Range Report Do Bullets Go to Sleep?

[Michael Courtney]

http://www.longrangehunting.com/articles/bullet-pitch-yaw-1.php

I thought the readers here might appreciate a link to a recent article.

Abstract
A bullet can leave the barrel with a significant yaw angle (or tip off rate leading to pitch and yaw) and then pitch and yaw in an oscillatory manner as the peak pitch and yaw angles slowly decrease as the bullet flies downrange. This paper presents an experimental design for detecting the in-flight damping and test results which support the theory of damping of pitch and yaw. Three chronographs were employed simultaneously to determine drag coefficients of bullets over near and far intervals 50 yards long for bullets fired at Mach 1.4 to Mach 3.1. Drag coefficients for the complete 100 yard interval were used at different Mach numbers to establish the curve of drag coefficient vs. Mach number. Since the drag coefficients will decrease as pitch and yaw are damped, the theory of bullets going to sleep predicts that the drag coefficients for the near 50 yard interval will be above the curve and the drag coefficients for the far 50 yard interval will be below the curve. This is, in fact, observed for Mach numbers above 1.5, so the theory of bullets going to sleep is supported in this case. Between Mach 1.0 and Mach 1.5, the damping of pitch and yaw may be obscured by the steep transonic drag rise.

 

[Graham]

It's been discussed at length. Bryan's simulations have been posted here.

And my bullets are sleeping - nestled together in a box - as we speak.

 

[Lukas Koukal]

It's been discussed at length. Bryan's simulations have been posted here.

And my bullets are sleeping - nestled together in a box - as we speak.

Graham, in your experience, does the performance of the bullets change based of the lullaby used?

Seriously, I consider Bryan´s (Litz) papers more comprehensive; what the "sleeping" or "calming down" of a bullet tells you is nothing but the range at which the given bullet performs best, without any coparation to the rest of the flight. Bryan´s papers explain and help you understand the entire bullet´s flight.

 

[Michael Courtney]

Thanks for the comments. We certainly consider this paper to be a contribution building on rather than a replacement for Bryan's excellent modeling work as expressed in his papers and videos.

Bryan's work in this area, though very good, has been limited to theoretical computations. There really have not been experiments verifying the modeling except for experimental verification of Robert McCoy's modeling work on a very small number of military bullets at the expensive and well-instrumented military ranges. Another weakness in Bryan's work is that it only tells you what the pitch and yaw dynamics are for a given tip-off rate (or peak yaw angle), it says nothing about what the tip-off rate (or peak yaw angle) really is for a given rifle and bullet combination.

This leaves application of the "going to sleep" theory as hypothetical in any given case. Is a given observation really due to a large tip off rate and subsequent damping of pitch and yaw, or is a given observation due to something else? Bryan's modeling work (in isolation) provides no way to answer this question in a specific case without some kind of experiment. Our paper provides a relatively simple and inexpensive experiment to demonstrate whether or not damping of pitch and yaw is a significant factor for a given combination of rifle and bullet.

 

[Lukas Koukal]

Fair say; I´ll give it more credit after another, more thotough read. Thanks for all effort in any case!

 

[TimK]

Thanks for presenting your experimental results. Not having read Litz's work on the subject, I'm curious how you decided to test at the ranges you did. Did Bryan predict that you'd see changes in the yaw behavior in just 100 yards, or was this decision made by some other criteria? I only ask because I find it intuitively surprising that a yawing bullet would damp itself so quickly. My intuition on the subject is meaningless as I've been thinking about it for only the time it took me to read your paper.

I'd be interested to see some results indicating at what range a bullet goes to sleep and whatever relations there might be to that and variables like bullet weight, MV, twist rate, etc. Sounds like a lot of work.

Thanks again for sharing your results.

 

[TiroFijo]

Check this:

http://www.nennstiel-ruprecht.de/bullfly/shortr.htm#header_shortranges

and this:

http://www.exteriorballistics.com/ebexplained/5th/25.cfm

if you can get it, also check the chapter 10 of "rifle accuracy facts" by H.R.Vaughn

 

[Aimsmall55]

I would say once past the supersonic stage the "settle down" this graph illustrates that point

 

[Aimsmall55]

My bad wrong g7.

 

[Aimsmall55]

All theoretical .....

 

[TiroFijo]

Aimsmall55, what do you think happens after the transition to subsonic?

 

[tobias]

Quote: "The drag coefficients at different Mach numbers for the complete 100 yard interval were used to establish the curve of drag coefficient vs. Mach number."
What do you mean with "complete 100 yard interval"?

 

[Michael Courtney]

Quote: "The drag coefficients at different Mach numbers for the complete 100 yard interval were used to establish the curve of drag coefficient vs. Mach number."
What do you mean with "complete 100 yard interval"?

The drag coefficients for the "complete 100 yard interval" were determined from the velocities of the near chronograph at 10 feet from the muzzle and the far chronograph at 310 feet.

The drag coefficients for the "near 50 yard interval" were determined from the velocities of the near chronograph at 10 feet and the middle chronograph at 160 feet.

The drag coefficients for the "far 50 yard interval" were determined from the velocities of the middle chronograph at 160 feet and the far chronograph at 310 feet.

 

[Michael Courtney]

Thanks for presenting your experimental results. Not having read Litz's work on the subject, I'm curious how you decided to test at the ranges you did. Did Bryan predict that you'd see changes in the yaw behavior in just 100 yards, or was this decision made by some other criteria? I only ask because I find it intuitively surprising that a yawing bullet would damp itself so quickly. My intuition on the subject is meaningless as I've been thinking about it for only the time it took me to read your paper.

I'd be interested to see some results indicating at what range a bullet goes to sleep and whatever relations there might be to that and variables like bullet weight, MV, twist rate, etc. Sounds like a lot of work.

Thanks again for sharing your results.

I think reading up on the Litz references and watching his videos will be very informative for you. Bryan's calculations do indicate that pitch and yaw will be mostly damped after 100 yards, with significant damping occurring in the first 50 yards. Also, after the first round of using drag as a tool to investigate stability (2011 experiments, published in Precision Shooting in 2012), using chronographs at the muzzle and 100 yards downrange, Don Miller suggested a third chronograph at the half way point to see if measuring the drag in the first 50 yards might me a more sensitive probe of stability than measuring the drag over the first 100 yards. It turns out that Don was right, and we've since transitioned to using drag measurements over the first 50 yards to better quantify stability. Don wanted to know why we had observed a reduction in drag at Sg = 1.23 and then drag reductions as Sg is lowered to 1.0. Finally, we've tried some other experiments to investigate the drag differences between separations closer to 100 and 200 yards, and the effects were more difficult to discern and less conclusive. (See the discussion section of http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA555975 )

The 50 and 100 yard downrange chronographs are also a lot easier to deal with. The chronographs at these ranges are easier to read and easier to align over the shorter distance. It's also easier not to hit the far chronograph at 100 yards than it is not to hit the far chronograph at 200 yards. A bullet with a BC close to 0.200 has a lot of wind drift and drop at 200 yards, especially when launching over a range of muzzle velocities from M1.4 to M3.3.

There may be useful work in seeing at what range the pitch and yaw of a bullet is well damped and how to improve bullet designs and match to twist rates for faster damping, but I think the more interesting question is how to better design bullets, barrels, and reloading techniques to effectively reduce tip-off rates (maximum pitch and yaw rates) in the first place. A load with a maximum yaw of 2 degrees is simply going to be better than a load with a maximum yaw of 11 degrees. I suspect that the best available load techniques with a tight chamber, quality throat, good barrel, and good crown probably already accomplish this when paired with a bullet whose center of mass lies on its geometric axis of rotation.

 

[tobias]

The drag coefficients for the "complete 100 yard interval" were determined from the velocities of the near chronograph at 10 feet from the muzzle and the far chronograph at 310 feet.

The drag coefficients for the "near 50 yard interval" were determined from the velocities of the near chronograph at 10 feet and the middle chronograph at 160 feet.

The drag coefficients for the "far 50 yard interval" were determined from the velocities of the middle chronograph at 160 feet and the far chronograph at 310 feet.

So you shoot one of your cartridges and get, say 800 m/s at the muzzle and 700 m/s after 100 yards. The calculated drag coefficient is allocated to the average velocity of 750 m/s. Then you shoot a cartridge with a lesser charge and get for example 770 m/s at the muzzle and 730 m/s after 50 yards. Again, the drag coefficient is allocated to (the same average velocity of) 750 m/s, but you expect/measure a higher value due to higher pitching and yawing at the first 50 yards. Is that right?

 

[Aimsmall55]

Aimsmall55, what do you think happens after the transition to subsonic?

Ha... Don't get me to lying. I understand that past supersonic it "calms down" but I'm no ballistician. Litz would be best suited on that one.

 

[Michael Courtney]

So you shoot one of your cartridges and get, say 800 m/s at the muzzle and 700 m/s after 100 yards. The calculated drag coefficient is allocated to the average velocity of 750 m/s. Then you shoot a cartridge with a lesser charge and get for example 770 m/s at the muzzle and 730 m/s after 50 yards. Again, the drag coefficient is allocated to (the same average velocity of) 750 m/s, but you expect/measure a higher value due to higher pitching and yawing at the first 50 yards. Is that right?

I think you have the gist of it, except that there were 10 shots for each powder charge. I have attached some jpegs with the experimental set-up and equations for further clarity.

 

[Michael Courtney]

Ha... Don't get me to lying. I understand that past supersonic it "calms down" but I'm no ballistician. Litz would be best suited on that one.

It depends on the bullet and what you mean by "calms down." The 168 SMK is not known to calm down. The attachment (from http://www.dtic.mil/ndia/2005smallarms/tuesday/newill.pdf ) also shows the long range yaw behavior of the M855 bullet in 5.56mm NATO. The damping of yaw in the first 50 to 100 yards is what I consider "going to sleep." The dynamic/nonlinear instabilities that show up at longer ranges are a different thing and depend on other issues.

 

[Aimsmall55]

It depends on the bullet and what you mean by "calms down." The 168 SMK is not known to calm down. The attachment (from http://www.dtic.mil/ndia/2005smallarms/tuesday/newill.pdf ) also shows the long range yaw behavior of the M855 bullet in 5.56mm NATO. The damping of yaw in the first 50 to 100 yards is what I consider "going to sleep." The dynamic/nonlinear instabilities that show up at longer ranges are a different thing and depend on other issues.

I could give a hoot. Killing those turkey birds at the present time. But what i meant was when a certain bullet not all, goes subsonic it "lays down" losing velocity and energy a lot less rapidly. Jeez dude. I said I don't and will never know it all. Cut me some slack

 

[TiroFijo]

Simply, the drag in the subsonic region is much smaller than in the supersonic range.

 

[Michael Courtney]

Simply, the drag in the subsonic region is much smaller than in the supersonic range.

Good point. However, it should be recognized that even subsonic drag will be much larger than expected if a bullet is dynamically unstable and develops significant pitch and yaw, especially for a long bullet like the 300 grain hybrid in .338. A yaw on the order of 10 degrees will cause both a significant increase in drag and a serious challenge for accuracy. The manufacturer of this bullet had a difficult time accurately measuring the G7 BC (or equivalently the CDO), so I tend to doubt that the other coefficients needed to determine downrange dynamic stability have been measured accurately (the quadratic yaw drag coefficient, the overturning moment coefficient, the gyroscopic stability factor, the lift force coefficient, the magnus moment coefficient, the pitch damping moment coefficient, and the damping rates for the fast and slow yaw modes). Some of these numbers can be accurately determined with PRODAS via numerical modeling, but the obtaining the complete set needed for reliably predicting dynamic stability requires a range fully instrumented with free flight spark photography. A range instrumented with an array of high speed video cameras would also work. An alternate approach to confirming long range dynamic stability would be to measure the drag after the subsonic transition. The Doppler RADAR technique is probably the best approach here.

 

[tobias]

[MENTION=70154]Michael Courtney[/MENTION]
Sorry, for OffTopic, but did you get my PM?

 

[Michael Courtney]

[MENTION=70154]Michael Courtney[/MENTION]
Sorry, for OffTopic, but did you get my PM?

Thanks for the heads up. Email is always better as sometimes I miss PMs on the forum. Thanks.

 

[CatShooter]

All theoretical .....

There is one basic flaw in all of these "theories", that negates them.

That flaw is the assumption that the bullet has some kind of force or desire to return to the original path, and they all ignore the fundamental laws of physics.

If a bullet is fired and deviates from the original direction, either in the direction of movement, or axis orientation (or both), there is no force to bring it back "on line"... it is off on it's own vagrant journey.

If the bullet is not sleeping (ergo, it is awake) the motion of precession has no dampening components, in fact, because of the angle of attack to the on rushing air, the moments of precession get worse, not better, so the bullet's angle of attack INCREASES, not decreases.

There is no tendency to go to sleep, it is the opposite, it gets more and more off axis until it tumbles.

Not my opinion... just about 300 years of the best physics including ol' guys like Newton.

 

[doc76251]

So if I'm reading all this correctly what you are trying to prove is the same thing that can be observed in real time with the use of a child's gyroscope or even a top. If you pull the rip cord REALLY hard the gyroscope/top will oscillate around on it's axis for a short period of time before it stabilizes and then "stand's still". As the energy bleeds off the gyroscope/top slowly becomes less stable until mean old Mr. Gravity finally wins again and the gyroscope/top falls over.

The real question should be at what Rotations Per Minute (RPM) does a given boolet fired from a given twisted barrel become "stable" and at what point (RPM) does it become "unstable" again.

As an example:

210gr Berger VLD fired at 2800fps in a 1-10 twisted tube results in a 3/4" group at 100 yards, a 1" group at 200 yards and a 3/4" group at 300 yards. That same bullet at 1760 yards (1 Mile) is subsonic but still maintains sufficient accuracy to keep 10 rounds on a 16" X 24" plate (it was a good morning to shoot).

Same rifle, 165gr Ballistic Tip type hunting boolet fired at 3000fps makes 1/4" groups at 100 yards, 3/8" groups at 200 yards and 3/4" groups at 300 yards, It also hits the ground somewhere in the general vicinity of the 1 mile target.

I know from the above that I am never going to win a BR match at 100 yards using a 210 but I can reasonably expect to be very precise after say 250 yards or so out to a mile because my boolet "went to sleep". The opposite is also known to me in that if I need to hit something precisely "in close" I should choose the 165 but not expect it to perform at extended ranges.

So with the above someone with more initials behind their name a bigger calculator than me "should" be able to figure out at what RPM a given bullet is "over stable" and therefore oscillating and at what RPM range the same boolet is stable given the twist rate and velocity. A table such as that would certainly go a long way in helping folks determine what twist rate and speeds they should be looking for based on their intended target distance.

Cheers,

Doc

 

[Aimsmall55]

There is one basic flaw in all of these "theories", that negates them.

That flaw is the assumption that the bullet has some kind of force or desire to return to the original path, and they all ignore the fundamental laws of physics.

If a bullet is fired and deviates from the original direction, either in the direction of movement, or axis orientation (or both), there is no force to bring it back "on line"... it is off on it's own vagrant journey.

If the bullet is not sleeping (ergo, it is awake) the motion of precession has no dampening components, in fact, because of the angle of attack to the on rushing air, the moments of precession get worse, not better, so the bullet's angle of attack INCREASES, not decreases.

There is no tendency to go to sleep, it is the opposite, it gets more and more off axis until it tumbles.

Not my opinion... just about 300 years of the best physics including ol' guys like Newton.

I just put up the graph. I had no intention to sound like I knew what it meant!!

 

[CatShooter]

So if I'm reading all this correctly what you are trying to prove is the same thing that can be observed in real time with the use of a child's gyroscope or even a top. If you pull the rip cord REALLY hard the gyroscope/top will oscillate around on it's axis for a short period of time before it stabilizes and then "stand's still". As the energy bleeds off the gyroscope/top slowly becomes less stable until mean old Mr. Gravity finally wins again and the gyroscope/top falls over.

Cheers,

Doc

Tops do not count, unless your bullets stand on their nose.

Gyroscopes do not behave as you described. I guess it has been a long time since you did this stuff.

 

[218bee]

catshooter nailed it