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Ballistic Theory The Different Types of Stability

Miles_M

HAM Specialist
Country flag
This is the first of a series of threads explaining the different types of projectile stability used by pellets. Many of you may have seen them on other forums, but there may be some who have not seen them before.

Quite often you will see someone mentioning stability, talking about how pellets go unstable as they slow down or are more accurate because they are more stable. But what is stability with regard to pellets, and how does it affect how a pellet flies?

A stable pellet is not one which comes out of the barrel and keeps pointing in the same direction. A stable pellet is one which comes out of the barrel and attempts to point directly into the airflow direction. As the pellet flies along its trajectory, the direction of the airflow will change, but a stable pellet will try to change the way in which it is pointing to stay with the airflow as below.

stable.webp

An unstable pellet will not point in the direction of the airflow and may eventually tumble, as shown here.

Unstable.webp


As far as pellets are concerned, there are actually three types of stability acting on them and affecting their flight. If we just think of normal dome type diabolo pellets they are what we call aero/gyro stabilized, that is, they rely on aerodynamic and gyroscopic stability. The third stability type pellets need is dynamic stability, this is not the same as gyroscopic stability.

To try to explain the difference between the different types of stability, think about a weight hanging on the end of a piece of string.

stability.webp

If you do not touch the weight, it will just hang down under the string. This is its zero yaw position, the position it likes to sit in. This is equivalent to a stable pellet pointing into the airflow. If you pull the weight slightly to one side and let it go, if it is stable, it will swing back towards its zero yaw position. This is because the forces and moments produced by the weight and the string are trying to push the weight back to its original position. If the weight and string were an unstable system, then as soon as we release the weight, it would move away from its zero yaw position. This type of stability is called static stability. The forces and moments on the weight and string are equivalent to the effects of aerodynamic and gyroscopic stability on a pellet. On most pellets, both the aerodynamic and gyroscopic stability will try to make the pellet face the air flow in which it is travelling as it moves along its trajectory. Aerodynamic and gyroscopic stability are both regarded as static stability.

When we have pulled our weight to one side and let it go, the first time it reaches its zero yaw position, it does not stop but goes on the other side until it eventually stops and then returns just like the pendulum on a clock. Because, unlike a clock, we don’t have a spring helping the weight to move, our weight will keep doing this with each swing getting a little smaller until it eventually stops at the zero yaw position. This is because the weight and string are dynamically stable, so the size of the swing reduces each time until there is nothing left. If the weight had neutral dynamic stability, it would keep on going, with each swing being the same size as the one before. This is what the spring on a clock is doing to the pendulum. The spring provides just enough force to keep the pendulum going with the same size swing until of course the spring winds down and the clock stops. If the weight and the string were dynamically unstable, the swings would get bigger until eventually the weight would go in a complete circle even though it is statically stable. Pellets have dynamic stability as well, though it is not quite so clear-cut.

When we fire a pellet, it is highly unlikely that it will be pointing exactly in the direction of the air flow. This is due to many things including wind, barrel vibrations, pellet manufacturing problems etc. The angle between the direction in which the pellet is pointing and that in which the airflow is moving is known as the yaw angle.

Yaw.webp

It is the yaw angle which the stability of the pellet will try to reduce. The diagrams below illustrate the effects on the yaw angle for the different stability states. First, we have a pellet which is both aerodynamically and gyroscopically unstable. That is, it is statically unstable.

yaw1.webp


Here, the pellet yaw angle will just increase until the pellet eventually faces backwards and tumbles.

Next is a pellet which is statically stable but dynamically unstable.

yaw4.webp


In this case the yaw swings through zero, but each swing gets bigger, and the pellet will eventually go sideways. Next, is a pellet which is statically stable but dynamically neutrally stable. Here, the swings of the pellet through zero yaw are always the same.

yaw3.webp


Last, is the situation we want, which is a pellet which is stable both statically and dynamically. The pellet swings through zero yaw, and each swing is smaller than its predecessor.

yaw2.webp


In reality most conventional pellets appear to be aerodynamically stable at speeds well below the speed of sound (1116.5ft/sec), that is, if we fired one from a smooth bore barrel it will continue to point in the direction of the trajectory. However, its aerodynamic stability is marginal and at high speeds disappears completely. Also, no pellet, or any other projectile, is made completely symmetrical and any differences from one side of the pellet to the other will produce an aerodynamic side force which will cause it to try to fly on a curved path. To reduce the effects of any projectile asymmetry, pellets and most other aerodynamically stable projectiles are given some spin so that the side force is not pointing in the same direction all the time. This will make the pellet wobble a bit but will not produce the curved flight path. The spin rate needed for this is very low, much less than is needed for gyroscopic stability.

Pellets are usually given much higher spin rates than those associated with reducing side force effects. This is because of the marginal aerodynamic stability. The spin rates of pellets are chosen to give a degree of gyroscopic stability in addition to the aerodynamic stability. This is why we say they are aero/gyro stabilized.

From the reported behaviour of pellets, they would seem to have pretty much neutral dynamic stability, possibly changing to dynamic instability at high speeds and long ranges. The change in dynamic instability is due to the increase in pellet spin rate relative to the pellet forward speed as the range increases. This apparent increase in spin rate is due to the pellet losing forward speed much quicker than it loses spin. The pellets are still statically stable, in fact the static stability has normally increased particularly at long ranges which in itself can produce strange flight effects, but the dynamic stability is also adversely affecting the pellet flight, allowing maximum yaw angles to increase.
 
Miles thanks for posting. There's a ton of material here - I have already read it though three times!

Personally I am interested to apply theory to practical shooting. So when I think about pellet stability, what is the "big hitter" that I can improve for myself?

This is on the basis that not all of the causes of instability will have an equal effect.

Is the main cause of downrange pellet instability likely to be the pellets themselves? Or would it be barrel-related? Or is wind likely to be greater than either of them? Or something else?
 
Miles thanks for posting. There's a ton of material here - I have already read it though three times!

Personally I am interested to apply theory to practical shooting. So when I think about pellet stability, what is the "big hitter" that I can improve for myself?

This is on the basis that not all of the causes of instability will have an equal effect.

Is the main cause of downrange pellet instability likely to be the pellets themselves? Or would it be barrel-related? Or is wind likely to be greater than either of them? Or something else?
For pellets in particular, the biggest problem seems to be too much stability rather than not enough, particularly at high speeds and long ranges. Slugs are different, but again, too much stability will reduce effectiveness.

Taking pellets first, as far as the aerodynamic stability is concerned, more is probably better in reducing group sizes. The biggest problems with aerodynamic stability are that as speeds approach sound speed, your aerodynamic stability tends to reduce until the pellet becomes aerodynamically unstable. Being aerodynamically unstable for a projectile with significant spin rates is not a big problem, it is the speeds where the aerodynamic stability changes from aerodynamic stability to instability, giving what is known as neutral stability at some speed. When you have neutral aerodynamic stability, you have infinite gyroscopic stability, which is bad for group sizes. Ways around this are the usual reduced twist rates and lower muzzle velocities. Changing to different pellet designs may also help, but finding pellets with the highest values of aerodynamic stability is not straight forward, as you need to be able to calculate the centre of gravity and the aerodynamic centre of each pellet design. This is not something most people can do.

The gyroscopic stability is more complex. Pellets do not become unstable as they fly down range, in fact, pellets and slugs become more gyroscopically stable as they slow down. The increase in gyro stability causes problems of its own with increased yaw wave lengths. I am currently trying to establish a link between gyroscopic stability factor, range, muzzle velocity and twist rate to find optimum twist rates. It is a big job, requiring hundreds of simulations which could easily come to nothing, but if it works it could give guidelines to matching twist rates to speeds and pellet design for minimum group sizes at different ranges. Currently, all you can do is find a pellet which gives the smallest group size at a given range and muzzle velocity.

Wind effects are a big problem, not so much for the average wind speed which can be compensated for on any given day, but for the wind variability. On one of my gun trials when I was working, I managed to get some samples of wind speed and direction measured every second for one hour. I had a couple of samples. The changes in both speed and direction can be severe from one second to the next, and it wasn't a particularly windy day. This is a short sample of the data.

wind dir.webp
Wind Sp.webp
It is the variability of the wind which gives the effect on group size. Choosing a pellet and muzzle velocity which minimizes the wind effect is all you can really do to try to improve group size. Even for heavy artillery, wind is one of the main reasons for large dispersion.

So down range static stability tends to increase, not decrease as is popularly thought. However, dynamic stability appears to decrease as the ratio between forward speed and spin rate changes. This can lead to a growth in maximum yaw angles, but the effect on group size is not as large as may be thought. A lack of dynamic stability cannot make a pellet or slug suddenly yaw, but it can rapidly increase any maximum yaw angles present, so the way to combat dynamic instability is to minimize the pellet or slug yaw to start with so that the dynamic instability has nothing or very little to work on.
 
great read!!
trying to wrap my mind around how i can use the information to get the most of of my gun.
short of keep the speed sub-sonic how can we best use this information.
As in my reply above, all you can really do is to find the pellet/slug which will best match your barrel to reduce the projectile yaw rates as it leaves the gun. Choosing a twist rate which is best for the ranges you want to shoot at is also a good idea, one turn in 16-20 inches at short ranges (25 yards) changing to around twice the length for one turn at 100 yards. Speed can be optimized for wind effects and minimum yaw on leaving the gun. As I said, if there is no yaw when the projectile leaves the gun then the dynamic stability and the increased yaw wave lengths have nothing or very little to work on.
 
For pellets in particular, the biggest problem seems to be too much stability rather than not enough, particularly at high speeds and long ranges. Slugs are different, but again, too much stability will reduce effectiveness.

Taking pellets first, as far as the aerodynamic stability is concerned, more is probably better in reducing group sizes. The biggest problems with aerodynamic stability are that as speeds approach sound speed, your aerodynamic stability tends to reduce until the pellet becomes aerodynamically unstable. Being aerodynamically unstable for a projectile with significant spin rates is not a big problem, it is the speeds where the aerodynamic stability changes from aerodynamic stability to instability, giving what is known as neutral stability at some speed. When you have neutral aerodynamic stability, you have infinite gyroscopic stability, which is bad for group sizes. Ways around this are the usual reduced twist rates and lower muzzle velocities. Changing to different pellet designs may also help, but finding pellets with the highest values of aerodynamic stability is not straight forward, as you need to be able to calculate the centre of gravity and the aerodynamic centre of each pellet design. This is not something most people can do.

The gyroscopic stability is more complex. Pellets do not become unstable as they fly down range, in fact, pellets and slugs become more gyroscopically stable as they slow down. The increase in gyro stability causes problems of its own with increased yaw wave lengths. I am currently trying to establish a link between gyroscopic stability factor, range, muzzle velocity and twist rate to find optimum twist rates. It is a big job, requiring hundreds of simulations which could easily come to nothing, but if it works it could give guidelines to matching twist rates to speeds and pellet design for minimum group sizes at different ranges. Currently, all you can do is find a pellet which gives the smallest group size at a given range and muzzle velocity.

Wind effects are a big problem, not so much for the average wind speed which can be compensated for on any given day, but for the wind variability. On one of my gun trials when I was working, I managed to get some samples of wind speed and direction measured every second for one hour. I had a couple of samples. The changes in both speed and direction can be severe from one second to the next, and it wasn't a particularly windy day. This is a short sample of the data.

View attachment 3906
View attachment 3907
It is the variability of the wind which gives the effect on group size. Choosing a pellet and muzzle velocity which minimizes the wind effect is all you can really do to try to improve group size. Even for heavy artillery, wind is one of the main reasons for large dispersion.

So down range static stability tends to increase, not decrease as is popularly thought. However, dynamic stability appears to decrease as the ratio between forward speed and spin rate changes. This can lead to a growth in maximum yaw angles, but the effect on group size is not as large as may be thought. A lack of dynamic stability cannot make a pellet or slug suddenly yaw, but it can rapidly increase any maximum yaw angles present, so the way to combat dynamic instability is to minimize the pellet or slug yaw to start with so that the dynamic instability has nothing or very little to work on.
Miles, thanks for that! Now I have more thinking to do...
 
As in my reply above, all you can really do is to find the pellet/slug which will best match your barrel to reduce the projectile yaw rates as it leaves the gun. Choosing a twist rate which is best for the ranges you want to shoot at is also a good idea, one turn in 16-20 inches at short ranges (25 yards) changing to around twice the length for one turn at 100 yards. Speed can be optimized for wind effects and minimum yaw on leaving the gun. As I said, if there is no yaw when the projectile leaves the gun then the dynamic stability and the increased yaw wave lengths have nothing or very little to work on.
How would this explain the good groupings at 50 yds and 100 yds with 22 mrds at 960 fps out of what im told is a 1 in 30” twist?
 
How would this explain the good groupings at 50 yds and 100 yds with 22 mrds at 960 fps out of what im told is a 1 in 30” twist?
For your muzzle velocity and range it is possible one turn in 30 inches is close to the optimum for that particular pellet design and size, however it depends on the projectile design, pellet barrel fit and manufacturing consistency as well as the speed and twist. This is why I am trying to use stability factor, as it includes many of the variables I am looking at.
 
Because of the use of feathers on a shuttlecock, there is not much similarity between them and a pellet when it comes to the stabilization method. Feathers are flexible and porous, plus the flare on the shuttlecock is much larger than the rest of the birdie, unlike a pellet. There is a report on the aerodynamics of shuttlecocks from wind tunnel tests by A J Cooke at Cambridge university, which is usually cited by most people.

Shuttlecocks don't tend to spin at forty odd thousand RPM either.
 
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It has always amazed me how fast a projectile spins when fired thru a rifled barrel. 40,000 rpm is only 666 fps from a 12" twist barrel. A 22 magnum, at 2000fps with a 16" rifling spins 90,000rpm. Almost incomprehensible. A friend had a 220 swift in the 70's. He reloaded some hot rounds, velocity ? Close to 4500 fps likely. Many of those rounds never hit the target, years later I learned the bullets where self destructing due to excessive centrifugal force, they where literally flying apart from spin. Those 220 swift bullets where spinning over 250,000 rpm. We were ignorant of this at the time.
 

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