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What are your thoughts on the optimum barrel time paper? That makes the most sense in my head. In a nutshell it says it’s more about disturbances in the bore than actual deflection of the barrel. This lines up with my doubt that a barrel could deflect fast enough for increments of .2gr of powder or .02 seating depth to affect POI the way I know an OCW can. The stress waves he describes as bouncing from bore to action multiple times during dwell time make perfect sense. This is why some say harmonics don’t matter. I think they are measuring the wrong thing.
Overall, I think the paper is interesting. I also think it's worth stating that the scientific method is really based around trying to disprove a theory - not looking for ways to prove it. That is usually where I'm at when I'm reading these types of papers or thoughts/suppositions/etc. on the interwebs. So my questioning/thoughts are not based around me trying to be a dick or trying to pretend I'm the smartest dude in the room. With that in mind, here are a few thoughts:
The typical complaint with "observations" that are used by reloaders (the author included), is that two 5-round groups is considered A LOT. Most reloaders are only using 3 data points to draw conclusions, which is nothing statistically, and guys that think they are serious will use 5-rounds. You'll basically never see anybody determining charge weight based on 30, or 40, or 50+ round samples per weight and then setting seating depth with 30, or 40, or 50+ round samples. Let alone going back to adjust seating depth on the "bad loads", and ultimately comparing the bad to the good to see a true difference. I get why guys don't, but it also calls into question the validity of the "good" loads since there really isn't a base line to compare against.
On the other end of the spectrum, the majority of 'scientific' papers that are moved around in the reloading circles seem to be awful light on modeling as well as providing the differentials that back it up (not to mention the observational data that I complained about above). Don't take this as me trying to shit on anyone trying to figure anything out. I just tend to be of the mindset that you need a robust data set in terms of observations, which are back-up by the mechanics, and are consistently and accurately predicted by the modeling program that is being employed if you are looking to truly prove anything. I also get that we can't let perfect be the enemy of great, but I don't think the precision rifle community is at a middle ground yet.
Now specific to the paper, the author's introduction seems to mimic my posts regarding the significant variance in "I", and yet there are 'standardized' loads that are "tuned" for these significantly different geometries. As I've stated multiple times, the variations in "I" are too large to just had wave away and pretend like they don't matter in the context of the "large scale" deflections (think of the slow motion footage from a skinny AK or AR that everyone has seen). And if we say they do matter (which I do say that), then you can't square the circle as to why a 20" M24 contour can have the exact same load (or within 0.2 grains or so) as a 26" #5 or a 24" medium palma, etc. Now admittedly, it's not like I own every length of every contour in every caliber and every chambering - I'm basing much of this off of the input of guys that share their special recipes, which happen to match or be extremely similar to others (and again, this circles back the my complaints regarding observations above).
From the 100,000-ft view and for the purpose of this discussion, it might be worth it to show the standard stress-strain curve. Stress-strain curves are different for different types of materials.
The initial straight line portion (bracketed by 'Hooke's Law" in the image) is the elastic portion and the modulus of elasticity that I keep referencing (aka Youngs Modulus) is described by the rise divided by the run of that initial straight line section. For context Chrome moly 4140 may have a young's modulus of about 205 GPA, 416 SS will be about 200 GPA, copper will be about 117 GPA, and lead is about 13.8 GPA.
While looking at the rate of change of muzzle deformation is interesting, I think we need to put it in context and also look at the actual total changes. As an aside, I think stepping back can be helpful for majority of reloaders or armchair scientists before they try to extrapolate concepts that they read about - especially if they don't have the background to fully understand the concepts. The total deformation associated with a larger contour and/or smaller bore would be less and therefore easier to tune (which is experienced by most), but obviously the heavier and/or smaller calibers are typically far easier to shoot. So what is noise and what is the actual players that matter?
Here are a few questions, and maybe I should think about them a little longer, but off the cuff:
- Looking at total deformation, the difference in contours matters (obviously), and there is still a large variation of contours to contend with. Moreover, we are see many more short(er) barrel rifles today than we were seeing in 10 years ago and definitely 20 years ago. Can we definitely show that the loads for a 26" M24 (for example) cannot work for a 20" or 16" M24?
- The difference in muzzle diameter would correspond to differences in total deformation at the muzzle (seems the Author concentrates on the effects at the muzzle). Can we consistently show that a load developed for a bare muzzle will have different results once the muzzle gets threaded?
- What is the dimensional tolerances of the barrel blanks that we receive, and what is the tolerance in machining that is kicked out by factories and/or smiths (both in reaming the chamber and cutting/crowning the muzzle)? I would be interested to see if/how the stacking tolerances just in the manufacturing process would/could impact load development (I'm not holding my breath for anyone to do this).
- The data set in the paper is small and does not prove or disprove anything from a statistical standpoint.
- Setting aside the small sample size (if that's even possible), the data set provided in the back portion of the paper is quite bad. Look at Figure 5, and then look at Tables 1, 2, & 3. The optimal barrel time for his 27" configuration is 1.240mS. The 1.277mS barrel time in Table 2 was the second best group. The Author does not provide the velocities of each projectile in each group, which would be far more valuable, but the 1.277mS time is right on the edge, and a slight decrease in velocity (increase in barrel time) would be a bad place to be if we go along with the paper as written. Also, look at the group sizes and barrel times in Table 2 and compare to Table 3 - basically no consistency at all.
- For longer barrels, more time would elapse between the points in which the muzzle experienced the stress wave (and associated strain). For shorter barrels, their would be less time elapsing between experiencing the stress wave (and associated strain). So although a short barrel may have more OBTs, there would also have to be a corresponding larger number of "bad" times. Unless I'm thinking of this incorrectly, the shorter barrels would have to be more finicky since a slight variation in barrel time (whether from varying charge weight, seating depth, neck tension, etc.) could result in the bullet exiting during max barrel strain vs min barrel strain. That doesn't seem to match reality for a lot of guys that prefer the shorter barrels.
With all that said, I fully recognize how much time, money, and effort it would take to fully evaluate IF harmonics are having an impact relative to group size, velocity variances, bullet deformation, etc. (from a practical aspect) and then determining to what degree. A single barrel in a single caliber at a set length isn't going to be enough. I think it's great whenever anyone takes any amount of time to try and evaluate this kind of stuff. I also think it's appropriate to be skeptical.
Overall, I think the issue is being solved much faster on the manufacturing side compared to the understanding that is coming out of the scientific side. Not to mention, generally precision rifle shooters are better fundamentally and more informed now more than ever. As I said before, if we assume that harmonics are a significant player, it is still only relative to the variances in the load that is being developed. I think this dovetails directly into what the OP has stated/questioned.
Sorry for the long winded reply, but you literally asked for it, haha.