Bullet Stability: Some Interesting Findings

[South Pender]

I’ve been playing with the stability calculator of the JBM Ballistics program and have discovered something that I found surprising, although I suspect many of you already know this. When determining stability of two .277 bullets each of identical length, in a barrel with 1:10 twist, I found one to be unstable at reasonable velocity and the other to be stable. This program uses the Miller Stability Factor in determining stability. The program lists a value of 1.3 as the point at which stability is present. Specifically, I looked at:

(a) the Nosler .277 150-gr. Accubond Long Range (length: 1.39") and

(b) the Woodleigh .277 180-gr. (length: 1.391").

The Nosler came up unstable at 2950 fps (with a stability factor value of 1.258), whereas the Woodleigh showed complete stability at 2693 fps (with a stability factor value of 1.462). (Velocity of the Woodleigh was estimated based on the same ME as the Nosler and turned out to be completely negligible, as the same result was obtained with varying MVs.)

So, if the JBM results are to be believed, there’s more than mere bullet length involved in determining stability.

The other thing that jumped out is the effect of a polymer tip in connection with the length calculation. With the Nosler 150-gr. ABLR, if I enter .05” as the plastic tip length, the calculation comes up stable (stability factor value of 1.35), where it had been flagged as unstable without this information about the plastic tip.

I don’t completely understand the reasons for my findings, so, for you guys that really understand ballistics, can someone provide an explanation?

 

[RegionRat]

Fluid dynamics and external ballistics are a long study. There were several parametric studies on spin stabilizing versus fin stabilizing of projectiles during my era, but getting hold of those papers isn’t easy or free.

Here is one free article on the update look at plastic tips. Once the Reynolds equation enters the stage, it takes a long time to explain the forces, so I will leave this here for nightstand reading. The formulas are only as good as the assumptions, and even then the data is compared to specific test items. Once the test items look different, all bets are off.

https://arxiv.org/pdf/1410.5340.pdf;

Nothing wrong with looking at the parametric equations, but they are not specifically trying to calculate stability in terms of a physical force. Instead, they model the parametric factors to estimate a “stability factor”, which is a very different type of science.

 

[chromatica]

You asked for it so here goes. Pour yourself a cup of coffee…

Long pointy bullets are inherently unstable. Their center of gravity is well behind the midpoint of the bullet axis. The onrushing air wants to flip it around so that the bullet flies backwards. This destabilizing force is called the overturning moment. This is where spin comes in.

When a bullet starts spinning, it has what we call angular momentum (also called rotational inertia). It’s a kind of inertia that causes the bullet to resist changes in orientation. When the bullet is spinning fast enough, the overturning moment is not large enough to counteract the angular momentum, and the bullet flies with the pointy end forward. This is the desired state of affairs.

The stability number, roughly speaking, is a ratio between the angular momentum of the spinning bullet divided by the overturning moment. When this number is greater than 1.0, the bullet has enough angular momentum to resist the overturning moment. When this number is less that 1.0, the overturning moment is stronger than the angular momentum and the bullet can start to wobble and even begin to tumble head-over-heels. Atmospheric conditions affect the amount of drag that a bullet experiences and therefore affect the overturning moment. Usually, we want to create a load that will be stable in all reasonable atmospheric conditions. Engineers like to create designs that include a safety margin. As long-range shooters, we typically look for stability of 1.5 or greater. (Benchrest shooters will often develop loads with a much lower stability factor, even less than 1.0. They do this largely by choosing barrels with slower twist rates.)

Twist rate of the barrel is part of the formula for stability. An 8 twist barrel causes the bullet to spin faster than a 10 twist barrel. Bullet length is also part of the formula for bullet stability, but so is bullet mass. Your 180 grain load, has more angular momentum because there is more mass rotating around its axis, with a barrel of a given twist rate. It is better able to resist the overturning moment. That is why its stability number is higher than your 150 grain load.

The formula for Miller stability is

SG = 30 m/(t^2 * d^3 * L (1 + L^2))

Where:

m is the bullet mass in grains
t is the rifling twist rate in calibers per turn
d is the diameter of the bullet in inches
L is the length of the bullet in calibers

This formula assumes the muzzle velocity is very close to 2800 fps. There is a small correction factor that can be applied to SG for velocities that don’t meet this requirement.

Source: Bryan Litz, Applied Ballistics for Long Range Shooting p. 428.

 

[mikecr]

First, how did you get the idea that stability is purely a matter of length?
You had to enter cal/diameter, and weight into the calc right?
If these didn't matter then you wouldn't need to enter them.

A polymer tip is lighter than bullet material. So for the bullet to weigh the same with this tip, weight was added behind it. That weight is usually of larger diameter than it would have been at the very tip. Larger diameter weight provides more centripetal force, contributing to greater gyroscopic force.

 

[South Pender]

First, how did you get the idea that stability is purely a matter of length?
You had to enter cal/diameter, and weight into the calc right?
If these didn't matter then you wouldn't need to enter them.

I had inferred that length was the determinative factor when comparing bullets of the same weight, caliber, and muzzle velocity, but differing in length. For example, using again the .277 150-gr. Nosler ABLR, but now also the .277 150-gr. Nosler Partition, we have the following:

1. .277 150-gr. Nosler ABLR: Length: 1.39"; MV: 2950; Stability factor value: 1.258, unstable.

2. .277 150-gr. Nosler Partition: Length: 1.25"; MV: 2950; Stability factor value: 1.715, highly stable.

 

[mikecr]

Specifically, I looked at:
(a) the Nosler .277 150-gr. Accubond Long Range (length: 1.39") and
(b) the Woodleigh .277 180-gr. (length: 1.391").

So, if the JBM results are to be believed, there’s more than mere bullet length involved in determining stability.

I don’t completely understand the reasons for my findings, so, for you guys that really understand ballistics, can someone provide an explanation?

This is two bullets of different weight & same length. It had to seem possible that they would calc out with different stabilities.
The other bullets are same weight but different lengths & build. It shouldn't be difficult to accept different stabilities there either.

Hopefully the explanations provided help, but, as mentioned earlier, 1.258 is not unstable.

 

[dcali]

You're right- there is more to it than length. There's a brief explanation of the math here that shows how the miller approximation deviates from the full classical equations: https://bisonballistics.com/calculators/stability

Long story short, Don Miller looked at a fairly sizable catalog of military projectiles for which we have good data, and discovered that you can approximate the hard to measure/calculate stuff with a much simpler equation and that when you do so, you lose very little accuracy. It's quite remarkable that it works so well (to me at least).

I've written software that does it the hard way and the easy way (Miller). The two numbers are always close to each other, and neither is perfect. In my experience, both are a little conservative (they overestimate the required spin).

The caveat with Miller is that it's based on a certain set of projectiles, and most of our bullets look more or less like those. But if you get into something strange, like say, a wadcutter, or even a very short flat base bullet, the numbers start to look a little off because Miller just isn't based on that type of bullet. Usually it works pretty well.

 

[dellet]

Shape, weight, length, material density all come into play. You can have the exact same shape and length, made out of different material, jacketed or lead vs brass or copper solids and have a different stability factor.

The basic stability calculators do not factor in shape or specific gravity. A copper solid will weigh about 80% of the same size and shape as a jacketed lead bullet. So a 1” long copper cylinder gets the same output as a 1” long VLD jacketed bullet based on same diameter, weight and length. Or even the same bullet shot forward and backward will have the same output.

Your questions/observations are probably better answered with a drag/twist calculator than a basic stability calculator.
JBM has one, https://www.jbmballistics.com/cgi-bin/jbmdrag-5.1.cgi
Geoffrey Kolbe has one, http://www.geoffrey-kolbe.com/drag.htm

Both allow you to input bullet dimensions and specific gravity that will generate tables or graphs showing stability factors at different velocity.

I find Geoffrey Kolbe version a bit easier for me to use. The inputs are based in inches instead of calibers,( boat tail is X inches long, vs calibers long). It also generates a rough idea of bullet shape.

Things really started to make much more sense to me when I could change input numbers, see a change in bullet shape drawn out and matched to the twist rate, velocity and stability on a graph or table. The Kolbe version will do this.

I shoot a lot of different shaped, caliber, and material bullets, at a wide range of velocities. What I was seeing with holes on paper, did not match the basic calculators.

There used to be a specific sub-forum for these type of topics, not sure how that would be accessed now other than detailed searches.

 

[Doom]

Simply put, stability is proportional to mass and inversely proportional to length. Therefor, a heavier bullet at the same velocity and length will have a higher stability factor.

 

[RGRobinett]

I’ve been playing with the stability calculator of the JBM Ballistics program and have discovered something that I found surprising, although I suspect many of you already know this. When determining stability of two .277 bullets each of identical length, in a barrel with 1:10 twist, I found one to be unstable at reasonable velocity and the other to be stable. This program uses the Miller Stability Factor in determining stability. The program lists a value of 1.3 as the point at which stability is present. Specifically, I looked at:

(a) the Nosler .277 150-gr. Accubond Long Range (length: 1.39") and

(b) the Woodleigh .277 180-gr. (length: 1.391").

The Nosler came up unstable at 2950 fps (with a stability factor value of 1.258), whereas the Woodleigh showed complete stability at 2693 fps (with a stability factor value of 1.462). (Velocity of the Woodleigh was estimated based on the same ME as the Nosler and turned out to be completely negligible, as the same result was obtained with varying MVs.)

So, if the JBM results are to be believed, there’s more than mere bullet length involved in determining stability.

The other thing that jumped out is the effect of a polymer tip in connection with the length calculation. With the Nosler 150-gr. ABLR, if I enter .05” as the plastic tip length, the calculation comes up stable (stability factor value of 1.35), where it had been flagged as unstable without this information about the plastic tip.

I don’t completely understand the reasons for my findings, so, for you guys that really understand ballistics, can someone provide an explanation?

There is the problem. If you desire reliable results, for almost and bullet, Use the McCoy based DRAG/TWIST calculator, about 1/2 way down the JBM calculator page. RG