics, there are situations where indeed,
small changes can add up to big differences in performance. One of these quantities
is a ball's pocket (entry) angle. A 2-3 degree difference in entry angle looks insignificant on paper, but is anything but when it comes to its effects on pinfall.
Once again, it's the "physics" behind these numbers that will always, without fail,
determine its effects on ball motion/pin carry/ etc.
On the contrary, there is an article in the latest BJ about the effect of lane topography
on ball motion and performance. Here I would argue that the amount of lane tilt
(in any direction) would have at the very very best, a negligible effect on ball performance. Here, I am restricting my disagreement on TILT alone. This disagreement applies only to situations where the tilt is still within USBC tolerances and with balls thrown at normal velocities (and not balls rolled down ramps, etc.).
At lane tilts of .040 (maximum USBC tolerances), the amount of (ball) acceleration
(or deceleration) would be very very miniscule and would have no overall effect.
If the tilts were extreme, then there would be an effect, but these tilts would have to be MUCH MORE than .040 to even begin to have any effect on ball motion down the lane. The angle (slope) of a .040 incline is only .191 degrees ( less than 2 tenths of a degree). The acceleration/ deceleration of a ball would be so tiny as to be insignificant, especially when considering how little time the ball spends traveling from release to the pins. It would take a ball rolling DOWN such a ramp approximately 18 seconds, at which time it would have accelerated only 0.387 mph in the direction of the slope. Quite insignificant.
So the upshoot of all of this is that numbers can have a significant effect depending on
what it is you are attempting to measure. Sometimes it just takes a small quantity to make a measureable difference. Other times, it does not.
