Boolit Going to Sleep?

[recoil junky]

I understand the "air bearing" is as close to being "without friction" as it is possible to get here on earth.

I understand gyroscopic stability (gs) even on something as small as a bullet.

I thought we went into the "rpm's thing" when that video came out of  all the bullets hitting that steel plate, where you could see the spin of the bullet but maybe I misunderstood. I've been known to do that from time to time.

What I'm getting at by saying "rpm's" is from watching a driveshaft being balanced. An imperfect driveshaft (as with cast bullets, no two of which are the same) has certain points in the rpm range before it's balanced where it "acts" balanced. In other words it doesn't vibrate at all. So, (I think) a bullet is the same way. No one at the bullet factory balances bullets as they drop off the little belt and into boxes, the same as Nels and I (and YOU) don't balance our cast bullets. We sort through them, weigh a few and the ones that look "bad" or are "too light" are thrown back into the pot and made into "good" bullets.

It's those "imperfections" we are trying to balance out by changing the velocity, hence the rpm's.

RJ

[Nelsdou]

These are all Lyman #2 alloy I bought on one of those $13/box shipping specials that makes my postman fond of me :grin:.

I dunno. I've never had a bullet get better going down range, but something happened when I switched from 100 to the 220 yd gong. BTW there was hardly a breeze stirring while shooting. A rare day.

When I get poor results at 100 yds, it's usually vertical spreading or horizontal spreading with a consistency to it and I have an idea what is going on. But when I get holes in the paper in all four quadrants around the POA my conclusion is that there is a variable "out of control" that has to be fixed before going any further. In this case since I was already pushing pressure and velocity (actually acceleration) I figured the bullet was getting distorted and out of balance leaving the muzzle, so I was resigned to drop the charge some, even before I decided to "unload" at the gong.

I've got 20 ready to go at the same charge and plan to load more at a slightly reduced charge. Angular velocity difference should be minimal.  We'll see what happens.

Nels

[Jamie.270]

Using Pauls analogy of the top, consider this a moment.  I have seen and maybe some of you have too, a top that isn't launched exactly on it's axis.  As a result it wobbles for a second before it's momentum(s) are stabilized or are overcome by gyroscopic effect, and the top stops wobbling and stabilizes on it's axis.
Now, as to what may destabilize the bullet slightly as it leaves the muzzle?  I would say it's muzzle blast, or the blowby of gasses and unburnt powder.  While these aren't enough to completely destabilize the bullet (tumble), they may be enough to induce a slight yaw in the bullet's attitude, relative to it's trajectory.  
This yaw, when induced during initial free travel is enough to cause the uneven air (wind) resistance to alter it's course slightly.
As the bullet travels further downrange, the gyroscopic forces (and possibly air [wind] resistance) serve to stabilize the bullet the same way they do the top.
Decreasing the powder charge may eliminate the problem, as has been witnessed.  
But I believe it is the corresponding reduction in "blowby" or "muzzle blast" that gives the desired results.

Something about bullet yaw and pitch, by Bryan Litz of Berger Bullets:
http://www.youtube.com/watch?v=KH9SCbCBHaY

[gitano]

Now that's an interesting comparison...

While I have no experience to draw on for drive shafts per se (other shafts though), I can relate to wheels having balance points that are a function of rpms. I can see where a shaft could have multiple rpm 'nodes' where it was "balanced" and those in which it was "unbalanced". That wouldn't explain "sleeping bullets", but it would further explain why some bullets "like" some muzzle velocities (MV translating directly to rpms).

The reason this wouldn't explain "sleeping bullets" is that the rpms don't change enough in 100 yds or so to cause the bullet to move off of an "unbalanced rpm node". At least the experts don't think so, and I agree with them.

Actual rpm could be measured from those hi-speed videos. To actually measure the difference over a realistic range, the bullet would have to be photographed at the muzzle and at say 100 yds.

Still, it doesn't "add up". 180,000 rpms is 3000 revolutions per second, and 120 revolutions in 0.04 seconds. Which is roughly the time it would take a bullet with a MV of 3000 f/s to travel from 100 to 200 yds - the "going to sleep place".)

I'll give this some more thought.

Paul

[recoil junky]

And thinking on this as "mass in motion" (mim) the smaller the mass, ie. a bullet, the faster it can be spun. Therefore (a big word for this bumpkin) the fewer rpm's it takes to "upset the balance" as it comes closer to hitting one of those nodes.

Nodes, that was the word I was looking for. Thanks Paul.

And I've had the "tire balancing" mystery happen to me. At certain speeds the unbalanced tire/wheel assembly will hit one of these nodes and act as if balanced perfectly. Often there are more than two of these nodes, but I've only experienced two myself. I was too scared to drive Dad's '73 F250 faster than 70 mph with it's 750/16, 10 ply bias tires.

An 11R24.5 tire's out of balance phase(s) is/are more noticeable than say a P185-70R13 tire's because of the mim.

So, IMO, this can be translated to a bullet (or boolit) but on a much smaller scale. If the bullet (boolit) is "balanced" at 181,234 rpm, but isn't at say 181,232 rpm it could be in one of those nodes.

Kinda like a girl. They can go from calm, kind and loving to high speed come-apart in less than 1 rpm.

RJ

[gitano]

All of this conversation got me to 'working' on this issue in depth again, and I think Jamie.270 and RJ have struck upon the causes of the phenomenon. The top analogy is right on - with one caveat - I think.

When throwing a top, the string and the smoothness with which it is thrown determine whether and how much it wobbles at the start. However, the law of conservation of momentum dictates that the top will stabilize at some point if the initial perturbations aren't too great. So... taking the analogy to bullet flight, if the perturbations at the point the bullet leaves the muzzle are 'great', it will take a while for the angular momentum of it's rotation to stabilize it. In this case, the bullet might print a relatively 'large' group at 100 yds, and a relatively "small" group at 200 yds, BUT NOT SMALLER.

One problem that still remains for me in this analogy is that the top has a fixed point of contact with an immovable surface. The bullet does not. Therefore, the bullet has no reference point/attachment against which its momentum can act. At least not one I can envision at the moment. More thought required on that issue.

While this removes a great deal of my skepticism, a small amount remains. (I'm just hard-headed.) ALL the unexplained elements need to be explained before I'll acquiesce to "sleeping bullets", but as I said, this takes care of most of them.

As to Berger's video... There's a GREAT deal of the initial conditions that are left unexplained. For example:

1) What exactly are the 6 degrees of freedom?
2) In a rotating object with no reference point, like a bullet in free flight, the "pitch" and "yaw" are indistinguishable without a specified reference point.

There are three axes of motion "x", "y", and "z".

1) Rotation on the x-axis is called "pitch". In an airplane this would be rotation on the axis that runs from wing-tip to wing-tip. Rotation on that axis moves the nose up or down - "pitch".
2) Rotation on the y-axis is called "roll". In an airplane this would be rotation on the axis that runs from nose to tail. Rotation on that axis "spins" the airplane or in our case spins the bullet.
3) Rotation on the z-axis is called "yaw" In an airplane this would be rotation on the axis that runs through the center of the plane top-to-bottom. Rotation on that axis moves the nose left and right.

The Berger simulation says that the plot is the relationship between pitch and yaw, meaning NOT the rotation or movement of the bullet around the line-of-flight, but rather how the left/right movement of the nose of the bullet bullet compares to the up/down movement (not the flight-path up/down, but the "wobble" up/down), of the bullet. I really question the application of this simulation to the idea of bullets "going to sleep". I know that's what Berger SAYS it is, I just think they are 1) Mistaken, or 2) Have incorrectly described the what the plot is. The nose of the bullet does not define the path of the bullet. The center of mass does. (There are those pesky laws of motion again.) Certainly the nose of a "pointy" bullet can influence the flight path, but the magnitude of that influence is not quantifiable unless you shoot the bullet in a vacuum because the instantaneous wind velocity and density will change from moment to moment which will in turn change the magnitude of the influence that the nose of the bullet has on the flight path.

What Berger's simulation COULD be pointing to (you can't tell from the explanation provided nor the graph), is that the point of a "pointy" bullet "moves" around for "a while" after it leaves the muzzle, and "settles down" some time later. IMPLYING that precision would 'follow' the bullet's nose. However, that's NOT what it shows.

What it does show, is that the left/right movement AS COMPARED TO THE UP/DOWN MOVEMENT changes with time. That means NOTHING. Keep in mind that the graph is left/right motion of the nose relative to the up/down motion of the nose NOT THE FLIGHT PATH. If the nose of the bullet was moving AN INCH left and right and AND INCH up and down, the graph would show ZERO RELATIVE MOTION. (By the way, there are a TON of assumptions in Bergers simulation, none of which are noted.)

Certainly less movement of the nose of a "pointy" bullet would suggest that precision would be better, but there's no proof or quantification of that assumption provided by the simulation.

Basically, all the Berger simulation "shows" is the THEORETICAL response of one end of a rotating cylinder to some initial perturbation. You can see that by spinning a top or toy gyro. But again, both the top and the gyro have fixed points of attachment to an immovable surface. That's not a trivial difference in the two systems under consideration.

Paul

[gitano]

Let me discuss the Berger simulation a little more, but separately. Let's examine what an individual point on the graph means.

On the graph,



at 3 yards the point being graphed is located at -3,0. That means that the point of the bullet was 3 degrees DIFFERENT in the left/right direction from the point of the bullet in the up/down direction. THERE IS NO INFORMATION ON HOW FAR OFF AXIS (line of flight) THE NOSE ACTUALLY IS. The point plotted is the position of the nose ONLY in the left/right direction RELATIVE to the position of the nose in the up/down direction. If the nose was 3 degrees off axis in the left/right direction and exactly on in the up/down direction. Unfortunately there are an infinite number of pairs of distances the two values could be that would produce a value of "-3" on the graph.

Now consider the graph three yards later at 6 yds,



Note that the point plotted is exactly at 0,0. What that means is that the distance that the nose is off of the line-of-flight in the up/down direction is exactly equal to the distance it is off of the line-of-flight in the left/right direction. However, IT DOES NOT MEAN THE NOSE OF THE BULLET IS COINCIDENT WITH THE LINE-OF-FLIGHT! The bullet could be completely SIDEWAYS at a 45 degree angle, and the point plotted would still be 0,0 because the position of the "yaw" to the "pitch" would still be equal so the difference would be 0! Furthermore, I have given Berger the benefit of the doubt in saying saying that the point plotted is relative to the "line-of-flight". There is NOTHING in the video that defines what the plotted point is in relation to.

Berger implies a certain 'sophistication' to the simulation by stating "6 degrees of freedom" (but doesn't state what they are). Degrees of freedom is a statistical term. Here are the "degrees of freedom" I can see in the graph:

1) Roll, (irrelevant if angular momentum or angular velocity is considered a "degeree of fredom")
2) Pitch,
3) Yaw,
4) Range, (not really a degree of freedom as it is a function of a fixed variable - MV and another fixed variable - ballistic coefficient.)
5) Angular momentum (derived from angular velocity, which is derived from twist rate and muzzle velocity, rendering neither it or roll, an actual "degree of freedom"),
6) Angular velocity (see "5")
7) Time

Twist rate and muzzle velocity are not degrees of freedom since they are fixed values - "fxed" is not "free"). Meaning that there are really only 5 "degrees of freedom" OF MOTION. This should not be confused with "degrees of freedom" for statistical purposes. In that case, fixing pitch as the independent variable removes one degree of freedom, making only three degrees of freedom for statistical purposes - time, pitch and yaw.

This simulation - as presented - IMPLIES a great deal and tells me NOTHING.

Paul

[recoil junky]

I gotta go get my glasses and by that time I'll have to got to work.

I'll take notes

One quick thought though: Can a bullet really be unstable on each of it's three axis at the same time due to gs? IMO, no, and to me that is what Berger is saying it can do.

But like I said I gotta find my glasses so's I can read this better AND I gotta go to work.

RJ

[Nelsdou]

I was too lazy to dig through my physics and mechanical dynamics books so I read this http://www.nennstiel-ruprecht.de/bullfly/index.htm#Contents Interesting read.

Nels

[gitano]

An EXCELLENT article. May be the best I have ever seen so condensed.

I want to point out some important-to-our-discussion comments though.

Let's start with the last of it, the "two-arm" model. The most important comment made is:

"Then the bullet's TIP moves on a spiral-like (also described as helical) path as indicated in the drawing, while the CG remains attached to the center of the circle".

The CG is what defines the flight-path of the bullet, not the "tip". Put another way, the bullet's center of gravity doesn't rotate around the center point of the graph, only its tip does.

Further,

"This figure schematically visualizes the general angular motion of a spin-stabilized bullet close to the muzzle.

Also,

"Note that the magnitude of successive maximum yaw angles is less than its predecessors, as the bullet in the drawing is assumed to be dynamically stable (the maximum yaw angle decreases as the bullet continues to move on)."

Meaning that each instantaneous value of the calculated yaw angle is smaller than the one immediately before it, and

At muzzle exit (t=0) the yaw angle can be small, but increases to a maximum of approximately 1°, then decreases again to almost zero.

Which means that the TIP of the bullet is never more than 1 degree off-axis RELATIVE TO THE BULLET. Which is why you cannot detect this "tipping" at the target.

I would also point out that reading the text carefully is very important. The author is defining ALL of the forces acting on a bullet, BUT not all of those forces are even present  and he always points out which ones go to zero or are "insignificant". In the end, the ones that "count" are gravity and ballistic coefficient.

This fairly substantiates the thoeretical rejection of bullets "going to sleep", and is why I conceptually reject the concept but remain open-minded because of trustworthy anecdotal observations.

Paul

[recoil junky]

I will need to reread the article a couple times to let my brain absorb all it's information.

I feel like Chris Farley in "Almost Heroes"  

One question (so far) in the FAQ's I did find "interesting" was "How fast does a bullet lose it's spin velocity?"

I think this needs further investigation as (IMO), "spin velocity" (RPM) has more to do with a bullet's flight than can be seen on doppler radar. IF we could do "shadowgraphs" for say the first 200 yards of a bullets flight we could probably see the nodes where the bullet has destabilized and restabilized because of RPM loss just as the top, driveshafts and tires do.

As Paul is hard headed with things mathematical and their ease of being proven "on paper" I'm as hard headed the other way. Which makes for some very interesting conversations by the way. I need physical proof and I've seen physical proof of a bullet "going to sleep". I guess the way for me to prove it is to line up targets say every 25 yards out to 200 yards and shoot a ten shot group without leaving the bench between shots and see where they all go. Now I need a flat place at least 250 yards long. In a building would be nice.

People said it was impossible for man to survive at speeds of more than 60 MPH, that we could never go faster than the speed of sound in the air OR ON LAND.

If there is someone who says it can't be done, there's someone who is going to go out and prove him wrong.

RJ

[gitano]

As Paul is hard headed with things mathematical and their ease of being proven "on paper" I'm as hard headed the other way.

Let me clarify my actual position a little bit.

What I'm REALLY hard-headed about is have BOTH anecdotal observation and theory jibe. If they don't, something's amiss - either the theory needs adjusting or the anecdotal observation has a different explanation.

In this case, I'm leaning toward the latter. Not that some form of down-range stabilization doesn't necessarily take place, but rather exactly what the real explanation of the observations is.

Your proposed experiment sounds good, RJ, but if the down-range stabilization wasn't observed it wouldn't mean it doesn't take place. There are a whole herd of variables to consider. That's one of the reasons it hasn't been experimentally approached. It's too tough, (expensive and time-consuming), to prove unless you REALLY want to. For the competitive and "practical" shooters, the cause is irrelevant. All they need/want is a "fix", not an explanation, and the "fix" is usually simply slowing down the muzzle velocity.

In the "grand scheme of things" what I think is happening is that "muzzle blast", in all its various forms, is "perturbing" the bullet immediately after it leaves the muzzle, the rotational forces "force" it back into stability in "short order". The real question is what is "short order" as measured in yards/meters, not time.

As for the rpms and nodes of stability occurring down-range, I am quite certain there are none. The rotational velocity fundamentally doesn't change within small arms OR "large arm" ranges because the "shaft" (bullet) is rotating on an air bearing. "Nodal instability" is an issue ONLY at the initial point when the bullet leaves the muzzle. If the rotational velocity is near an "instability node", then the bullet will be unstable for a longer time, maybe long enough to show at 100 yds, and "settle down" beyond. That "settling down" is due to the stabilizing effects of rotational momentum, not changing rotational velocity. Therefore, there won't be an "opportunity" for the bullet to hit another "unstable" rotational velocity node before it hits the ground.

Paul

[recoil junky]

Paul, us hard headed fellers gots' tah stick together. It makes for interesting dinner conversation. I think we're both on the same page, it's just that my page has been through the wash, is wrinkled and harder to read. :frown

 I wish I could better understand the math part. In Algebra I was , shall we say, not too good? All the formulas went right over my head. I could understand them if there were numbers instead of letters. When given a problem "solve for 'b'" I could do it using my own "formula"and get the answer right (most of the time). To me letters just don't add up. :D


"In the "grand scheme of things" what I think is happening is that "muzzle blast", in all its various forms, is "perturbing" the bullet immediately after it leaves the muzzle, the rotational forces "force" it back into stability in "short order". The real question is what is "short order" as measured in yards/meters, not time."
I agree.

I think I'm stuck on the RPM thing (in the sense of rotational forces) because that's what I understand. My theory is that the bullet is spinning so fast that it takes a smaller percentage of RPM change to hit a node of instability than say the drive shaft. I've seen an unbalanced drive shaft go through it's nodes and watched the tachometer when it nears and passes through one. Sometimes it take as little as 5 RPM to go from "smooth" to "vibrating" and back to "smooth" again.

 Lets say the drive shaft hits a node between 200 and 205 RPM. That's 2.5% (I think) of the RPM at that point. Now, see'ins as how a bullet's mass is much smaller than a drive shaft, wouldn't it take a far less percentage of RPM loss to "destabilize" it? Am I correct in thinking that a bullet, even though it's rotating on an "air bearing", will still lose RPM at a predictable rate over distance and hit a node of instability and smooth out in short order (distance)?

RJ

[gitano]

Now, see'ins as how a bullet's mass is much smaller than a drive shaft, wouldn't it take a far less percentage of RPM loss to "destabilize" it?

and

Am I correct in thinking that a bullet, even though it's rotating on an "air bearing", will still lose RPM at a predictable rate over distance and hit a node of instability and smooth out in short order (distance)?

Are important sentences in your post.

First is the use of "percentages". When you do that, you "normalize" or "standardize" the effect, removing the differences in the masses of the two objects being compared. When you use the "percentage" term, I have to answer the second sentence/question "No".

Please don't interpret that response as "cute" or simply "playing with words". "Percentage" is the correct way to compare two "things" as different as a bullet and a drive shaft. If you hadn't used it, I would have. Let me digress for a moment to point to some of the significant differences between the two "systems".

1) The shaft doesn't ride on an air bearing. It's connected at both ends. That REALLY matters.
2) As far as I know, all drive shafts are hollow to save weight. Of course bullets are not hollow and in fact, higher densities are sought, at least most of the time. Hollow vs solid (mostly the rigidity of the 'shaft') makes a BIG difference in resonant frequency AND the response to hitting a resonant node.

Back from the digression, the primary reason that the percentage of rpms to reach a resonant node is significant in answering your question is the respective rotational velocities and momenta of the shaft and bullet. In other words, even though the mass of the bullet is so much less than the mass of the shaft, the angular moment is "equally" (not necessarily "equal", but certainly proportionally), small because the bullet is so much smaller in diameter. Therefore it is mathematically demonstrable, (and in this case, the math is the simple engineering of drive shafts), that the angular momentum between a drive shaft of a certain length (very important to resonance) and rotational speed and a bullet of certain length and "spin rate" could have the exact same "moment" of angular momentum. Meaning that the same percentage/proportion of change in rpm (angular velocity) would result in the same transition from resonant ("unstable") to non-resonant.

Let's take your initial conditions of starting the bullet off at a resonant node when it leaves the muzzle. Lat's say we also start the bullet "perturbed" by "muzzle blast". The force that is acting to stabilize the bullet is the same  - angular momentum - and in both cases, the result is the same. The angular momentum FORCES the bullet to "settle down" gyroscopically. The rpm of the bullet will never slow down enough to reach another "instability" (resonant) node, and I'm not sure that it can even be resonant since it is not "attached" to anything solid at either end.

Consider other "things" that you (the collective "you") are familiar with. All wind instruments. They make music by vibrating at resonant nodes. The different nodes are the different notes. The instrument is fixed at the player's mouth.

The classic vibrating wine glass. Vibrating at resonance either with a wet finger rubbing the rim or being impinged upon by sound at the resonant frequency. The glass is fixed at its base resting on the table. If it wasn't fixed, it wouldn't vibrate.

Consider the "music" we make when we blow across the top of a beer bottle. The "fixed" part of the system, without which there would be no "music" (resonance) possible is the bottom of the bottle.

So, I'm not certain that there even ARE "resonance" nodes for an unfixed shaft rotating on an air bearing. I can't envision what would allow "vibration".

Finally, let me try to make clear that I greatly disdain those "scientists" and "engineers" that can't explain simple phenomena without resorting to symbolic algebra. It is a common malady of those that know rules but don't know reality. When pressed, they always retreat into symbolic math because they know that in most cases, most regular Joes can't follow. I consider the scientists and engineers that so commonly take that path as cowards and bullies.

That's not to say that I don't use and rely on symbolic math. I do, and I do heavily. However, I try not to use it when I am explaining or discussing some natural phenomenon. It is my opinion that if symbolic math is the only method one has at their disposal to explain a natural phenomenon, then they need to learn more about what their arguing. "Ivory Tower" academics have spent a great deal of time learning and memorizing the "rules". One only has so much time. Time spent learning the "rules" doesn't leave time for "experience". The "guy" with the most tools in his toolbox is the one that knows the rules AND has lived long enough outside the womb of academia to have experience as well.

So much for my sermon for today.

Paul

[Nelsdou]

OK, I reloaded my set with a slightly lighter charge and repeated my previous range session, this time shooting 4 foulers, a set of ten at 100 yds, then shooting 10 at 200 yds. The four foulers had the same boolit but had entirely different charge from a previous experiment, so I taped these over in the first round. The rifle used is a Yugo 24/47 with open sights.



The first set of 10 at 100 yds are the ones circled. The second set of 10 at 200 yds did not make the paper as I over-compensated for the lower charge and set my sight way too high, so the second 10 hit the cardboard about a foot above this target.  The numbered holes are from my 6.5x55  sporter using a 4X scope, 135 grain cast boolit, at 100 yds, and reflects a couple of scope adjustments.

Funny thing is the "group" of the second 10 at 200 yds is approximately the same as the 10 at 100 yds, which I think is somewhat a fluke. Trying to aim open sights at this paper at 200 yds with honest accuracy is a lot tougher that pining down a 12x12 inch gong at 220 yds.

Anyway, I think this particular cast boolit has good long range potential in a scoped rifle and obviously shoots flatter that I expected. A little more fiddling with the charge and the use of a scope should cut this group in half.

In an earlier post I mentioned seasoning the barrel with a number of foulers before this boolit might settle in. To see if that's the case this gun's barrel is not getting "cleaned" between further sessions of tuning this load.

Nels