Wow, Larry, true to form as always. You managed to not directly answer a single question in your initial replies, and to do so with
dripping condescension. You were right not to expand on your RPM Theory and go back and
crib more from your references. For you to expand on
errors you already didn't understand would have lead to you making more mistakes I would have called you on. Unlike you, who have repeatedly suggested I was making errors or lacked depth in my comprehension of ballistics without ever citing examples, I have always described anything I objected to and why. All you appear to be capable of is casting
vague aspersions and condescension without substance.
Let's not forget to compare and contrast to your most recent posts the
gibberish you started out with posting in your (half-dozen) pastes of your RPM Theory:
“the bullet is unbalanced or becomes unbalance due to obturation in the bore during acceleration. The unbalanced bullet is forced to conform while in the barrel and its center of mass is revolving around it's geometric center. When the bullet is free of the barrel's constraint, it will move in the direction that its mass center had at the point of release. After exiting the muzzle, the geometric center will begin to revolve about the center of mass and it will depart at an angle to the bore (line of departure). At 54,000 RPM to 250,000 RPM, depending on velocity and twist, the centrifugal force can be tremendous. It will result in an outward or radial acceleration from the intended flight path (line of departure) and will try to get the bullet to rotate in a constantly growing helix.”
The above
bunk is what I have a problem with, not the work of professional ballisticians -- your improvisation, Larry. I have no problem with the italicized
cribbed part, and never have. If you are attributing all of the above to Rinker, then yeah Larry, Rinker is spouting bunkum (truly awful aphysical wording at the very least) and you couldn't tell the difference and quoted it repeatedly. Please do provide a page and paragraph citation, or post a copy -- I
really doubt that is a verbatim quote, as no professional ballistician with a rudimentary understanding of physics would write that way (and no editor would allow the typos and redundancies). 'Fess up as to what parts are your own, or post a copy of the original text in full from the book.
Yeah, I like my own professional references, Larry. I'm pretty sure Rinker would be a great big step down from re-deriving analyses from old AGARDOGRAPHs. Maybe
your choice of references is the source of the problem, here. On the other hand, I would hate to impugn Rinker when I suspect it's your
lack of comprehension that's at fault.
The only thing you made obvious with your initial reply is that while you've stated the bullet is flying in a helical trajectory due to centrifugal force (an impossibility), you have
absolutely no idea as to the frequency of the trajectory, it's size, or how you would go about predicting them.
Kind of what one would expect with a fictional helix resulting from a nonsense theory, right? :D Your answer even sounds like you are wondering if it's much of a helix at all. Which, as you probably guessed, is
exactly what I was going to tell you how to demonstrate for yourself by test --
that there is no helical trajectory causing dispersion for all our high velocity cast bullet flights. The shot dispersion in Bullshop's and my own tests is entirely attributable to other factors. And in fact, the relevant (correct) portion of your theory that you
cribbed doesn't result in a helical motion of the bullet post separation from the crown but a simple constant velocity crossrange drift (velocity in the plane normal to the bore axis).
You keep talking about 200 yards, but you are skirting the fact that all of Bullshop and my testing has been at 100 yards or less, and yet you have continually insisted that our results evidence the results of your theory. You can't have it both ways, Larry. Either Bullshop's good results at 100 yards and my constant MOA vs. range call into question your theory, or your theory says nothing about our results.
You cannot have a helical trajectory of a free-flying bullet without aerodynamic forces and bullet yaw, which you have never made any mention of, and occur irrespective of any RPM threshold. Conversely, the simple crossrange drift that results from an offset between the CG and geometric center at separation from the muzzle also occurs regardless of RPM, but
has no possibility of resulting in a helical trajectory. While it is true that you can have strength of material related failures as a function of
all the stresses imposed upon a bullet, and that these are likely to result in bullet imbalance, these are not exclusively related to RPM, and will be a STRONG function of caliber with rpm related limits
decreasing with
increasing caliber, the opposite of your predictions. Strength of material related failures can occur because of not only RPM, but too much angular acceleration, skid, "set-back", gas cutting, bore roughness, etc. "
Obturation," or the bullet sealing the bore against gases, while solely mentioned in your theory in the context of a displacement between the CG and geometric center, in and of itself has nothing inherent to do with bullet imbalance and RPM. Aerodynamic forces due to rotation about other than the geometric axis of symmetry will cause increasing dispersion with range (as will gravity in combination with muzzle velocity SDs and wind), but has nothing to do with "centrifugal forces" or an RPM threshold (other than as related to bullet damage, which really is a "
NO, DUH" isn't it). Lateral dispersion down range due to the misalignment of CG and the geometric center and the event of separation at the crown
do not result in the creation of a radial force -- they result in the release of the radial force and the departure of the round from the bore with a tangential component of velocity. Again, any "helical" downrange trajectory of significance has to be due to aerodynamic forces acting on lower frequency nutation of the bullet nose. Larry, you have conflated enough different phenomenon and are just a tiny bit right and a
lot wrong in enough different directions at once that I don't see how you think you have
any passing understanding of this subject matter, much less
judge yourself competent to remark on the qualifications of others. Are you under the impression that our dialogue so far has been of benefit to me, or your
ignorant condescension other than an
annoyance? It's been pretty clear to me, at least, that you've just been posturing for the benefit of others rather than engaging in any substantive dialogue on the points. You've been
rude and condescending to one member after the other on this thread... frankly,
I'm not seeing much redeeming virtue in your having a keyboard at all.
The more
uncomprehending pronouncements on statistics and ballistics of yours I read, Larry, as contrasted to the
obviously cribbed passages (so strongly contrasting to your own ctrl-v'ed theory) the more I become convinced that this whole (three year?)
debacle of your RPM theory is entirely a result of your
lack of reading comprehension. I think all of this could have been avoided if you simply had stuck to what others had written, distinguished between your own efforts and that of others, and attributed the work of the professionals to the professionals instead of
cribbing some and improvising the rest on your own in your CTRL-V'ed "theory". Throw away all the parts of your copied
franken-theory that are original but wrong (the helical trajectory absent any consideration of aerodynamic forces, the centrifugal force post bore departure, the obturation (well, not wrong but unnecessary)), and keep the part that is completely unoriginal but right (that a bullet will rotate about the geometric center while in the bore, and that the center of gravity will consequently depart the crown with a tangential velocity) and you will be back to a semblance of reality pertinent to what Bullshop and I tested (and incidentally, without a Larry RPM Theory to paste).
Despite your suggestion and your own contrary example, I don't condescendingly assume that anyone is uneducated, or that fools (even principally) reside among the uneducated. You have caused me to have doubts based on what you've written, however, and you have stated doubts about me. I propose we do a little exercise to test our respective reading comprehension of what you yourself have copied:
Tell us according to the copied (correct) part of your theory what the deviation on target of a 40 grain .224 diameter bullet is fired from a 1/14 twist rifle at 100 yards, as resulting from a .003 offset in the mould halves (resulting in the nose being that much longer and the base flat). Let's provide the answer in Minutes of Angle, and use a nominal density of lead of .4 lbs/inch^3. This scenario should sound relevant to you in the context of the recent tests.
I'm wondering if you'll even be able to start, even though the part of your theory that you copied which is correct is the part that tells you how to do it! I did the calculation from first principles, Larry -- but you go ahead and do it open book. I'll show all of my work, Larry -- please do show all of yours. Maybe one of Rinker's neat ballistic's equations will give you something to "play with."
I'll post the answer here tomorrow. I'll predict you won't even try... but will just offer more of the same condescension and personal attack. Come on Larry, put up or shut up. You want to pretend that you know anything about external ballistics as compared to incorrectly cribbing from a reference? Then demonstrate you know something about the trivial basics like conservation of momentum according to words you've been presenting in your own theory for years. When you get the answer maybe you'll be so thoughtful as to explain what it means, and why it's necessary for us to have a Larry RPM Theory in light of it?
As far as your other points, Larry:
- you don't understand basic statistics well enough to argue them yourself (instead you copy what you don't understand, misapply it, and then say -- well, all the experts can't be wrong! Which is exactly the point -- they aren't Larry, you are).
- you don't understand that angular acceleration increases with increasing radius and believed exactly the opposite until I corrected you.
- you don't understand that a bullets trajectory may be modelled as an equation of a point in space (I thought the helix thing as a choice of trajectory as explained as resulting from RPMs & "centrifugal force" in your theory is absurdly aphysical, but it was your theory, so please don't stick me with that);
- or that there is no role of "centrifugal force" in free flight "causing a bullet to fly in an ever expanding helix" (ever heard of principal axes, you know, the ones that by definition pass through the center of gravity?);
- easily the most offensive of your many peccadilloes: you insist on making up your own definition of "threshold" when we all have dictionaries.
After all of the above, you are going to try to paint
me as the ignorant one here? :D
Larry, I am degreed in aerospace engineering and earned a doctorate, and while I did some work for the university to pay my way, and some NASA centers over the years, I spent most of my time in industry. But no matter where I worked or how I earned a living, I have always had the honesty to concede the limitations of my knowledge when confronted by reality. I would never be caught dead going around and inventing new meanings for perfectly good words like "threshold" to try to obscure the fact that my pet predictions had failed time and again. :violin:
I think there are some pertinent things I said in the prior post that may help some of the other folks here with some of the redundant points you've just tried to make that were previously answered.
Here's one:
I'm sure there are a bunch of folks here who will get the point of the above, Larry, and realize on their own that there
isn't a one-size-fits all fixed sample size for every situation, every population, and every statistical inference. How many data points are required to correctly make a relative determination about the size of the means of two different populations depends: 1) on the proximity of the means; 2) the variance of the populations; and 3) the desired statistical confidence. When you start talking about linear or multiple linear regression, the number of model parameters (degrees of freedom) and geometric distribution of the points in the independent variable space also become important. It may be I am talking about something you don't comprehend, Larry, but don't you think that means you might want to listen to what I am explaining to you a little more closely?
By the way, to the gentleman who posted earlier about using standard deviations instead of group size:
I completely agree with his point. If you make the usual random normal distribution assumption, group sizes will statistically grow with increasing sample size ad infinitum... whereas estimates on the standard deviation, x and y, will converge about their true values according to the central limit theorem, and you can estimate the confidence and error of the estimates. They will also show evidence of the effects of muzzle velocity variance and wind dispersion which "group size" will combine (and this is a potentially confounding factor for falsifying your "RPM Theory" Larry as range increases).
The reason folks do it the way they do is that group size is easy to measure with a ruler, whereas calculating the standard deviation on x and y requires locating each hole, calculating means on x and y, and then calculating the respective standard deviations. In my experimental design for the hornet test I ran it with individual targets for each shot for each variant, with the order of the shots distributed to average out fouling and heating effects between the variants. Consequently I had to measure the individual shots and compute SDs, group sizes, etc.
DrB