Warning: wall of text incoming, responding to several different people.
@Precision Underground
Whether or not you have a hard time believing the model, the overall curve shape Al shows matches with both my experimental measurements and my own modeling. The magnitude of movement in the vertical plane is roughly an order of magnitude higher than that in the horizontal, so a simplification that allowed him to cut his model size in half is understandable. It's mostly significant because a symmetry condition meant he couldn't include rifling, which Eichhorst et al. showed to have a small but measurable effect on model accuracy.
As for inclusion of the case, your intuition is mostly incorrect. A small amount of energy does go into expanding the case to fully contact the chamber walls, but not an amount that has a significant impact on overall barrel response. Most researchers neglect the case during modeling for this reason.
Weight towards the end of the barrel only lowers the initial position and angle of the muzzle. That's not a guarantee that the muzzle will be lower during bullet exit, or that even if it does that the POI will be lower. Remember that there are 7 quantities of interest at exit (3 velocity components, pitch, yaw, pitch rate, and yaw rate) and the way those interact to produce a trajectory is not immediately intuitive.
@Secant
I started to type up a response to your question earlier, but decided I needed to give it more thought. I will freely state up front that my explanations at this point are nothing more than informed conjecture. First, the further I go in my research, the more I agree with the point Dthomas has been trying to make, that good reloading practices combined with quality components means that nearly any load will shoot well. If we accept that as true, a likely reason the loads end up similar between rifles is that they simply offer good velocity at a safe pressure.
Another possibility is that it has some relation to the % of case fill. Minnicino and Ritter from the Army Research Laboratory have shown that ullage in the case can be responsible for bullet tilt during firing, leading to asymmetric engraving and subsequent balloting. Maximizing case fill while maintaining safe pressures would therefore benefit accuracy regardless of barrel geometry.
I also have some ideas kicking around regarding the degree to which high frequency behavior is driven solely by the primer impulse, but I haven't quite got that reasoned through yet. That said, I think it's actually largely independent of geometry. I'll have to do some more work before drawing firmer conclusions.
@NamibHunter
Thanks for the link! That was an interesting read. I certainly fall into the category he talked about, someone just using experimental data to validate a model rather than using it as the main focus. I would say the obvious downside to his method is that relying on PC in that way only works at a given distance, something he repeatedly points out. That said, I think his methods were sound and he proved his point.
I will be doing more test firing, but I doubt I will ever do a full 20 shot string. Here are two plots of the same three test firings taken at a point 6 inches from the muzzle. I'm still having a few issues with the firing mechanism causing overall drift in the data (data series 3 gaining amplitude at the beginning), but you can see that even the higher frequency data is relatively consistent between shots. In this case bullet exit occurs at about 1.37ms.
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