Sorry that I haven't been able to make myself clear Steve:
I would like to see a SUPERPOSED images because it is hard to compare things when they are isolated from each other.
It SEEMS to be that the "Artillery hold" pushes the pellet exit about half a ms later, but without superposing the plots its hard to see.
It also SEEMS that a few tenths of ms error on the "walk back" of the pellet exit time to the real exit time point could create problems in our understanding. If you look at the "Firm Hold" plot of TMV (Transverse Muzzle Velocity), the plot seems to be going from an area of relatively high TMV towards an area of relative calm, whereas if we look at the "Artillery Hold" plot there is a strong re-bound where after a few tenths of a ms, the velocity goes south again, strongly. In the chart you show just above, the TMV is starting from a bad condition and getting substantially worse just after, so that a delay in the pellet exit would have have a rather large effect.
Remember that what I am trying to get at here is how "sensitive" the POI is to SMALL CHANGES of MV, and for that, we need to look at points where the TMV is close to zero.
It doesn't really matter what the muzzle's position is, what matters is what is its velocity (and in real life, we should be looking at both planes: XZ and XY). I would maintain that the smooth curve you show for the displacement is a mathematical figment. IT CANNOT be that smooth, so reverting to the RELIABILITY OF THE BASIC QUANTITY MEASURED principle, let's look at the velocities, and try to figure out what needs to be done to achieve a pellet exit at the best of times: when the TMV is as close to zero as possible.
For numerology's sake (and assuming I didn't make a mistake):
For a spring gun having an MV of 890 ± 9 fps (good tune, single digit SD), the max MV would be about 917 fps, and the min would be 863 fps.
Under these conditions, assuming a 16" barrel, linear acceleration and zero for V0 (all big assumptions), the shortest Barrel Time (BT) would be 2.91 ms, the longest BT would be 3.09 ms, or about 1/5th of a ms difference.
IF the MV is the same for both holds (somewhat questionable assumption), AND the plots are correct in the pellet exit time, then the gun should be slightly more accurate with a firm hold than with an artillery hold.
And let me remind you that experience with springers tells me that the best point of support is NOT the CoG but forward of that, sometimes considerably forward of that.
Of course it could be that the system is, up to a point, self correcting and when the MV is lower, the TMV is also lower, but without some "sample" and average + sSd curves, it is hard to think of all the possibilities.
As a gunsmith, I have always preferred to go in steps:
1.- Find the best pellet
2,- Find the best lube (Sometimes, repeat #1 to settle the matter)
3.- Find the most accurate velocity for the above defined projectile
4.- Tune the vibrations to that.
It is a long and hard process, but in the end you are usually rewarded by good performances. Few shooters understand this anyway, LOL!
Again, sorry for not making myself clear, and thanks for the effort and hard work.
HM