Bullet Dispersion

[Bryan Litz Ballistics]

To prevent derailing the discussion on the 'Shoot thru Target Challenge' thread, I've started this new thread to answer a good question that was asked there. I think it's an important topic to discuss, but isn't in line with the purpose of the other thread, which is specifically to discuss the 'shoot thru target challenge'.

So can someone please re assure me here, especially Bryan.
If a load shoots 1/2 Moa at 100 yards, theoretically it should shoot 1/2 moa upto transonic range? Of course I'm removing shooter error and wind here.

When I first started loading, lot of "experts " told me to test my loads at longer ranges(200 to 500) because what works at 100 yards may not work at 1000. But based on this thread if average dispersion of a given load is 1/2 moa it should stay 1/2 moa till it hits transonic range? So can I say it doesn't matter if I develop load at 100 or 300yards, if it groups good at short range it will group good at any range as long as shooter is upto task?

Note: This post has been edited. The original explanation for dispersion was based on tof, which was found to be in error.

The corrected model of dispersion is conical. Bullet imbalance and misalignment result in angular dispersion, not related to tof.

And, the rest of the story.

Other factors which make dispersion greater at long range is wind and MV variation.

Barrel harmonics can either amplify or reduce vertical dispersion at long range due to MV variation. If the barrel is pointed down (or moving down) in it's vibration pattern when the faster bullets are exiting, there is a compensating effect which would allow the shots to have less vertical dispersion at long range than you would expect from the MV variation alone. On the contrary, if the slow shots are exiting when the barrel is pointed down (or moving down) in it's vibration, then the barrel harmonics will amplify vertical dispersion.

Note that this 'compensating' effect between MV and barrel harmonics is a known and accepted mechanism for groups to have less vertical at long range than their MV variation would suggest. It's not the answer to the question being asked in the 'Shoot thru Target Challenge', because there we're looking for groups to shrink in MOA in all directions, not just vertical.

There's a whole load development practice called 'ladder testing' which is designed to find these 'nodes', so you can load to the ideal MV for your barrel, where MV variation effects will be minimized. Personally, I've never used such methods for two reasons. Once, I feel that the heavy barrels we use in competition have relatively minor harmonics compared to thin, sporter barrels. Also, the effect of temperature on your average MV may take a rifle out of tune if you compete in a different temperature environment from what you developed the load in. My load development for long range is to shoot groups at 100, and look at group size and MV variation. When I'm shooting good groups with an SD under 10 fps (5 fps for F-class), then I know the load will perform at long range.

-Bryan

 

[calgarycanada]

Thank you very much Bryan, I really appreciate you taking time to explain everything in great detail.
See now I know what type of supernatural power is at work.

It's also very satisfying to know I use same technique for load development that is used by a REAL Expert.
Thanks again
Av

 

[m500]

Note that this 'compensating' effect between MV and barrel harmonics is a known and accepted mechanism for groups to have less vertical at long range than their MV variation would suggest. It's not the answer to the question being asked in the 'Shoot thru Target Challenge', because there we're looking for groups to shrink in MOA in all directions, not just vertical.

Bryan, thank you for clearing this up. I had asked about this in your shoot thru thread with no response. Now I know what you are looking for. Thanks.

 

[allenn]

Bryan, why are bullets out of balance. If they are out of balance how do we fix the problem. Is it possible to sort them into groups.
What causes bullets to pitch and yaw.

 

[calgarycanada]

Bryan, why are bullets out of balance. If they are out of balance how do we fix the problem. Is it possible to sort them into groups.
What causes bullets to pitch and yaw.

Bryan can answer 100 times better but here's what I believe

Bullets being out of balance is in manufacturing, no matter how hard manufacturers try it's very hard to produce perfectly balanced bullets at large scale using current swagging methods. Density of materials, thickness variation of jacket material around the core are main causes of imbalance. Imbalance along with any amount of runout in loaded rounds or anything that makes bullet engage rifling at an angle (banana shaped cases, poor sizing techniques etc)will cause it wobble around its centre of gravity. How much depends on all factors above and lot more.

 

[Joe Grad]

Bryan,

When you're talking about bullet imbalance, are you talking about defects from manufacturing or bullet instability due to insufficient rifle twist?

Also...You mentioned a heavy barrel. What else can we as shooters do to minimize "time of flight" errors?


-joe

 

[Bryan Litz Ballistics]

Balance and stability are very different things.

Balance refers to the mass distribution in the bullet. It's the same in flight as when the bullet is sitting still on your loading bench.

Stability is a flight condition, and is determined by mass and aerodynamic properties including forward and rotational velocity.

I recently provided the below description of balance and stability which goes into more detail (maybe more than you want )

Jerry,

We have to clarify some definitions here.

When referring to bullets, static balance is not front to rear, but radial. It's an offset of the center of gravity from the center axis of the bullet. Static imbalance is typically introduced in bullets from jacket eccentricity (jacket is thicker on one side than the other, thereby causing the core to be off-center). This is why jackets with low run-out are so critical to precision. A small amount of static imbalance (0.0001") will make it impossible to shoot BR winning groups. Dispersion from static imbalance is related to twist rate, which is why many BR shooters choose the slowest twist possible.
A football has static imbalance due to the weight of the laces on one side.

Dynamic imbalance is harder to explain/envision. In engineering terms, we say that bullets have a geometric axis (simply the line defined by the bullets shape) as well as a principle axis of inertia which is determined by the mass distribution within the bullet. These two axis are the same if the bullet is perfectly balanced. If these two axis are not parallel, the bullet has 'dynamic imbalance'. If the two axis are parallel but not together, then the bullet has static imbalance.
Back to football, when you see a ball thrown that is 'wobbly', that perceived 'wobbly-ness' is what dynamic imbalance looks like. Note this analogy isn't strictly accurate, because the ball itself isn't dynamically unbalanced, it just wobbles because of being thrown imperfectly.
You could introduce a dynamic imbalance to a bullet by drilling a 0.030" deep hole (for example) 1/4" behind the CG on the left side of a bullet, and another hole of equal depth 1/4" ahead of the CG on the right side. This wouldn't necessarily ruin the static imbalance of the bullet, but would introduce a dynamic imbalance.

It is possible for a bullet to have purely static imbalance, or purely dynamic imbalance. In reality, every bullet has some amount of both, even if it's not measurable (because nothing man-made is 'perfect')

Static imbalance is the big enemy of precision. When the bullet is in the barrel, it's confined to spin around it's geometric axis. But when it emerges from the confines of the muzzle, it immediately begins spinning around it's principle axis of inertia (CG) (because it's now in free-flight). For a bullet having no static imbalance, it will come out of the barrel and fly straight. But if there is static imbalance, the bullet will gain some lateral velocity as it exits the muzzle.

Your question referred to static imbalance being related to the fore-aft position of the CG, which, for a bullet spinning on it's proper (long) axis, wouldn't have an effect on balance.

The fore-aft location of the CG does affect the bullets *stability*, which is entirely different from balance. A bullet can be stable and un-balanced. It's also possible for a bullet to be balanced and unstable.

Balance is a property of the bullet itself. Stability is determined/affected by it's spin rate, velocity, air density, as well as it's mass and aerodynamic properties.

On the subject of precision, stability has very little effect until you fall below the critical stability factor where the bullets don't fly point on and start key-holing on target. Even keyholing bullets can be relatively precise. I shot a 300 yard group with 300 grain solids from a .338 LM, 1:10" twist which printed ~1" long keyholes and the group was under 1 MOA. This is not typical or desirable, but just shows that stability and precision aren't necessarily linked.

For stability levels below 1.5, you can measure a decrease in the bullets effective BC due to the bullet flying with greater pitching/yawing angles, but again, groups don't suffer from this marginal stability. In fact, if you're dealing with bullets that have a great deal of static imbalance, you can expect *better* groups from marginally stabilized bullets because the slower spin rate results in less dispersion from the same static imbalance. Again, consider the tendency of short range BR shooters to choose slow twist barrels. Typically, stability factors of short range BR shooters are in the 1.1 range and it's not uncommon to see minor key-holing if conditions (air density, MV) are not favorable to stability on any given day.

Imbalance is a manufacturing imperfection. The primary cause of static imbalance is jacket eccentricity which results in off-center cores. To put it into perspective, BR quality jackets typically have 0.0003" of TIR (Total Indicated Runout). This results in the CG of the finished bullet to be about 0.0001" from the geometric center of the bullet (0.0001" of imbalance). It's a really small amount, but when you spin the bullet over 200,000 RPM, that slight imbalance is enough to show up as dispersion in short range BR groups.

Also...You mentioned a heavy barrel. What else can we as shooters do to minimize "time of flight" errors?

That's a good question. Heavy barrels and well balanced bullets will minimize tof dispersion.

However, the majority of dispersion at long range is typically due to wind (horizontal) and MV/BC variation in the vertical.

-Bryan

 

[Joe Grad]

Thanks for the response.

There's never too much detail...

Is there any risk of introducing additional static or dynamic imbalances during the meplat "pointing" process? If so, is there a point at which those risks outweigh the benefit of the higher BC at long range?

-Joe

 

[mman]

Take bullet imbalance for example. Bullet imbalance contributes to dispersion because as the bullet exits the muzzle spinning at around 200,000 RPM, it will fly off on a tangent as it exits the muzzle. Another way to say this is: "A small component of lateral velocity is introduced". This small component of lateral velocity will displace the bullet in proportion to the *time of flight* (velocity times time = displacement).

So let's say you have bullet imbalance that causes a bullet to strike up to 1/4" away from the center of the group at 100 yards, and the time of flight to 100 yards is 0.1036 seconds. Now let that bullet fly 1000 yards. How far will it be from the center of the group there? Well, first determine how much lateral velocity the bullet has: 0.25" in 0.1036 seconds is 2.41 inches per second. Time of flight to 1000 yards is 1.5306 seconds, so the bullets lateral displacement at that distance will be: 2.41*1.5306=3.69", which is more than the 2.5" you would expect based on the 0.25" dispersion at 100 yards.

Visually, the dispersion pattern is shaped like a trumpet.

-Bryan

Bryan,

I have learnt a lot about ballistics from you but this is something I have to disagree. You presented this theory in your first book already and I dropped you a line about it. However I didn't get an answer so we couldn't have a debate. So I think this forum is a proper place to have an open discussion.

I agree with you that some of the dispersion components are nonlinear to range (bc variation, MV variation, wind) but some are linear. However the way I see it, there is no way how lateral initial velocity of bullet alone could lead to nonlinear dispersion or "trumpet like trajectory". Let's think about this...

I'll quote you the newton's first law:

"Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it."

I ask you this: What is the force which makes the dispersion to curve along the trajectory if bullet gets a lateral velocity component at the muzzle?

Let's think about this another way. Bullet has a velocity vector when it leaves the muzzle. Vector can always be divided into components but drag affects to all of those components equally (this is because bullet aligns against incoming airflow as you show in your books). That leads to conclusion that "lateral" velocity component slows down also. So the velocity component due to launch dynamics leads still only to linear dispersion, not TOF dispersion.

For example let's assume a perfect bullet with 1000 m/s MV launched from rigid barrel. Then there is no dispersion at all. Now let's assume same bullet leaving from a flexible barrel with lateral velocity of 1 m/s. Now bullet leaves the barrel with initial velocity of (1000^2+1^2)^0.5 = 1000.0005 m/s and angle of atan(1/1000)*180/pi*60 = 3.44 MOA. So in practice initial velocity is still the same but now bullet got 3.44 MOA of LINEAR dispersion.

To make this clear I value your work and always look forward to read your new research. But we all make mistakes and I think it's time to correct this one.

 

[Joe Grad]

Bryan said...

Visually, the dispersion pattern is shaped like a trumpet.

different than...

nonlinear dispersion or "trumpet like trajectory"

 

[mman]

Bryan said...

Visually, the dispersion pattern is shaped like a trumpet.

different than...

nonlinear dispersion or "trumpet like trajectory"

Nope. Same thing. If dispersion is ToF depended then it is nonlinear to range which means that something "trumpet like" has to happen during flight. Please read the books for more accurate description of the ToF dispersion theory (related to lateral initial velocity component on muzzle).

 

[Joe Grad]

Nope. Same thing. If dispersion is ToF depended then it is nonlinear to range which means that something "trumpet like" has to happen during flight.

Disagree... Dispersion (position at different ranges) is different than trajectory (position through time).

Here are the graphs of the same bullet with a constant 2.41 in/sec trajectory due to a bullet imbalance. Notice the trajectory is linear. Nothing trumpet like at all. The dispersion, however, is non-linear or "trumpet like".

This is an actual Barnes bullet and the same time values were used for both graphs.

 

[mman]

Disagree... Dispersion (position at different ranges) is different than trajectory (position through time).

OK. That is true of course, I may have misused the terms. But that is not my point at all.

My point is to challenge the hole concept of this ToF depended dispersion theory. Bryan states that if bullet has given lateral velocity component at the muzzle, it will lead to ToF depended group sizes.

What I'm trying to explain is that bullet imbalance or barrel harmonics cannot give a bullet constant lateral velocity which would lead to time of flight depended groups. This lateral component slows down at the same rate as bullet velocity which leads to groups that are depended on shooting range only.

Please, let Bryan answer this since he knows his own theory.

 

[Joe Grad]

This lateral component slows down at the same rate as bullet velocity

So your assumption is that the change in the bullet's forward velocity and the change in it's lateral velocity are not independent. You seem to be saying that one must affect the other. I don't think this is a safe assumption.

Each of the 3 axes of the "velocity vector" you spoke of are independent of each other, as are the changes in velocities with respect to time (acceleration vectors). Forward motion and lateral motion are on two different and independent axes. (See attached)


-Joe

 

[mman]

So your assumption is that the change in the bullet's forward velocity and the change in it's lateral velocity are not independent. You seem to be saying that one must affect the other.

Yes that is the case when we are talking about drag. Drag or air resistance always affects against bullet resultant velocity vector. This is something Bryan and I agree with at least in general level. You can check this from his books. Now it's a clear conlusion that all of the components of velocity vector slow down equally due to drag, including initially induced lateral velocity component.

Each of the 3 axes of the "velocity vector" you spoke of are independent of each other, as are the changes in velocities with respect to time (acceleration vectors). Forward motion and lateral motion are on two different and independent axes. (See attached)

First of all you shouldn't include gravity since it has nothing to do with this concept, it just shades the point. Just include drag and divide velocity vector into two components as shown in figure below. This is the system where bryan states that group size would be linearly proportional on time of flight while I say that it is linearly proportional on range. So in other words Bryan is saying that drag force here should be parallel with X. While in thruth drag always is parallel with bullet velocity resultant vector.

And finally I repeat that please give Bryan a word... It makes no sense for us to discuss about it when I'm challenging his theory not yours.

 

[Bryan Litz Ballistics]

mman,

The tof based dispersion for bullet imbalance came from Harold Vaughn's book: "Rifle Accuracy Facts". Harold was an aeroballistics guy at Sandia labs who developed the tricyclic theory of yaw: http://books.google.com/books/about/A_Detailed_Development_of_the_Tricyclic.html?id=bo5NAAAAYAAJ

among many other accomplishments in the field.

I can't cite the exact page his equation appears on (I'm currently in Las Vegas for the NRA SHOT show), but it's in the chapter on bullet imbalance. TOF is a term in the equation for dispersion based on imbalance, twist rate, and MV. When it comes to physics, I tend to trust the published literature on the subject, especially when it's published by highly credible sources.

Having said all that, I think you may be right.

The small component of lateral velocity induced at the muzzle from bullet imbalance would act to re-orient the bullets direction of travel by a small *angle*. The bullet would then be on this line, with it's drag vector realigned along this line, and drag acting straight back thru the bullets axis. In this configuration, dispersion would be linear with range (angular) for bullet imbalance and misalgnment, as you described.

I don't have my books, but I did find on my laptop, a spreadsheet where I had programmed McCoy's formula for lateral throw off (which is similar to imbalance effects, but is for axis mis-alignment with the bore). TOF does not appear in this equation, but range does which means the lateral throw off dispersion is angular.

Sir, thank you for persisting on this subject. Learning new things is always exciting, but correcting flawed information is equally important. I'll address the places in this forum where I was describing tof dispersion, and eventually in my books as well.

Now, taking a step back, what can we as shooters do with this corrected understanding of dispersion? I don't think it will change any practices; we'll still try to make the best balanced bullets, and optimize alignment in the bore. It is good though to have an accurate understanding of dispersion, which is, aside from wind and MV/BC variation, conical. It will certainly be relevant to my work with the shoot thru target. Rather than dispersion based on tof ratio representing the least possible dispersion, the minimal dispersion model is conical.

If I may ask (mman), who are you and what do you do for a living?

-Bryan

 

[mman]

Bryan,

It's a shame we couldn't have this discussion years ago. I have red Harold Vaughn's book: "Rifle Accuracy Facts". A great book and smart guy but some errors in it including this one, nobody is perfect.

I like your myth busting view of ballistics. Most of us are now a bit smarter than before you started your work.

Well, I work with FEA and CFD for a living. Other than that I prefer to stay anonymous for the forum but I'll PM you my contact information.
I have also some things to share that might interest you. For example I've done CFD simulations for bullets and FE-modelling for firearms..

 

[Joe Grad]

We get it ... drag affects lateral velocity too...

Now what are the drag effects of something moving at 2.14 in/sec? lol

 

[mman]

We get it ... drag affects lateral velocity too...

Now what are the drag effects of something moving at 2.14 in/sec? lol

That's a good question but very hard to answer without knowing anything about shape of the object or atmospheric conditions. In general that would be insignificant for many practical applications.

However if you are still referring the bullet travelling 2300 fps with a lateral velocity component of 2.14 in/sec that would be significant. If the bullet slows down 50 %, the lateral component slows down the same percentage. Drag affects to resultant, remember .

 

[Joe Grad]

mman.... we all make mistakes and I think it's time to correct this one. HAHAHAHAHAHAHA