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All Springer/NP/PCP Air Gun Discussion General > "Bob and Lloyds Workshop"

External Ballistics of Pellets by Ballistician Miles Morris

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ballisticboy:
Thanks to Bob Sterne's kind offer I have now been able to post the first of the threads on stability from the UK forums onto the GTA making it accessible to everyone. Having said that I hope it is now visible to all with all the diagrams.

This is going to be a bit long. I have tried to make it as simple and none technical as possible. It does not describe the actual mechanism for stability on a pellet only the different types of stability and how they affect the pellet.
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. As the pellet flies along its trajectory the direction of the airflow will change due to winds and the pellet being pulled towards the ground but a stable pellet will try to change the way in which it is pointing to stay with the airflow (Figure 1).

Fig 1
An unstable pellet will not point in the direction of the airflow and may eventually tumble (Figure 2).

Fig 2
 When a pellet is not facing into the airflow we say it is at an angle of yaw (Figure 3) and pellet stability is all about trying to control and reduce that angle of yaw.

Fig 3
There are two basic types of stability working on any projectile as it flies through the air. These are static and dynamic 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 (figure 4). If you do not touch the weight it will just hang down under the string. This is its original position, the position it likes to sit in. This is equivalent to a stable pellet pointing directly into the airflow at zero yaw angle. If you pull the weight slightly to one side and let it go, if it is stable, it will swing back towards its original 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 original position. This type of stability is called static stability.
 
Fig 4
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 towards its original position from the other direction. Our weight will keep doing this with each swing getting a little smaller until it eventually stops back in its original position. It does this 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. 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.
 As far as pellets are concerned there are actually three types of stability acting on them and affecting their flight as there are two types of static stability. If we just think of normal dome type diabolo pellets they are what we call aero/gyro stabilised, that is they rely on aerodynamic and gyroscopic methods for static stability. The third type is dynamic stability, which is needed to stop the pellet continuously yawing about its zero yaw position as it flies along the trajectory.
When we fire a pellet it is highly unlikely that it will be pointing exactly in the direction of the air flow after it has left the barrel. This is due to many things including wind, barrel vibrations, pellet manufacturing problems etc. so it will usually have a yaw angle soon after it has left the barrel.  The diagrams below illustrate the effects on the yaw angle for the different stability states. In each case the vertical value is the angle of yaw in degrees and the horizontal is the range in yards. First (figure 5) we have a pellet which is both aerodynamically and gyroscopically unstable. That is it is statically unstable.

Fig 5
Here the pellet yaw angle will just increase until the pellet eventually faces backwards and tumbles.
Next (figure 6) is a pellet which is statically stable but dynamically unstable.

Fig 6
In this case the yaw swings through zero but each swing gets bigger and the pellet will eventually go sideways. Next (figure 7) is a pellet which is statically stable but dynamically neutrally stable. Here the swings of the pellet through zero yaw are always the same.

Fig 7
Last (figure 8 ) 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.
 
Fig 8
In reality most conventional pellets appear to be aerodynamically statically 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 static 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 statically stable projectiles are given some spin so that any 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.
Most barrels give pellets much higher spin rates than those needed to reduce side force effects. This is because, with the marginal aerodynamic stability, a degree of gyroscopic stability in addition to the aerodynamic stability is beneficial. This is why we say they are aero/gyro stabilised.
From the reported behaviour of pellets they would seem to have pretty much neutral dynamic stability, possibly changing to dynamic instability if fired at high speeds for long ranges. The change to dynamic instability is due to the increase in pellet spin rate relative to the pellet forward speed as the pellet flies along its trajectory. This apparent increase in spin rate is due to the pellet losing forward speed much quicker than it loses spin until it causes the pellet to become dynamically unstable. It appears to be the dynamic instability produced by the excess spin rate which may lead to apparent spiralling and accuracy effects at longer ranges or at higher speeds. The pellets are still statically stable, in fact the gyroscopic  stability has increased, but the dynamic instability is adversely affecting the pellet flight.
So next time you are shooting just pay those little pellets some respect and marvel at the way they still manage to go through all the complications of the different stabilities and still hit a small target. Or forget about all the science and just get on and enjoy your shooting.

rsterne:
Miles thank you VERY much for this clear explanation of static and dynamic stability, as it applies to pellets....  I am making this a "sticky" so that it stays near the top of the Workshop pages.... You can still add to it, and comments will be accepted, providing they stay on topic....

Bob

WhatUPSbox?:
Yes, thank you for starting with a definition of the terminology as you use them. The term stability has a broad range of uses in different engineering discussions. I'm looking forward to the rest the threads.

rsterne:
I have combined both of Miles' threads on Pellet Stability into one, which will remain a "sticky" in the Workshop.... This should make them easier to find for all concerned.... My apologies that some of the Avatars and signatures have been lost, but I have credited the replies to the person who submitted them, and they are exact copies of the original posts....

Bob

Debunking the Myth of Drag Stability by ballisticboy (Miles)….

I have previously tried to explain the different types of stability used by pellets. Here I hope to be able to debunk a very common myth on pellet aerodynamic stability and that is the myth that pellets are drag stabilised.
In a recent video by one of the leading air rifle video producers he went to great lengths to explain pellet aerodynamic stability and how it differs from slugs. Unfortunately, he just repeated everything else which has been said before. Fig 1 below is close to one of his main diagrams and is typical of many diagrams used to explain drag stability on pellets.

 
Fig 1

The claim is that the drag pulls back on the pellet due to the centre of pressure (CP) being behind the centre of gravity (CG) thus making the pellet stable. This is complete bunkum based on a total lack of knowledge on the basics of aerodynamic stability. It also fails to explain why a wadcutter pellet is apparently still stable despite the vast majority of its drag being at the front rather than the back of the pellet.
Before we get into the true aerodynamic stability on pellets I need to explain a few basic definitions. First is the CP. On any projectile moving through the air there are not just one or two forces acting on it. The air is working all over of the object producing forces of differing sizes and directions everywhere on the objects surface. To simplify things we create an artificial point in the object where, if we sum all of the different forces to produce one total force, we can say that if that total force were to act through that point it would produce the same force and moment about the centre of gravity as all the individual forces acting over the object (fig 2).

 
Fig 2

The other terms which need defining are lift and drag. Drag in particular is a commonly used term without many of its users knowing exactly what it is. In fig 2 you can see that I have drawn a force acting through the CP at an angle to the pellet. This single force is usually split up into two separate forces acting at right angles to each other commonly referred to as lift and drag (fig 3).

 
Fig 3

The drag is defined as the force acting in the direction of the air flow and the lift is the force acting at right angles to the air flow. The yaw angle of the pellet is not relevant, the lift always acts at right angles to the airflow and the drag in the line of the airflow. The lift is often shown as acting vertically but on a projectile it can act up, down sideways or any combination of the directions which are at right angles to the air flow. It is the forces acting at right angles to the airflow which principally define the position of the CP, drag has very little effect.
Aerodynamic stability does not depend on forces. Aerodynamic stability is a function of the aerodynamic moments about the CG. Aerodynamic moments are derived from the product of the force multiplied by the distance between the CG and the line of action of the force. If a force acts through the CG it does not matter how large it is it cannot produce a stabilising or destabilising moment as there is no distance between its line of action and the CG. This is something many presenters do not seem to understand as they constantly talk about forces.
Pellets, like all unguided projectiles, can only be accurate if the yaw angles are kept small. In the case of pellets the angles need to be 1 degree or less after leaving the barrel. This means that the distance between any drag force line of action and the CG is minute. The line of action of the lift force going through the CP however is relatively very large enabling the lift forces to produce stabilising moments. The diagram (fig 4) shows the length of the relative distances if the pellet were at 5 degrees i.e. five times greater than normal.


Fig 4

Now some will argue that the drag at very low angles is much greater than the lift. This is true but there is another problem about where the line of action for the drag force actually lies and which component of drag it is which could be providing any stabilising moment. To look at this it is convenient to look at the forces in another way.
When modelling pellet trajectories using the complex models or looking at pellet stability it is rare that lift and drag are used. Instead what are called normal and axial forces are used. The normal and axial forces are the same as the lift and drag except that they use the pellet as the reference rather than the air flow direction (fig 5). They give a better representation of the forces and moments acting on the pellet and make it easier to understand.


Fig 5

If you compare the two diagrams (fig 3 and fig 5) you can see that the normal force provides the majority of the lift and the axial force provides the majority of the drag and hence at small angles, because it acts directly through the CG, most of the drag cannot provide a stabilising moment. It has been shown in wind tunnel tests that the axial force does not change in magnitude until large angles of yaw are obtained so any change in drag at low yaw angles is caused by the tiny component of normal force in the drag direction. The normal force component acting in the drag direction is going to be much smaller than the component acting in the lift direction further reducing any stabilising moment contribution.
Some people have tried to explain drag stability by claiming that when a pellet is at yaw the frontal area is greater as the air will be able to hit more of the flare than it could see before thus producing a correcting force on the flare. If your pellet was travelling at 6000ft/sec in the upper atmosphere this argument would have some validity. The subsonic aerodynamics of pellets work in a totally different way through suction forces not high pressure impact forces.
This is why the correct term is flare stabilised, not drag stabilised as it is the lift produced by the flare which gives the dominant stabilising moment, not the drag and certainly not as in fig 1. True drag stabilisation requires a completely different type of stabilising device which you wouldn’t want on your pellets.

My thanks to Bob again for making it possible to post this thread.

rsterne:
By Devil's Luck....

A very interesting read.

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