Help me understand stability and bullet construction

[dellet]

Stability calculators are wonderful tools, but seem to have some pretty big holes or missing explanations. A good example is Berger’s own calculator that has the disclaimer of inaccuracy with flat base bullets. That leaves out most cast.

Another issue is the cardinal rule of “it’s length, not weight” that determines stability. That also becomes an issue. If all you change in the calculator is weight, you get different stability factors.

Finally there is shape, really there is no way of knowing if the bullet is flying backwards, forwards or even sideways. Or where the centers of balance and pressure are.

How does someone sort all that out?

Here’s a hypothetical bullet and what I am struggling to understand when plugged into JBM.

This would be a copper bullet

Stability
Input Data
Caliber: 0.257 in Bullet Weight: 100.0 gr
Bullet Length: 1.000 in Plastic Tip Length: 0.000 in
Muzzle Velocity: 2000.0 ft/s Barrel Twist: 12.0 in
Temperature: 59.0 °F Pressure: 29.92 in Hg
Output Data
Stability: 1.154
01-Jun-19 06:55, JBM/jbmstab

If the same bullet was made from lead

Stability
Input Data
Caliber: 0.257 in Bullet Weight: 125.0 gr
Bullet Length: 1.000 in Plastic Tip Length: 0.000 in
Muzzle Velocity: 2000.0 ft/s Barrel Twist: 12.0 in
Temperature: 59.0 °F Pressure: 29.92 in Hg
Output Data
Stability: 1.442
01-Jun-19 07:14, JBM/jbmstab-5.1.cgi

Made from tungsten

Stability
Input Data
Caliber: 0.257 in Bullet Weight: 175.0 gr
Bullet Length: 1.000 in Plastic Tip Length: 0.000 in
Muzzle Velocity: 2000.0 ft/s Barrel Twist: 12.0 in
Temperature: 59.0 °F Pressure: 29.92 in Hg
Output Data
Stability: 2.019
01-Jun-19 07:15, JBM/jbmstab-5.1.cgi

This does not begin to touch on bullet shape as in the examples of the Berger flatbase bullets being much more stable than the calculator would lead you to believe. Some of this was touched on in the Applied Ballistics series, some was not.

How does one who is not a rocket scientist begin to sort this out?

Any help or sources appreciated

 

[mikecr]

Sorting it out is a matter of understanding, which takes a helluvalot of work, -because it is rocket science.
Gyroscopic stability goes up with your example inputs because you locked in all things equal except weight.
A way to understand this: Weight affects sectional density, which form factor is applied to for ballistic coefficient. Higher BC equals less drag, which means less overturning force, for higher stability.
It's a chain you can't follow with greenhill or Miller Stability rules of thumb that many sites are using. And of course the relatively few inputs provided there are not enough to calculate actual stability (just close for today's 'normal' bullet configurations & use). Today, meaning Miller is relatively more accurate than Greenhill, today.

You mentioned shape, which brings up a valid point about rules of thumb -vs- truths. You could fire boat tails backwards in a smoothbore, it wouldn't tumble(therefore stable), because center of gravity would be on or ahead of center of pressure. Flat base bullets are inherently more stable because the higher base drag pulls center of pressure rearward. You could also use tungsten pills to alter center of gravity in same shape copper bullets, changing their stability, and no rule of thumb will know it.

 

[dellet]

I chose weight as the example since part of stability is based on the distance between center of pressure and center gravity. If the external shape, is the same then, the only way to change the resistance to tumble would be to increase weight. I think this also ties in to the idea of "scaling" the same bullet shape through different calibers in some ways.

What triggered new questions, is trying to predict stability in cast bullets. In general they seem more stable than the calculators predict. In general they are flat based, but also have lube grooves. They create the same problem as comparing boat tail and flat base using the calculators.

If you have the same basic shape and weight, where you place the lube grooves will change the centers of balance and pressure.

It also brings up the question of the grooves themselves effecting stability, since they tend to create their own shockwaves by disrupting and or increasing the airflow over the bearing surface.

Does this help or hurt stability?

How would you even begin to calculate for this?

 

[Ned Ludd]

You can't constrain the stability calculator to keep bullets manufactured from materials of dramatically different density at the same length without changing bullet mass and/or sectional density. Likewise, if you want to keep bullet mass the same, the length dimension must be free to change. It's an issue we face in the actual use of copper monolithic bullets...they are very long for their weight because the caliber (diameter) is constrained and they must be made much longer to fall within a certain weight class than a comparable weight lead core bullet. Because of this, the copper solids also typically require must faster twist rates than the same weight class of lead core bullets (i.e they're much longer).

There are a number of factors than influence bullet stability including boattail design, location of the center of gravity, bearing surface length, jacket thickness uniformity, etc. I would suggest obtaining copies of one of Bryan Litz' books, or Harold R. Vaughn's "Rifle Accuracy Facts" as a starting point. There are probably other texts available that will also address your questions.

 

[dellet]

I do not have Vaughn's book, I do have the Litz series and a couple others. I will look at it.

The copper and brass monolith's for the most part follow my first example. A good example would be that a 240 SMK is much more forgiving in subsonic shooting than a 194 Lehigh. The SMK is longer by about .070" but is far more stable in a 1/9 and they do not even compare in a 1/10. This does show up in the calculators tho, I am assuming mostly do to density, then shape and centers.

If flat base bullets are inherently more stable, is shape or weight distribution the largest factor?

 

[mikecr]

https://www.amazon.com/dp/0764338250/?tag=accuratescom-20
Robert McCoy's work is math heavy reading, but also the most comprehensive information on this topic.
There is an appendix of corrections out there (for some of the math).
Much of McCoy's endeavor was put into software by Bill Davis (which also has a few errors/assumptions).
The two go hand in hand to follow. Lija Barrels provided:
http://riflebarrels.com/bullet-design/

 

[Ballisticboy]

In order to calculate the true gyroscopic stability factor you need to be able to calculate the bullet moments of inertia, both axial and transverse, and the aerodynamic overturning moment over the full Mach number range and then incorporate them into the standard equation. To calculate the aerodynamic overturning moments you need either a powerful computer based aerodynamic prediction program or a full set of reference aerodynamic charts. Not many people will have the latter or access to them as often they are classified or commercially restricted access. It also helps if you have had training in their use as it is easy to make a mistake.
As for the software there are a few programs available which use the bullet external shape along with the centre of gravity position. There is a program on the JBM site specifically for calculating the aerodynamic overturning moment but I would not recommend it as it is based on a program I created very early in my career. If you are rich there is PRODAS but I have never been very impressed whenever I have tested this particular software. It is too easy to get a very wrong answer.
So most people are left with the very much simplified calculators which are obviously very limited in their application. They can give a rough guide but should not be relied upon for detailed information.
Any change in the external shape or mass distribution of a bullet will change the gyroscopic stability factor. Mass changes will tend to change the stability factor through changes to the values of the inertia terms. This can be seen by examination of the equation for stability factor where mass is not one of the variables. Bullet length will affect the overturning moment and the transverse inertia which is why it is considered important. A boat tail will also increase the aerodynamic overturning moment as they produce a destabilising moment thus reducing stability. Nose shape can also have a small effect on the aerodynamic stability.
If you put a boat tailed bullet backwards into a smooth bore it will not be stable. The boat tail will act like a nose and the nose will act like a boat tail giving you a very unstable projectile which will need spin. Also the drag of a cylindrical base has no contribution to stability. The reason cylindrical tails require less spin than boat tailed bases is due to the destabilising moments produced by boat tails not any stabilising moments from a cylinder.

 

[dellet]

Also the drag of a cylindrical base has no contribution to stability. The reason cylindrical tails require less spin than boat tailed bases is due to the destabilising moments produced by boat tails not any stabilising moments from a cylinder.

If I understand this correctly it helps a lot. A perfect cylinder shape base would be the standard to compare all others, from a stability perspective.

 

[Ballisticboy]

The thing to remember with stability is that it is moments about the centre of gravity which matter, not forces. A force which acts through the centre of gravity will make no contribution to stability no matter how big it is. This is true for both aerodynamic and gyroscopic stability.

 

[dcali]

Most if not all online calculators use the Miller rule. All of the complexity that's been described in earlier posts was simplified by Don Miller, who came up with a surprisingly good approximation that does not require moments of inertia or overturning moments to be calculated. He did this by fitting curves to data on handful of known projectiles from the BRL (most of which are in BRL Report 1630). If you look closely at that data, it fits boattail bullets better than flat based bullets. Miller's version of the calculation is not based on physics, but rather empirical observation of a relatively small number of projectiles. Its reason for existing is to be simple, so making more thoughtful compromises is counterproductive. I'm fairly amazed at how well it works to be honest.

I've written a calculator that does it the hard way - calculating detailed moments of inertia based on jacket and core dimensions, and using Intlift (the software Ballisticboy mentioned above) to calculate overturning moment coefficients. Practically speaking, it works pretty well and spits out very reasonable looking numbers, but I'm not sure it's worth the extra effort over the Miller version for our purposes. It might be better for odd cases, like short flat based bullets or really long pointy ones, but I'm just speculating. The accuracy of Intlift is not claimed to be terribly good, so at the end of the day, I'm not sure if it’s really better.

 

[dellet]

It would be interesting if you could take a look at any of the Berger bullets since they have a recommended twist rate published.

An example would be the .308 115 grain. Using Berger's own calculator they suggest a 1/13. In their specs it's 1/19. Others are similar.

 

[dcali]

I don't have any Berger 115s on hand, but I do have some 7 ogive 118 BIBs. The detailed calculations require a 20.6 twist to achieve a 1.0 Sg at standard atmospheric conditions and a muzzle velocity of Mach 2.5. The Miller formula predicts that a 18.1 twist is required to hit 1.0 Sg.

I know for a fact that the BIBs will stabilize out of my 18 twist just fine at Quantico (39' elevation), so I'm inclined to say, that for this bullet, Intlift + detailed inertia calculations wins. I would not say that's automatically true for every bullet. The two numbers are usually much closer to each other for normal long range boattail bullets. That's not surprising given the data used to create Miller were all military projectiles, and mostly boattails.

Incidentally, you can use these same methods to determine a crude measure of accuracy called jump sensitivity for lack of a better term. You can see an explanation here: Jump Sensitivity.

Long story short, here are some examples (lower is better):

.284 180 grain Sierra Matchking: .166
.308 185 grain Berger Juggernaut: .122
.308 118 grain BIB 7 ogive: .046 !!!!

You can see why people love those BIBs. This is why we don't want to over-spin bullets in pursuit of a couple of points of BC.

 

[dellet]

Plugging the BIB into Berger it came out similar with a .921 SG and recommending a 1/13 twist.

I understand the formula assumes a certain shape, but I feel like there is something obvious I am missing.

Is part of my confusion coming from spin rate for maximum BC, vs adequate stability?

Is the flat base that much more forgiving?

 

[dcali]

I don’t know why Berger is saying 13. My BIBs at .972” for what it’s worth. Are you looking at Sg of 1.0? When I put .972” and 118 into Berger at 2850 FPS, with a 13 twist, I get about 2.0 Sg.

I also don’t know why Berger has a field for BC, as it doesn’t matter at all.

 

[dellet]

If you plug in a 1/19 twist, which is Bergers’s recommendation for their bullet, it comes out with the SG in the low 9’s and recommends the 1/13 twist. I used your velocity of 2500.

They use 1.5 as a minimum recommended SG. To ensure max BC, and openly state and provide a linke to the recommended twists for their fb bullets to keep knuckleheads like me from asking questions.

This helps refine my question,
It the calculator off, or is it that flat base bullets are more stable at a lower SG and it’s the recommended twist, based on a boat tail, that is off?

 

[Ballisticboy]

It the calculator off, or is it that flat base bullets are more stable at a lower SG and it’s the recommended twist, based on a boat tail, that is off?

Flat based bullets are not more stable at a lower Sg it is just that, if you take two bullets which are identical except one has a boat tail and the other has a flat base, the flat based one will have a higher value of Sg for a given twist rate.

 

[dellet]

Flat based bullets are not more stable at a lower Sg it is just that, if you take two bullets which are identical except one has a boat tail and the other has a flat base, the flat based one will have a higher value of Sg for a given twist rate.

This again is a sticking point in my thinking. For the comparison to be valid, not only length and shape of the rest bullet need to be the same, but some how the weight and center of gravity would need to be the same.

If I am thinking right, the shape of the base should slightly change the center of pressure. That in itself changes the stability factor, in this increase it.

 

[Ballisticboy]

This again is a sticking point in my thinking. For the comparison to be valid, not only length and shape of the rest bullet need to be the same, but some how the weight and center of gravity would need to be the same.

If I am thinking right, the shape of the base should slightly change the center of pressure. That in itself changes the stability factor, in this increase it.

Correct. A boat tail, because it produces negative lift, will move the cente of pressure forwards thus increasing the aerodynamic instability of the bullet. A cylindrical base at small yaw angles produces little or no lift and thus has no effect on the position of the cente of pressure. The centre of pressure will be very close to the front of the bullet. On an artillery shell with a boat tail the centre of pressure lies approximately on the fuse which is why using canards at the very front to try to manouver a shell or bullet would never work in a controlled repeatable manner.

 

[dellet]

Correct. A boat tail, because it produces negative lift, will move the cente of pressure forwards thus increasing the aerodynamic instability of the bullet. A cylindrical base at small yaw angles produces little or no lift and thus has no effect on the position of the cente of pressure. The centre of pressure will be very close to the front of the bullet. On an artillery shell with a boat tail the centre of pressure lies approximately on the fuse which is why using canards at the very front to try to manouver a shell or bullet would never work in a controlled repeatable manner.

If the cylindrical base has little or no effect on the center of pressure, is the center of gravity more or less important?

Or would that be dictated more by nose shape?

 

[Ballisticboy]

Changes in the position of the centre of gravity will change both the aerodynamic over turning moment and the transverse moments of inertia. In real life changes in the base shape from boat tail to cylindrical will also change the moments of inertia as well as the aerodynamics which will complicate matters. Which change has most effect will depend on the individual designs and how critical one or other of the parameters is.
The centre of pressure position on a bullet at low angles of yaw will be dependent on the nose length, shape and distance from the centre of gravity, the boat tail angle, length and distance from the CG and to a small degree the length of the cylindrical section. Nose length will usually have more effect than nose shape but large changes in meplat could be significant. If you use Intlift on the JBM site it can give you an idea of the effects of changes. Just don't try anything too radical.