Improved Stability Formula for Plastic Tipped Bullets

[Michael Courtney]

The latest issue of Precision Shooting (Jan 2012) includes an article that I co-authored with Don Miller where we present an improved stability formula that more accurately predicts stability for plastic tipped bullets. The stability formula that Don published several years ago works well for bullets of near uniform density, but tended to underestimate stability of plastic tipped bullets owing to the much lighter density of the plastic. Consequently, the original twist formula might have caused shooters to lean away from a given plastic tipped bullet design for rifles twist rates and conditions where they are fully stabilized. It was a pleasure working with Don in the development and testing of the new formula, and we expect that the new formula will prove useful.

 

[elkaholic]

The latest issue of Precision Shooting (Jan 2012) includes an article that I co-authored with Don Miller where we present an improved stability formula that more accurately predicts stability for plastic tipped bullets. The stability formula that Don published several years ago works well for bullets of near uniform density, but tended to underestimate stability of plastic tipped bullets owing to the much lighter density of the plastic. Consequently, the original twist formula might have caused shooters to lean away from a given plastic tipped bullet design for rifles twist rates and conditions where they are fully stabilized. It was a pleasure working with Don in the development and testing of the new formula, and we expect that the new formula will prove useful.

Interesting! We tend to speak of more twist for heavier bullets which of course is not really true, it is bullet length that is the issue. Along with that is balance of the bullet i.e. weight forward, weight back etc. It would make sense that a lighter tip would have a lesser affect on twist needed to stabilize as opposed to a heavier tip of the same length.....Rich

 

[Mikecr]

It would make sense that a lighter tip would have a lesser affect on twist needed to stabilize as opposed to a heavier tip of the same length

How does this make sense?
I know plastic tip bullets are stable beyond predicted, but I don't understand why.

It would seem to me that lighter plastic tip -for a given weight and length of bullet, would move center of gravity backward,, reducing stability.
I might think that the smaller meplat of the tip could move the center of pressure backward, apparently even moreso than center of gravity moved backward. BUT, BC of plastic tipped bullets is no better to worse than typical HP LR bullets. So this Cp notion is not supported with that, because if I form a non-tipped meplat smaller, both BC and stability go up..

What am I missin?

 

[elkaholic]

How does this make sense?
I know plastic tip bullets are stable beyond predicted, but I don't understand why.

It would seem to me that lighter plastic tip -for a given weight and length of bullet, would move center of gravity backward,, reducing stability.
I might think that the smaller meplat of the tip could move the center of pressure backward, apparently even moreso than center of gravity moved backward. BUT, BC of plastic tipped bullets is no better to worse than typical HP LR bullets. So this Cp notion is not supported with that, because if I form a non-tipped meplat smaller, both BC and stability go up..

What am I missin?

You may not be missing anything I am not stating scientific fact but merely my own opinion. It is my belief that imperfections are amplified in bullets near BOTH ends. It makes sense to me because the heavier the tip with ANY imperfections, whether ballistic tip or simply the meplat without a tip, the more likely the bullet rotation is likely to throw it off balance. This seemed to happen when I replaced an identically shaped aluminum ballistic tip with a mild steel tip which weighed 15 grs. as opposed to 5. The accuracy went south. I realize this might not happen in every case as there could be different balance issues with different bullets in regard to jacket, core ,etc. The posters theory just seemed to support what I have experienced....Rich

 

[Michael Eichele]

Deleted

 

[Michael Courtney]

The effect of the plastic tip is usually to change the gyroscopic stability (Sg) by 15-30%. It does not have a big effect on the center of gravity or the moments of inertia, but it does move the center of pressure forward.

The consequence of just using the total length in the original Miller twist rule is that the rule predicts that some plastic-tipped bullets will be unstable when they are, in fact, stable. This will restrict the user to shorter bullets with Sg's much higher than they need to be and leave the shooter with the mistaken impression that some longer, usually higher BC, bullets will not be stable in a particular rifle with given environmental conditions.

The article in PS not only presents the formula, but also discusses a lot of the science behind it. Don Miller's previous articles on stability are also highly recommended background. Here are some links:

http://www.jbmballistics.com/ballistics/bibliography/articles/miller_stability_1.pdf

http://www.jbmballistics.com/ballistics/bibliography/articles/miller_stability_2.pdf

 

[RBBeers]

JBM Ballistics has graciously added an input for the length of the plastic tip to their stability calculator to reflect the "new and improved" formulas presented by Mr. Miller and Mr. Courtney in their January and February 2012 Precision Shooting articles.

And, although it has not yet been tested and confirmed, for hollow-tip match bullets, inputting the length of the hollow tip (in lieu of the plastic tip) may provide more accurate results than with the original Miller twist rule as well.

 

[Mikecr]

The effect of the plastic tip is usually to change the gyroscopic stability (Sg) by 15-30%. It does not have a big effect on the center of gravity or the moments of inertia, but it does move the center of pressure forward.
The consequence of just using the total length in the original Miller twist rule is that the rule predicts that some plastic-tipped bullets will be unstable when they are, in fact, stable.

Do you know HOW this is so?
I searched both these reference documents and see no accounting of tipped bullets, or improvement to Miller's rule of thumb.

When Cma(overturning moment) rises, stability goes down.
Cma = X(Cp-Cg)
Cp & Cg are taken from bullet base
As bullets approach Mach1 Cp moves forward, reducing stability. So moving Cp forward is destabilizing.
Cg allows yard darts to fly point forward with no other forces acting to stabilize them.
For stability at a given spin rate, you keep center of gravity relatively close or forward w/resp to center of pressure.

The only way I could see a plastic tip NOT reducing stability, is if the solid plastic weighs as much or more than the copper hollow point it's displacing(holding Cg), or, if the smaller plastic meplat is moving Cp backwards on the bullet(without moving Cg), or both.

What doesn't make sense is that plastic tipped bullet stability would go up, while it's BC doesn't seem to change. Normally affecting one, affects the other(either up or down).
This is why I ask if you know HOW it does just this.

 

[Michael Courtney]

Do you know HOW this is so?
I searched both these reference documents and see no accounting of tipped bullets, or improvement to Miller's rule of thumb.

When Cma(overturning moment) rises, stability goes down.
Cma = X(Cp-Cg)
Cp & Cg are taken from bullet base
As bullets approach Mach1 Cp moves forward, reducing stability. So moving Cp forward is destabilizing.
Cg allows yard darts to fly point forward with no other forces acting to stabilize them.
For stability at a given spin rate, you keep center of gravity relatively close or forward w/resp to center of pressure.

The only way I could see a plastic tip NOT reducing stability, is if the solid plastic weighs as much or more than the copper hollow point it's displacing(holding Cg), or, if the smaller plastic meplat is moving Cp backwards on the bullet(without moving Cg), or both.

What doesn't make sense is that plastic tipped bullet stability would go up, while it's BC doesn't seem to change. Normally affecting one, affects the other(either up or down).
This is why I ask if you know HOW it does just this.

It depends on what is held constant. Your comments make sense if you are adding a plastic tip to a bullet, thus making it longer.

My comments make sense with respect to the stability formulas. The total length of the bullet is the total length. The plastic tip is part of the total length, thus violating the assumption in the original Miller twist rule that the bullet has constant density. The center of gravity is moved backward (compared with a bullet of constant density) and the tumbling moment of inertia is reduced. Stability is increased relative to a constant density bullet of the same dimensions.

Find the Jan and Feb 2012 articles in Precision Shooting, they should clarify things.

 

[elkaholic]

It depends on what is held constant. Your comments make sense if you are adding a plastic tip to a bullet, thus making it longer.

My comments make sense with respect to the stability formulas. The total length of the bullet is the total length. The plastic tip is part of the total length, thus violating the assumption in the original Miller twist rule that the bullet has constant density. The center of gravity is moved backward (compared with a bullet of constant density) and the tumbling moment of inertia is reduced. Stability is increased relative to a constant density bullet of the same dimensions.

Find the Jan and Feb 2012 articles in Precision Shooting, they should clarify things.

Agree!.....an example is the new Berger hybrid with the long hollow nose (approx. .4") If the lead core were to extend to the tip, it would change the stabilty, and twist required, considerably. Just an example of what I think you are getting at.......Rich

 

[Catfur]

The gyroscopic stability of anything (including a bullet) is based on the rotational momentum. Rotational momentum is Iω, that is moment of inertia x angular velocity. The moment of inertia is affected more by the mass of the object that is farther away from the axis of rotation than by mass that is near the object of rotation (and the relationship is based on distance squared).

For a given weight bullet, an FMJ has more of the total mass nearer the axis of rotation than a hollowpoint or plastic tipped bullet. The hollowpoint or plastic tip displaces the lead that is usually located at the point, and distributes it out farther away from the axis. This increases the moment of inertia (I) and thus allows the same rotational momentum to be achieved with lower angular velocity (ω).

 

[Mikecr]

The center of gravity is moved backward (compared with a bullet of constant density) and the tumbling moment of inertia is reduced.

This is opposite of reality.
The closer Cg is to a bullet tip, the greater it's stability.
In extreme, if you moved most of a bullet's weight to the nose, leaving void the bearing and boat tail, you would be launching a yard dart, and need no rifling at all.

There are folks out there 'turning' new bullets daily. They could make a 140gr 26cal bullet, with a good BC, that wouldn't benefit from rifling. This is where yet another adjustment to Miller's rule of thumb would be needed. And this can go on & on with base angles and grooves, etc..

But the point is, there is a real explanation for observed affects with plastic tips.
I just don't know what it is..
Yet

 

[Michael Courtney]

The closer Cg is to a bullet tip, the greater it's stability.
...

Right, but only if everything else is held constant. But everything else is not held constant when comparing a plastic tipped bullet with an identically shaped bullet with constant density. In addition to moving the center of gravity slightly backwards, the effect of the plastic tip increases the axial moment of inertia and decreases the tumbling moment of inertia. Both of these effects on the moments of inertia tend to increase the gyroscopic stability and they more than compensate the change in the center of gravity.

The fundamental equation for gyroscopic stability is shown above, taken from

http://www.nennstiel-ruprecht.de/bullfly/gyrocond.htm

Ix is the axial moment of inertia; it appears twice in the numerator, so increasing Ix, increases stability strongly. Iy is the tumbling moment of inertia; it appears in the denominator, so decreasing Iy also increases stability. Moving the center of mass backward slightly increases CMa, the derivative of the overturning moment coefficient.

So the plastic tip changes three terms in the stability equation. The change in one term tends to decrease stability, but the changes in the other two terms tends to increase the stability, so the net change is an increase in stability.

If you don't believe the theoretical explanation, then believe the experiments reported in the Precision Shooting papers. We've also conducted additional experiments showing that the original twist formula is accurate for metal bullets, but it underestimates the stability for plastic tipped and open tipped bullets. The effect of a plastic tip or an empty space in the tip of a bullet is to increase stability relative to a constant density bullet of the same dimensions.

 

[RBBeers]

So the plastic tip changes three terms in the stability equation. The change in one term tends to decrease stability, but the changes in the other two terms tends to increase the stability, so the net change is an increase in stability.

The effect of a plastic tip or an empty space in the tip of a bullet is to decrease stability relative to a constant density bullet of the same dimensions.

Should the second quote read "The effect of a plastic tip or an empty space in the tip of a bullet is to increase stability relative to a constant density bullet of the same dimensions."?