GTA

All Springer/NP/PCP Air Gun Discussion General => "Bob and Lloyds Workshop" => Topic started by: ballisticboy on February 23, 2020, 08:49:23 AM

Title: External Ballistics of Pellets by Ballistician Miles Morris
Post by: ballisticboy on February 23, 2020, 08:49:23 AM
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).
(https://i378.photobucket.com/albums/oo221/rsterne/Miles/stable_zpshf4brw9z.jpg)
Fig 1
An unstable pellet will not point in the direction of the airflow and may eventually tumble (Figure 2).
(https://i378.photobucket.com/albums/oo221/rsterne/Miles/Unstable_zpsygc4ilsv.jpg)
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.
(https://i378.photobucket.com/albums/oo221/rsterne/Miles/Yaw_zpsdyky0wal.jpg)
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.
(https://i378.photobucket.com/albums/oo221/rsterne/Miles/stability_zpsmuj6wxjt.jpg) 
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.
(https://i378.photobucket.com/albums/oo221/rsterne/Miles/yaw1_zpsxeysp0r8.jpg)
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.
(https://i378.photobucket.com/albums/oo221/rsterne/Miles/yaw4_zpso0shpfsr.jpg)
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.
(https://i378.photobucket.com/albums/oo221/rsterne/Miles/yaw3_zpsowydijvy.jpg)
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.
(https://i378.photobucket.com/albums/oo221/rsterne/Miles/yaw2_zpstnobp2ny.jpg) 
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.
Title: Re: Types of Stability Affecting Pellets
Post by: rsterne on February 23, 2020, 01:48:52 PM
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
Title: Re: Types of Stability Affecting Pellets
Post by: WhatUPSbox? on February 23, 2020, 03:41:47 PM
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.
Title: Debunking the Myth of Drag Stability
Post by: rsterne on February 28, 2020, 02:13:30 PM
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.

 (https://i378.photobucket.com/albums/oo221/rsterne/Miles/1%20Drag%20Stability%20Wrong_zpsoqzvy3ex.jpg)
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).

 (https://i378.photobucket.com/albums/oo221/rsterne/Miles/2%20Lift%20Stability_zpslmzqqx5g.jpg)
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).

 (https://i378.photobucket.com/albums/oo221/rsterne/Miles/3%20Lift%20and%20Drag_zpscdslbfgh.jpg)
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.

(https://i378.photobucket.com/albums/oo221/rsterne/Miles/4%20Moment%20Arm_zpslai3c3in.jpg)
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.

(https://i378.photobucket.com/albums/oo221/rsterne/Miles/5%20Normal%20Forces_zpsioqhnhw6.jpg)
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.
Title: Re: Types of Stability Affecting Pellets
Post by: rsterne on February 28, 2020, 02:18:03 PM
By Devil's Luck....

A very interesting read.
Title: Re: Types of Stability Affecting Pellets
Post by: rsterne on February 28, 2020, 02:20:03 PM
By TPL (Timo)

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.
I made a pair of pictures based to same diameter same length bullet by Kolbe's calculator which I have tested in practic and found to be spot on by few %. We must call this slug because Kolbe does not include pellet form. But anyway there is something interesting for this particular question.

First picture is sharp nose blunt base bullet and what interest us the most is subsonic speed.

(https://img.aijaa.com/b/00556/14801853.jpg)

...compared to blunt nose boat tail bullet of same size.

(https://img.aijaa.com/b/00393/14801855.jpg)

Remarkable difference in BC and drag. I'm sure you as a ballistic expert can explain this to me.
Title: Re: Types of Stability Affecting Pellets
Post by: rsterne on February 28, 2020, 02:22:47 PM
By MJP (Marko)....

Oh man, your static force picture is way out. First of all the normal force is pointed inward from the arc of flight, and so is gravity, you have one force forward and that is the momentum of the pellet, in tangent of the arc of flight.
Then there is air friction slowing the pellet down force vector pointing straight against from the direction of movement. From your picture I would say the pellet has no mass and it would just float to space.

Marko
Title: Re: Types of Stability Affecting Pellets
Post by: rsterne on February 28, 2020, 02:24:34 PM
By superchikn (Ray)….

My head hurts!
Title: Re: Types of Stability Affecting Pellets
Post by: rsterne on February 28, 2020, 02:25:56 PM
By ballisticboy (Miles)….

Not sure which picture it is you appear to be miss-understanding bit I will try to work through your comments.

Oh man, your static force picture is way out. First of all the normal force is pointed inward from the arc of flight, and so is gravity, you have one force forward and that is the momentum of the pellet, in tangent of the arc of flight.

The normal force on a projectile is defined as any force at 90 degrees to the projectile axis so it can be up, down to either side, any direction as long as it is at 90 degrees to the central axis based on the projectile axis based system. Normal forces are usually produced by the projectile being at an angle of yaw to the airflow with the force being in the same direction as the yaw. Momentum is not a force, it is normally taken as mass times velocity. The diagram is of aerodynamic forces. Projectile weight from the acceleration due to gravity is not included as it is not an aerodynamic force and makes no contribution to the stability moments since by definition it acts through the centre of gravity.

Then there is air friction slowing the pellet down force vector pointing straight against from the direction of movement. From your picture I would say the pellet has no mass and it would just float to space.

Marko

Air friction is only one small part of the total projectile drag force which consists mainly of form drag, friction drag, base drag (the main contributor in many but not all pellets) and yaw induced drag. Again, because the line of action of the drag force acts through or very close to the centre of gravity, it produces negligible stabilising moments. I am not sure why you want mass in a diagram of aerodynamic forces, particlarly as mass is not a force and is irrelevant to stability having no moment about the centre of gravity.

Perhaps I did not explain things clearly enough in the OP.
Title: Re: Types of Stability Affecting Pellets
Post by: rsterne on February 28, 2020, 02:26:58 PM
By ballisticboy (Miles)….

I made a pair of pictures based to same diameter same length bullet by Kolbe's calculator which I have tested in practic and found to be spot on by few %. We must call this slug because Kolbe does not include pellet form. But anyway there is something interesting for this particular question.

First picture is sharp nose blunt base bullet and what interest us the most is subsonic speed.

...compared to blunt nose boat tail bullet of same size.

Remarkable difference in BC and drag. I'm sure you as a ballistic expert can explain this to me.

I would suggest that you are attempting to use the Kolbe calculator way outside its limits of applicability. I believe it is based on the Bob McCoy equations and the drag calculation is probably the same. Bob made the assumption that a flat meplat makes no contribution to drag in the McDrag software. This was a perfectly reasonable assumption for the shell and bullet meplats the program was designed for. However, when meplats start to get larger than 10-15% of calibre then the errors start to get large and when it is as big as in your example then it is completely wrong. The program is assuming the flat front face makes no contribution to the drag which is obviously wrong. I know about Bob McCoys software as we exchanged aerodynamic prediction programs when we were both working for our respective government departments, that is how RARDLIFT ended up on the JBM website.
Title: Re: Types of Stability Affecting Pellets
Post by: rsterne on February 28, 2020, 02:27:36 PM
A couple of things I will try and explain.... First, Timo is correct, when you use the Kolbe Drag Calculator, at subsonic velocities the Meplat diameter has little effect on the drag.... I always wondered about that, but since it, and the nearly identical drag calculator on the JBM website, had the same conclusions, I assumed that was correct.... Interestingly , the JBM calculator will not allow you to input a Meplat larger than 30% of the caliber (a restriction the Kolbe calculator does not have, but should)…. They are both based on the math of Robert McCoy, from his "McDrag" software, and Miles kindly explained to me that McDrag was developed for calculating the drag of artillery shells, none of which have much of a Meplat…. Therefore, using them for the large Meplats typical of airgun slugs will produce flawed results.... Miles is a contemporary of McCoy, and with over 40 years of employment studying Exterior Ballistics for the UK Government, we would be well advised to heed his advice.... Large Meplats will increase the drag, particularly if the edge between the Meplat and the Ogive is sharp.... A surprisingly small radius there reduces the drag a lot....  8)

As to the concept that diabolo pellets are not "drag stabilized", but instead stabilized by lift forces, acting through the CP, and creating a "moment" about the CG that corrects the flight path, I freely admit that was not something I was familiar with, nor had I even considered it.... I have always assumed it was the drag being behind the CG the made the pellet "straighten out and fly right" (apologies to Nat King Cole)…. Miles correctly points out that with a Wadcutter, where a large part of the drag is on the front, will not have the CP much, if at all, aft of the CG, so the concept that the drag, which is almost exactly on the centerline and acts parallel to it, produces enough moment about the CG to "steer" the pellet straight makes no sense.... I got it wrong, and I apologize for perpetuating the myth....  :-[

The key for me, in understanding what Miles was saying about pellet stability, was to ignore the shape of the pellet and think about it acting like the tail of an aircraft.... If it is yawed to the line of flight, it produces lift, which acts "normal to" (ie at 90 deg.) to the centerline of the pellet.... That lift acts through the CP.... If the CP is behind the CG, then that provides a correcting moment which tends to reduce the yaw.... After oscillating from side to side, and assuming the pellet also has dynamic stability, the yaw reduces and the pellet flies straight, or nearly so.... Yes, the pellet isn't shaped very efficiently to be considered a wing, but the lift is a "vector sum" of all the side forces on the pellet (positive and negative), and those forces will always be away from the line of flight because the yaw is creating an "angle of attack" for the pellet as a whole.... By definition, the CP is the point through which the sum of the lift forces act.... Since that is behind the CG that causes a moment, or "torque" if you like, about the CG.... and that moment reduces the yaw angle.... which is the definition of aerodynamic stability (yaw is reduced in flight instead of increased)…. The flare at the rear of the pellet is the main contributor for moving the CP aft, hence why you would consider a pellet to be "flare stabilized"....

With a slug, the CP is forward of the CG, so the slug is unstable, and without spin the yaw would increase until it tumbles.... That is why a slug requires gyroscopic stability, because its aerodynamic stability is negative....

I would like to thank Miles for explaining the various types of stability, and for correcting my erroneous use of the term "drag stabilized".... I got it right when I said that there is a correcting moment because of the CP being behind the CG.... What I didn't realize is that it was actually a lift force, acting at right angles to the line of flight (ie "normal to" ) that created this moment, not the drag force acting parallel to it....

Bob
Title: Re: Types of Stability Affecting Pellets
Post by: rsterne on February 28, 2020, 02:28:18 PM
By MJP (Marko)….

Ok my mistake interpreting your picture on my mobile.
Well I used air friction as my native language is not English. Drag would have been a better word but it slipped my mind at the time of writing.
I see now where that lift comes from, but do you call it lift if the pellet is at its opposite oscillating position nose pointing downward.
As with that is the nominal flight model if there is no spin stabilization the pellet is jawing in a circular manner in flight wagging it's tail as the lift goes from up down side to side with wind and as the lifting force changes.
Oscillating wobling, I don't know the term in English.
As the high and low pressure areas change as the orientation is bound to change with the lift vector.
Lift pushes the skirt up and the high and low pressure areas follows the motion accordingly now the lift vector is pointing down and so on.

Marko
Title: Re: Types of Stability Affecting Pellets
Post by: rsterne on February 28, 2020, 02:30:13 PM
By WhatUPSbox (Stan)….


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.

Do you have any links or references to pellet tests with varied yaw angles? I've found wind tunnel and CFD results for pellets but they are all aligned with the flow.
Title: Re: Types of Stability Affecting Pellets
Post by: rsterne on February 28, 2020, 02:30:33 PM
Quote
do you call it lift if the pellet is at its opposite oscillating position nose pointing downward.

Yes, it's just lift in the downwards direction.... It could just as easily be to the side, or on any angle in between, since the pellet can be yawed in any direction.... as it would be if it left the muzzle crooked.... In fact, since the pellet is spinning, and hence seeing precession and nutation (wobbling), the lift vector is always changing.... What is important is that since the CP is behind the CG, it is always trying to reduce the yaw at that instant.... which is what we call aerodynamic stability....

It's a slightly difficult concept to grasp, but once the lightbulb goes on, it makes perfect sense....  8)

Think about a football (pointed elliptical) shape, with an internal weight inside the nose, so that the CG is well forward of the CP.... It would tend to fly straight, even without spin.... Now move the internal weight to the back, so that the CG is behind the CP.... It will tend to swap ends and fly backwards, right?.... Now spin it fast enough so that it has gyroscopic stability.... Even with the weight in the back, it will remain flying point forward.... Normal footballs (not talking a soccer ball, sorry non-North Americans) have the CG at the center, and because of their shape and speed, the CP is slightly forward of that.... so unless you spin them, they tend to tumble.... Give them even a relatively slow spin rate, and then they fly straight....

Bob

Thank you for your patience while I combined Miles' threads on Stabilty…. It will be much easier to find them as a single "sticky"....
It is the plan for Miles to add additional topics in this thread to make it a valuable archive on External Ballistics.... Stay Tuned !!!!


Bob

Title: Re: Types of Stability Affecting Pellets and Other Stability Topics
Post by: johnnyfoos on February 29, 2020, 07:58:33 PM
Thanks to ALL !

Yes my head did feel this some, but
I do understand.

SO-
"and Other Stability Topics"
I didn't see anything about the old round ball, ?
I was looking for anything to explane why they work so good,
{enough for what I use them for at least}
I know why they fly so much farther than the pellets
but
 a slightly difficult concept to grasp
is why almost no one likes them,
I do and use them and hit what I'm shooting at.
Just
sayn
$0.02
Title: Re: Types of Stability Affecting Pellets and Other Stability Topics
Post by: rsterne on February 29, 2020, 10:53:56 PM
The only reason for twist when shooting a roundball is to even out the deflection from any imperfection in the ball.... ie the CG not being in the center, or the sphere not being accurate.... You certainly don't need to have a rifling twist any faster than 100 x the caliber.... ie 45" on a .45 cal roundball…. and even slower may be just fine....

Bob
Title: Barrel Twist Rate Effects on Impact Error Caused by Pellets with an Offset CG
Post by: ballisticboy on March 01, 2020, 07:58:37 AM
There are plenty of videos on YouTube which will tell you anything you want to know about your gun and pellets including rifle twist rates but they cannot go into the detail. Scientific experiments on twist rates are virtually impossible to carry out since you cannot eliminate the other sources of error which will have a primary effect on your results. This is where modelling has to take over as we can set up any experiment we want inside a computer.
I have recently come across a different trajectory model in which we can put asymmetries into the ammunition. There are some problems with the output for pellets where the units are only to the nearest millimetre but we can get some preliminary results.

I have been modelling the effects of the centre of gravity (C of G) not being exactly on the centreline of the pellet. In fact I assumed it was 0.1mm off the centreline and then carried out a lot of runs to see the effect on the group size at 50 metres range. I had to use 50 metres and not 50 yards as the model works in metres and I haven’t had time to change it yet. The aerodynamic data was the same as I have used for other modelling work I have posted on here and is strictly only applicable to the AAField type pellets in .22 calibre. The muzzle velocity was 585ft/sec which gives just barely over 12FPE.

If you fire a pellet which is a perfect fit in your barrel but with an offset C of G there are two sources of error. One is the effect of the C of G offset during the pellet flight and the other is due to what happens to the pellet as it leaves the barrel. Now what happens to the pellet as it leaves the barrel is not exactly clear. When the front of the pellet leaves the barrel the C of G will start to move sideways due to the rotation of the pellet and the offset distance from the centreline. The back of the pellet is still in the gun barrel and cannot move sideways so the pellet will start to yaw away from pointing in the straight ahead direction. At some point the back of the pellet will also leave the barrel and is free to move sideways but it will not move sideways if the yaw rate of the pellet is high enough for the sideways movement of the C of G. Someone, who knows far more than me about theoretical ballistics, suggested that the best approximation is to assume the rotational momentum of the offset C of G is entirely transferred into the yaw momentum so that we can calculate an initial yawing rate for the pellet. This is what I have done for the following results involving yaw rates.

The first set of results, figure 1, are for a pellet which leaves the barrel perfectly, i.e. no yaw rate, but which has an offset C of G (I would like to see someone try to set that up in an experiment). So this is purely down to the effect of the offset C of G on the pellet flight. The figure shows how the error at 50 metres will change depending on the barrel twist rate. Each point represents a result from the model and the line is just a best fit for the data. In this case a straight line represents it fairly well. It shows how as pellet spin rates get higher i.e. less inches per turn, the error due to the offset itself gets to be insignificant.

(https://i378.photobucket.com/albums/oo221/rsterne/Miles/Off1_zpssrdtfdek.jpg)
Fig 1
 
As I said above the pure offset error is only half of the total effect. There is also the effect of the initial yaw rate created as the pellet leaves the barrel. The figure 2 shows the effect of barrel twist rates on the error caused by the initial yaw rate.

(https://i378.photobucket.com/albums/oo221/rsterne/Miles/Off2_zpsuazso5t1.jpg)
Fig 2
 
In this case the best line fit is a curve which is very close to being proportional to  the reciprocal of the barrel twist rate. As you would expect, the error gets worse as we increase the spin rate of the pellet and thus the initial yaw rates on barrel exit.
So it would appear that there are two conflicting results from the two components of the total error. If we combine both the C of G offset effects and the initial yaw rate effects we get the result shown below in figure 3.

(https://i378.photobucket.com/albums/oo221/rsterne/Miles/Off3_zpsallcp9ze.jpg)
Fig 3
 
In this case the line is not a very good best fit as the relationship is fairly complex. It does show that there is a range of values for barrel twist rates which will minimise the effects of pellet offset C of G. The area of interest which encompases most of the current barrel twist rates is shown in more detail in figure 4.

(https://i378.photobucket.com/albums/oo221/rsterne/Miles/Off4_zpskjv0eyhp.jpg)
Fig 4
 
It would appear that there is a fairly flat area for twist rates between about 16 inches per turn up to 50 inches per turn. These values coincide well with the currently used common twist rates which have evolved over time. It looks like very small gains could be made by going for twist rates around 35 inches per turn but the gains are very small.
The work so far had been for .22 pellets. I repeated much of the exercise for .177 sized pellets. I have only looked at the total effect this time, not the separate components of the error as before.
Below in figure 5 is the result for the .177 pellets fired at just under 12 FPE. The CG offset I used this time is slightly less than .1mm. I did this to keep the CG offset the same percentage of the pellet diameter as for the .22 results.

(https://i378.photobucket.com/albums/oo221/rsterne/Miles/177off_zpsosykbavv.jpg)
Fig 5

You can see that the result is very similar to the previous .22 result but the optimum twist rate range seems to be narrower. It is interesting that again the optimum twist rate appears close to though just above the commonly used values.
The diagram below shows the results for both the .177 and the .22 pellets in figure 6. It shows that for this particular design the .22 appears to have slightly less error than the .177 over much of the range. The .22 though is worse at the high twist rates which is what you would intuitively expect.

(https://i378.photobucket.com/albums/oo221/rsterne/Miles/17722off_zpsjht9ummo.jpg)
Fig 6

The twist rates of most interest are shown in more detain in figure 7, again comparing the .177 and .22 results.

(https://i378.photobucket.com/albums/oo221/rsterne/Miles/17722off2_zpsjrxwqmcg.jpg)
Fig 7

You must remember that the results are for only one pellet type fired at one velocity for each calibre to a range of 50 metres. Changing any one of these variables could change the optimum value.
You should also remember that, going to the lower twist rate, could drastically reduce the variety of pellet designs which could be used in the gun and would eliminate the possibility of gyroscopically stabilised pellets. Finally, an offset C of G is not the only source of error in a gun pellet combination, others may require greater or lesser twist rates and have a bigger effect at the target.
Title: Re: Types of Stability Affecting Pellets and Other Stability Topics
Post by: rsterne on March 01, 2020, 02:38:09 PM
Miles, that is an excellent article.... I see a relationship between the caliber and the twist rate, expressed in calibers.... The "sweet spot" for the twist rate appears to be between 100 and 200 calibers, IMO.... ie 17-35" for the .177 cal and 22-44" for the .22 cal.... although twist rates just outside that range are still quite acceptable.... It is extremely interesting that traditional airgun barrels with a 16" twist are at the "fast" end of the sweet spot.... It would be very interesting to see similar data for a much higher velocity, eg. 950 fps....

Bob
Title: Re: Types of Stability Affecting Pellets and Other Stability Topics
Post by: MJP on March 01, 2020, 04:42:51 PM
This is all nice and interesting but it's just an opinion if there is no technical studies and references to actual research that have been conducted in laboratory environment to be repeatable.
So at least I for one want to see the data that has been referenced and what are their sources and reliability?

Marko
Title: Re: Types of Stability Affecting Pellets and Other Stability Topics
Post by: rsterne on March 01, 2020, 05:49:44 PM
I believe Miles clearly stated that these charts are the result of a computer model.... because of the difficulty of obtaining experimental data because of the wide number of variables.... As to the validity of using slower twists rates for pellets than what has for years being considered the "norm", you only need to look at the current offerings of slower twists barrels, and their use in benchrest competitions.... To me, this is a matter of the models confirming what we are seeing, which is always nice to see, instead of them pointing us in a different direction.... I'm sure FX has conducted the studies you seek before releasing their much slower twist pellet barrels.... but I doubt you can convince them to share that data.... although there is nothing stopping you from asking them....

Bob
Title: Re: Types of Stability Affecting Pellets and Other Stability Topics
Post by: ballisticboy on March 01, 2020, 05:56:00 PM
This is all nice and interesting but it's just an opinion if there is no technical studies and references to actual research that have been conducted in laboratory environment to be repeatable.
So at least I for one want to see the data that has been referenced and what are their sources and reliability?

Marko

This is not an opinion it is a modelling exercise based on a NATO approved sixdof model. The aerodynamic data has been created using standard projectile estimation methods and where possible calibrated against measured performance. If I start to add lists of aerodynamic references plus calibration certificates for the models it will become a scientific report not a thread on an airgun forum.
This is a typical exercise which would have to be carried out to establish the parameters needed to be observed in an experimental programme. The experimental programme would follow on as carrying out experiments without first carrying out such an exercise would be pointless since you will have no idea what to look for or what variables to control.
If you want to know more in much more depth I suggest you study basic aerodynamic slender body theory and McCoy's book on ballistics as a starting point. The blunt body handbook will also help in your own assessments of pellet aerodynamics with the report of Vaughn and Reise to help you to determin Magnus estimates.
Title: Re: Types of Stability Affecting Pellets and Other Stability Topics
Post by: WhatUPSbox? on March 02, 2020, 02:22:40 PM

If I start to add lists of aerodynamic references plus calibration certificates for the models it will become a scientific report not a thread on an airgun forum.


Miles,
Thank you for your work and taking the time to put together this informative thread.
My hope for the "Bob and Lloyds workshop" and the Engineering - Research & Development sections of the forum is that here there is an opportunity to do more of a deep dive into the technical and theoretical basis of airgunning. Unfortunately labeling results as generated from computer models or spreadsheets, for me does not provide any additional information. There is no need to defend a certification of the analysis, but some pointers to additional information for that model helps.
For example, the Wiki for external ballistics https://en.wikipedia.org/wiki/External_ballistics (https://en.wikipedia.org/wiki/External_ballistics) has a great summary of the range of computer models in use. A natural question for air guns is how are the aerodynamics modeled in the multi DOF models. It appears that some of the models use empirically generated characteristics for the projectiles. The diabolo shape is different than the typical blunt body projectile, it is not clear to me how one can decompose measured drag results into the affect yaw angle has on pellet aerodynamics.
There is some information on pellet specific analysis and testing. Ron made a great start on CFD analysis here https://www.gatewaytoairguns.org/GTA/index.php?topic=140314.0 (https://www.gatewaytoairguns.org/GTA/index.php?topic=140314.0) where he included several pellet shapes and spin (it would be great if small yaw angles could be added). A similar analysis with the affect on drag through the transonic region is here  https://www.researchgate.net/publication/316599956_Aerodynamic_and_dynamic_analyses_of_three_common_45_mm-caliber_pellets_in_a_transonic_flow (https://www.researchgate.net/publication/316599956_Aerodynamic_and_dynamic_analyses_of_three_common_45_mm-caliber_pellets_in_a_transonic_flow) .
An interesting wind tunnel test of pressure profiles on pellets and a comparison to drag data is presented here https://www.researchgate.net/publication/332156350_Influence_of_air_rifle_pellet_geometryon_aerodynamic_drag (https://www.researchgate.net/publication/332156350_Influence_of_air_rifle_pellet_geometryon_aerodynamic_drag) .

I guess my point is that in this part of the forum, there is interest in drilling down into the available data (until our heads hurt). All that is needed is some Google breadcrumbs that we can use to better understand your work without you having to post a treastise.

Thank you again, this is not a criticism, just a request for more goodies.  ;D
Title: Re: Types of Stability Affecting Pellets and Other Stability Topics
Post by: rsterne on March 02, 2020, 03:14:09 PM
Stan, those are some excellent links.... Thank you for posting them in this thread....

Bob
Title: Re: Types of Stability Affecting Pellets and Other Stability Topics
Post by: ballisticboy on March 05, 2020, 10:30:20 AM

Miles,
Thank you for your work and taking the time to put together this informative thread.
My hope for the "Bob and Lloyds workshop" and the Engineering - Research & Development sections of the forum is that here there is an opportunity to do more of a deep dive into the technical and theoretical basis of airgunning. Unfortunately labeling results as generated from computer models or spreadsheets, for me does not provide any additional information. There is no need to defend a certification of the analysis, but some pointers to additional information for that model helps.
For example, the Wiki for external ballistics https://en.wikipedia.org/wiki/External_ballistics (https://en.wikipedia.org/wiki/External_ballistics) has a great summary of the range of computer models in use. A natural question for air guns is how are the aerodynamics modeled in the multi DOF models. It appears that some of the models use empirically generated characteristics for the projectiles. The diabolo shape is different than the typical blunt body projectile, it is not clear to me how one can decompose measured drag results into the affect yaw angle has on pellet aerodynamics.
There is some information on pellet specific analysis and testing. Ron made a great start on CFD analysis here https://www.gatewaytoairguns.org/GTA/index.php?topic=140314.0 (https://www.gatewaytoairguns.org/GTA/index.php?topic=140314.0) where he included several pellet shapes and spin (it would be great if small yaw angles could be added). A similar analysis with the affect on drag through the transonic region is here  https://www.researchgate.net/publication/316599956_Aerodynamic_and_dynamic_analyses_of_three_common_45_mm-caliber_pellets_in_a_transonic_flow (https://www.researchgate.net/publication/316599956_Aerodynamic_and_dynamic_analyses_of_three_common_45_mm-caliber_pellets_in_a_transonic_flow) .
An interesting wind tunnel test of pressure profiles on pellets and a comparison to drag data is presented here https://www.researchgate.net/publication/332156350_Influence_of_air_rifle_pellet_geometryon_aerodynamic_drag (https://www.researchgate.net/publication/332156350_Influence_of_air_rifle_pellet_geometryon_aerodynamic_drag) .

I guess my point is that in this part of the forum, there is interest in drilling down into the available data (until our heads hurt). All that is needed is some Google breadcrumbs that we can use to better understand your work without you having to post a treastise.

Thank you again, this is not a criticism, just a request for more goodies.  ;D

I will try to answer as best as I can, but first I think I need to explain the purpose of the exercise in question. A modelling exercise such as the one I reported on is not and never will be a final answer. It is only the first stage in trying to look at what the effects of certain parameters are on the flight of pellets and how important each of those parameters is. It is up to the experimentalists to use the information to guide the experiments to prove or disprove the work the work in the real world. As for whether the post provides additional information or not that is really down to the reader and exactly what he expects from what is written. Perhaps some are expecting too much from such early work.
One other thing I would make clear here is that pellets are no different to any other projectile in the way they are analysed or tested. There are plenty of projectiles of similar shapes, including long rod proof shot or shuttlecocks which are more difficult.

As to the provenance of the trajectory model reference material is difficult as much of it is classified and thus not available. As I have said before the trajectory model is a standard six degree of freedom model specifically produced for spinning shell, unlike many which are adapted from missile programs and thus not always suitable. It uses the standard Runge Kutta fourth order integration routine using time stepping.
More important than the model is the data used for the aerodynamic and mechanical input. I first created the model about 10 years ago using the same methods and reference material I had used for predictions on projectiles ranging from orbital capability gun launched rockets down to particle sized warhead slugs at velocities ranging from 10 kilometres per second down to 60 metres per second. The basic system is common to all aerodynamic prediction in that the projectile is broken down into separate components and then summed to give the overall prediction. Mechanical properties were produced by creating a small program which takes the external and internal shape of the projectile, slicing it along its length into hundreds of discs which are then summed to produce the overall CG, mass and inertial values. The program was checked against standard shapes such as cones, cylinders, hemispheres etc. to assess its accuracy.

The production of the aerodynamic and inertial model is only the starting point for the data package. The standard method for producing projectile data packages for projectile flight and artillery fire control uses the same methods for aerodynamic predictions. The next stage is to fire range and accuracy trials under carefully controlled conditions (much more controlled than specified in the NATO stannags) and to use the information to adjust the data to fit the results. For large calibres spark ranges can be used to generate more detailed data but they are not very effective for small arms. This is due to the distance between the spark stations which tend to be too far apart for small projectiles and thus miss much of the data. Alternative systems such as flight follower camera systems or radar based MRDR systems can produce a continuous set of data over a short range but each have their own limitations. Obviously such data is not available for pellets but there is some data and reported behaviours to guide the data package. For example, drag is relatively easy to modify as there is much data available. The drag data I use in my pellet data is based on my own measurements and many other measurements. The spin damping term is based on measured Australian data published some years ago. The Magnus terms are more questionable. They have been adjusted from the initial estimates to reflect known pellet behaviour, such as the loss of dynamic stability. There is still room for improvement in the high speed behaviour. Recent modelling is giving the loss of dynamic stability but not showing the expected increase in dispersion. The sub 12FPE shows much better correlation, probably due to having received much more attention. Other properties such as the aerodynamic centre position (CP) are much harder to pin down but not impossible. Spin drift is a very good indicator but difficult to measure. I have devised a method by which I think it ca be derived but it needs a carefully set up trial preferably indoors. What can be said though is that pellets have very small values of aerodynamic pitching moments due to the small distance between the CP and CG which drives much of the pellet behaviour and problems. It also means that for small dispersion pellet yaw angles must remain very low. Since yaw drag is a function of yaw squared then yaw drag will be largely negligible in a well behaved pellet.

Although much of the useful material is classified there is some available. For ballistics the best reference is the "Textbook of Ballistics and Gunnery" Volume 1 published by Her Majesty's Stationery Office in 1987. It is very difficult to find but I know some people have managed to obtain copies through libraries. It contains all of the maths and much more. An alternative which is much easier to obtain is McCoy's Modern Exterior Ballistics, but I believe there may still be some errors present even in the latest revised versions so if you can always try to follow the maths and check it. Any reference on external ballistics will tend to be maths heavy and not light reading as it is a very mathematical subject. For aerodynamic prediction a good starting point is the Handbook of Blunt-Body Aerodynamics Volume 1 produced by NOL. Additional drag data can be found in Hoerner's Fluid Dynamic Drag. Both of the aerodynamic books can be found from internet searches.

As for the references quoted in the post above, I personally have always been disappointed in the Wikki entry and I did not find the entries on trajectory models very good at all. It concentrates far too much on historical obsolete methods and largely ignores the work of the US pioneers such as Murphy or Lieske in the 50's and 60's. Maybe it is because it seems to be biased more towards small arms rather than artillery. The small arms industry as a whole is of course only just catching up with large calibre ballistic methods now, 50 years late. Unfortunately they seem to be trying to re-invent everything rather than using what is already well known. The wind tunnel tests seem to be better except for the pellet choice. The dome pellet is a high drag design whereas the wadcutter has very rounded edges. The pellet choice has influenced their conclusions on the drag distribution. I am also puzzled why they chose .177 rather than .22 which would have reduced interference from the sting etc. As for the use of CFD it is always useful for producing pictures but it has always been extremely difficult for producing accurate aerodynamic data for projectiles with unknown aerodynamic properties. Projectiles with known properties can be analysed and results produced which match. My comments are based on CFD results for many projectiles over the last 30 years.
Title: Re: Types of Stability Affecting Pellets and Other Stability Topics
Post by: rash on March 05, 2020, 11:40:45 AM
Thanks Miles!

I figured most of your work was and still is, classified.
Title: Re: Types of Stability Affecting Pellets and Other Stability Topics
Post by: TPL on March 07, 2020, 08:52:03 AM
I couldn't imagine how secret this is. Please save me about all the details you could tell but then have to kill me.  :-X
Title: Re: Types of Stability Affecting Pellets and Other Stability Topics
Post by: rsterne on March 07, 2020, 02:11:13 PM
Timo, no reason to be rude....  >:(

Bob
Title: Re: Types of Stability Affecting Pellets and Other Stability Topics
Post by: rgb1 on March 08, 2020, 10:44:09 AM
I have Blunt Body Aero and McCoy corrections if anyone wants them.


                                                                     Ron
Title: Re: Types of Stability Affecting Pellets and Other Stability Topics
Post by: rsterne on March 08, 2020, 01:56:31 PM
It would be helpful if you explain that, please, Ron.... and I would love a copy....

Bob
Title: Re: Types of Stability Affecting Pellets and Other Stability Topics
Post by: WhatUPSbox? on March 08, 2020, 03:14:48 PM
The blunt body handbook is available on DTIC https://apps.dtic.mil/dtic/tr/fulltext/u2/776586.pdf (https://apps.dtic.mil/dtic/tr/fulltext/u2/776586.pdf)
Title: Re: Types of Stability Affecting Pellets and Other Stability Topics
Post by: rsterne on March 08, 2020, 03:41:51 PM
Thanks, Stan.... but it's way beyond me....  ::)

Bob
Title: Gyroscopic Stability
Post by: ballisticboy on March 16, 2020, 07:45:54 AM
I am going to try to explain how gyroscopic stability works. It is a relatively simple phenomenon, easy to demonstrate in a 3D environment but not easy to show on a 2D screen. Some people misunderstand what gyroscopic stability does to their pellets. Gyroscopic stability does not keep a pellet or any other spin stabilised projectile pointing in the same direction as the barrel. Gyroscopic stability turns a projectile to face directly into the airflow. In this way a projectile can follow the curve of a trajectory.
 
If there is gross gyroscopic over stability then the projectile has problems in being able to turn to follow the trajectory and will try to keep pointing in the direction of the barrel. However, the levels of gyroscopic over stability required to reach this state are unlikely to be attained by pellets or any other airgun fired projectile unless it is fired straight up into the air or from the top of mount Everest. It has also been suggested that gyroscopic over stability is a cause of spiralling. I cannot see how gyroscopic over stability can be a cause of pellet spiralling, particularly as I have encountered over stable projectiles and they drifted sideways by a long way rather than develop an apparent spiral. The other factor against this theory is that the level of gyroscopic stability required is about a factor of ten higher than seen on pellets, even at long ranges from pellets fired at high speeds.

In order to try to explain how spin stabilisation works I want you to imagine a pellet which is not pointing directly into the airflow, it is at an angle of yaw (fig 1). The angle is shown as being vertically up but it could be in any direction.

(https://i378.photobucket.com/albums/oo221/rsterne/Miles/Gyro1_zpspwc9v5a1.jpg)
Figure 1

The object of any type of stabilisation is to try to reduce the angle of yaw. Spin stabilisation achieves this through a feedback system. For a pellet at yaw a lateral force is created by the airflow around the body usually centred at a point behind the centre of gravity (CG) called the centre of pressure (CP). The lateral force produces an aerodynamic moment about the CG. It is the aerodynamic moment which is important.

It is a popular misconception that stability is dependent on forces. It is not. Stability is all about moments about the CG, not forces. Yes forces are required but only in that they are one component of the moment, the other being the distance between the CP and the CG. If you had an infinite force acting through the CG it wold make no contribution to stability as the moment about the CG would be zero. Similarly gyroscopes react to moments, not forces when they change their attitude.

When a spinning projectile is subjected to an aerodynamic moment as in figure 1 the gyroscopic reaction is to cause the projectile to yaw about the CG, not in the same direction as the applied moment as you would expect, but in a direction at ninety degrees as shown in figure 2.

(https://i378.photobucket.com/albums/oo221/rsterne/Miles/gyro2_zpsfsbyymfe.jpg)
Figure 2

In figure 2 you are looking directly at the front of the pellet coming towards you with right hand spin. As a result of the movement of the pellet about the CG we now have the original vertical yaw angle from figure 1 and a second yaw angle caused by the gyroscopic reaction at ninety degrees to the original angle as seen in figure 3.

(https://i378.photobucket.com/albums/oo221/rsterne/Miles/gyro3a_zpshrsrckbc.jpg)
Figure 3

The pellet now has a sideways yaw angle as well as the original vertical one. As a result of the new yaw angle to the side the pellet will have a new aerodynamic side force causing a side aerodynamic moment about the pellet CG. This new aerodynamic moment will produce a gyroscopic reaction in a vertical direction as can be seen in figure 4.

(https://i378.photobucket.com/albums/oo221/rsterne/Miles/gyro3b_zpshm0rmhka.jpg)
Figure 4

As can be seen in figure 4 the gyroscopic reaction to the new sideways aerodynamic moment is to reduce the original vertical yaw angle. The reduction in the vertical angle will in turn reduce the sideways yaw angle as the aerodynamic moment is getting less reducing the gyroscopic reaction. Thus both yaw angles are reducing (figure 5) and the pellet is getting closer to pointing directly into the airflow as a stable pellet should.

(https://i378.photobucket.com/albums/oo221/rsterne/Miles/gyro5_zps5uz6x1z3.jpg)
Figure 5

All of the figures have shown how a spinning pellet reacts. Pellets are usually aerodynamically stable i.e. the CP lies behind the CG. Slugs and bullets are generally aerodynamically unstable and have a CP in front of the CG. This causes differences but the fundamental mechanism remains the same. For example, if we are looking at our pellet from the back as it flies away from us, an upwards vertical yaw will cause the pellet to yaw to the left as a result of the gyroscopic reaction. A slug or bullet will yaw to the right, not the left, as a result of being aerodynamically unstable. I will leave an explanation of this to another post as this one is quite long and complicated enough for now.
Title: Re: Types of Stability Affecting Pellets and Other Stability Topics
Post by: rsterne on March 16, 2020, 04:44:04 PM
That is an EXCELLENT article on how Gyroscopic Stability affects a pellet, Miles.... The step by step sequence makes it understandable, and the drawings are excellent.... Thanks for your continuing contributions to our understanding of a very complex subject....

Bob
Title: Re: Types of Stability Affecting Pellets and Other Stability Topics
Post by: WhatUPSbox? on March 18, 2020, 01:53:48 PM
Miles,
Thank you for the detailed descriptions.

In your first post you showed several stability characteristics as a function of range. I realize those plots were there to help define the terminology, but is that a standard output of your model? For a specific set of parameters (pellet type, velocity, twist rate, atmospheric conditions, etc.) will your model produce a flight path of the other 5 DOF as a function of range? It would be interesting to see which effect dominates and if that changes over the flight path.

In your charts of the effect of twist rate, you used a CG offset of .1 mm. For a 4.5 or 5.5 mm pellet, that seems to represent a fairly large defect. Do the results scale down as you reduce the CG offset or do other effects dominate?

Thank you again for putting together this series.
Title: Re: Types of Stability Affecting Pellets and Other Stability Topics
Post by: ballisticboy on March 23, 2020, 09:21:24 AM
Miles,
Thank you for the detailed descriptions.

In your first post you showed several stability characteristics as a function of range. I realize those plots were there to help define the terminology, but is that a standard output of your model? For a specific set of parameters (pellet type, velocity, twist rate, atmospheric conditions, etc.) will your model produce a flight path of the other 5 DOF as a function of range? It would be interesting to see which effect dominates and if that changes over the flight path.

In your charts of the effect of twist rate, you used a CG offset of .1 mm. For a 4.5 or 5.5 mm pellet, that seems to represent a fairly large defect. Do the results scale down as you reduce the CG offset or do other effects dominate?

Thank you again for putting together this series.

First of all let me apologise for not responding earlier. The model output can be almost anything you want. The standard outputs are range, height, drift, velocity, total yaw, vertical yaw, horrizontal yaw, and SG. Things such as spin rate, energy etc. could also be output if wanted.

At usual twist rates the effect of a CG offset is largely a function of the offset squared. At very low twist rates this relationship changes due to the effect of the offset on pellet attitude in flight. In practice pellets will have other defects as well. One I have modelled in sub 12FPE is the effect of a small flat area facing the airflow on the front of a pellet creating an offset drag force which creates a small moment about the CG. There will also be the effects of yaw rates created by vibrations generated when the pellet is in the gun barrel.

All these things can be modelled both individually and in combination if you know their relative sizes and orientations. It is the measuring and knowing the relative sizes which makes it impossible to recreate individual shots. All we can do is assume certain sizes for each defect and look at the relative effects on the pellets. Modelling can show us which are important and which we should not worry about, it will not give us exact answers. One thing which has come out so far is that the orientation between the different defects can have a large effect on the dispersion which may go some way towards explaining some of those random flyers.
Title: Why Pellets Drift Downwind
Post by: ballisticboy on April 04, 2020, 06:45:27 PM
One thing which affects all shooters, but in particular the air gun shooter, is the effect of a cross wind giving downwind drift. Here I will try to explain in a simple way how downwind drift is produced and how it varies with range and speed so that readers may understand better how their pellets are affected. I will not look at the vertical effect of a cross wind as that is much more complicated but I will say that contrary to popular myth it is not due to Magnus.

When a pellet is fired in the air, as everyone knows, it slows down. To reach a certain range from the gun, because it slows down, it will take longer to reach that range than it would have done if it had just kept on going at the same speed. Because the pellet starts to slow down almost immediately after it has left the barrel it will always take longer to travel a certain range matter how large or small the chosen distance is.

Suppose we choose a fixed range, say 30 yards, and a .22 pellet with a muzzle velocity of 585ft/sec. To reach 30 yards that pellet will take 0.1635 seconds (AA Field pellet). Now if that pellet did not slow down at all but just kept on going at the same speed it would take 0.1538 seconds to travel 30 yards so we can say that in the air it takes 0.0097 seconds longer to travel 30 yards than it would have done if it had kept going at the same speed. The downwind drift at 30 yards for our pellet fired in the air is then given by the cross wind speed multiplied by that time difference. So in our case, for a 5mph cross wind, which is the same as an 88inches/sec cross wind, the downwind drift will be 0.0097 X 88 which comes out to 0.8536 inches. But the question is, why is downwind drift dependent on how much the pellet slows down?

The most popular misconception is that a crosswind blows on the side of a pellet. It is not surprising that this myth is popular, before now I have seen it written down in magazines, stated in videos and on forums. The wind will not blow on the side of the pellet if the pellet is stable (unless the pellet is grossly gyroscopically over stable in which case you will have much more than a cross wind to worry about). A stable pellet, by definition, will always turn to face the direction from which the air is coming when it meets the front of the pellet. If there is no cross wind the only thing giving a direction for the air to come from is the pellets own speed as it moves through the air so the pellet will face in that direction.

When there is a cross wind then the air direction is not just due to the pellet speed. There is also the wind speed to think of. The pellet though does not see two separate wind directions, it sees a combination of the directions of the cross wind speed and the wind speed from the pellets own movement creating a relative airflow.  Again, by the definition of a stable pellet, the pellet will turn to face the direction of the relative air flow from the cross wind and the pellet speed. The diagram below shows what is happening.

(https://i378.photobucket.com/albums/oo221/rsterne/Miles/wind3a_zpszh7pzjdh.jpg)

If the pellet is facing into the combined relative airflow then there cannot be any flow on the side of the pellet to push it sideways down wind.
Since the pellet is facing the airflow the only force acting on it is drag and it is part of the drag force which produces the downwind drift. The next diagram shows how this happens.

(https://i378.photobucket.com/albums/oo221/rsterne/Miles/wind2_zps3t5cjezv.jpg)
 
It all comes about because the pellet is not actually pointing in the direction in which it is travelling so the drag force is at an angle to the pellets direction of travel which makes some of the drag act in the direction of the wind. It is this small component of the drag which produces your downwind drift.

But what proof is there that the above is true? From the diagram above, if there is no drag there should be no downwind drift and if the drag is negative then the projectile should drift upwind, not down wind. These effects can be seen with rockets. If a rocket is fired with a motor which exactly equals the drag giving no overall force a crosswind has no effect on it where as an accelerating rocket can be seen to drift upwind. Projectiles fired at the same speed and weight but with different drags have also been shown to have downwind drift proportional to the drag so the theory is well proven.

While the drag provides the force for the downwind drift, the pellet weight will decide on the acceleration rate of the sideways velocity producing the rate of the downwind drift. This is where BC becomes useful as it combines a factor for the pellet drag with the pellet weight. The BC also determines how much the pellet will slow down and thus contributes to the time difference we looked at before.

The other factor which will determine what the time difference calculated above will be is the pellet velocity. The velocity will affect the size of the drag force as well as the time taken to reach the range of interest.
Title: Re: Types of Stability Affecting Pellets and Other Stability Topics
Post by: rsterne on April 04, 2020, 10:33:36 PM
Thanks for an excellent explanation of the mechanics of downwind drift.... It explains away the idea that the "side area" of the pellet, or the caliber, are the critical factors.... While velocity is still part of the equation, the drag of the pellet, and the sectional density, which together are represented by the BC, is the important factor....

Bob
Title: Re: Types of Stability Affecting Pellets and Other Stability Topics
Post by: WhatUPSbox? on April 04, 2020, 11:44:24 PM
Miles,
I am curious, in your model results for the 30 yd example. How long does it take the pellet to correct from the muzzle exit orientation to meeting the stable pellet definition?

Is the resulting drift equation based on longer flight time the same for pellets regardless of shape? Even round balls?

Thank you for the graphics and clear explanation.
Title: Re: External Ballistics of Pellets by Ballistician Miles Morris
Post by: ballisticboy on April 05, 2020, 01:23:57 PM
The pellet will start to turn the moment it encounters the total airflow at an angle to its direction of travel. The time it takes to turn will depend on the level of gyroscopic stability, the higher the stability the longer it will take. The evidence which exists suggests that for a normal pellet with the normal level of gyroscopic stability the pellet will turn into the airflow almost instantaneously due to the very small inertial moments involved, though obviously not completely instantaneously. In turning the pellet will not stop turning once it is pointing into the airflow, it will continue turning and yaw about the angle it is trying to attain with the oscillations hopefully damping out. Due to the time the pellet takes to turn into the total airflow being a finite amount and the oscillations about the angle facing into the total airflow direction the simple equation will not be entirely accurate but the difference should be minute in the vast majority of cases.

The shape and design of the projectile does not make a lot of difference providing the projectile is not neutrally stable. A round ball should also follow the same rules. A neutrally stable projectile will not be able to turn into the total airflow as by definition there will be no aerodynamic moments acting around its CG and will display different behaviour.
Title: Early Experiments on Low Mass Subsonic Bullet Type Designs
Post by: ballisticboy on May 15, 2020, 10:40:56 AM
About 30 years ago, around the late 80’s, I started working with Gerald Cardew on experimental pellet designs.
 The idea was that I would create new designs for pellets. I tried to produce designs which were relatively easy to make and would produce significant improvements over the classic design. Gerald had the difficult part of the work, actually making the pellets and testing them.
I wanted to design a pellet which was less barrel sensitive through inherent ballistic accuracy i.e. an ability to reduce errors caused by pellet/barrel defects and fit, and had low drag to give high energy retention, low wind response and a flatter trajectory.
Because of the traditional diabolo pellet shape giving a small degree of aerodynamic stability, most pellets do not need a lot of spin to be stable. This has led to relatively low twist rates on most air rifle barrels which give any designer of new pellets a problem with true spin stabilised designs as the rifle may not give the pellet enough spin. Ballistic accuracy, as described above, requires larger values of aerodynamic overturning moment which in turn require higher twist rates for stability. The use of carefully controlled weight distribution can reduce the required twist rates to acceptable values.
Solid bullet shaped designs tend to be too heavy for the permitted energy in rifles in many countries in the world. The obvious way around this problem is to make the pellet in something other than lead or to make the bullet hollow. This has been tried but the resulting mechanical properties (inertias, projectile wheelbase etc.) are not good for ballistic accuracy.
The first attempts (figure 1) tried to use a mixture of plastic and lead. I wanted to get the mass of the pellet towards the rear to improve the ballistic accuracy. This pellet had most of its mass at the back but it was not easy to make and had plastic in contact with the barrel which is never a good idea. There were many other problems in getting consistent manufacture (which is obvious from the pictures) which not surprisingly gave poor accuracy.

(https://hosting.photobucket.com/images/oo221/rsterne/pelex1.jpg?width=1920&height=1080&fit=bounds) (https://app.photobucket.com/u/rsterne/a/43501805-6ace-4789-abfd-61699e2bd07b/p/83b85333-1c32-44b8-870a-b848b0475b49)
Figure 1

I refined the design and Gerald also worked on improving the consistency of manufacture. More and more small changes were made to the proportions and angles ending up with the experimental design in figure 2.

(https://hosting.photobucket.com/images/oo221/rsterne/pelex4.jpg?width=1920&height=1080&fit=bounds) (https://app.photobucket.com/u/rsterne/a/43501805-6ace-4789-abfd-61699e2bd07b/p/e85ad444-739e-4bd4-a1d4-c8d6bf0b5380)
Figure 2
 
The consistency was much improved. Figure 3 shows what was achieved in terms of group size at 30 yards. These were homemade experimental pellets with novel construction methods so the presence of fliers is to be expected. Consistent manufacture and detailed design improvements should help to resolve that problem.

(https://hosting.photobucket.com/images/oo221/rsterne/fig3.jpg?width=1920&height=1080&fit=bounds) (https://app.photobucket.com/u/rsterne/a/43501805-6ace-4789-abfd-61699e2bd07b/p/9ea823ca-20b4-4ad1-9701-58dc974ae040)
Figure 3
 
It was in the energy retention where the biggest gains were made. Velocity loss over thirty yards for a 14.5 grain .22 pellet was just over 40 ft/sec. This is equivalent to a BC of 0.049 giving an energy loss of just over 13%. A 14.7 grain relatively low drag manufactured pellet lost 67 ft/sec over a similar distance for a BC of 0.030 and an energy loss of just over 22%. The energy loss of the conventional pellet is greater at 30 yards than that of the new design at 50 yards. The drop of the low drag pellet would also be slightly less, about half an inch less at 50 yards.
The basic design seemed to be sound and worked in .177 as well as .22 sizes. A heavy 10.5 grain .177 pellet was achieving a BC of around 0.041, a figure better than nearly all .22 conventional pellets (figure 4).

(https://hosting.photobucket.com/images/oo221/rsterne/177MMCar2.jpg?width=1920&height=1080&fit=bounds) (https://app.photobucket.com/u/rsterne/a/43501805-6ace-4789-abfd-61699e2bd07b/p/165d0264-e6c5-4274-9baa-f7e6f8167b24)
Figure 4
 
Perhaps more important than the energy loss, is that the high BC figures would mean a big reduction in the effect of winds.  The values quoted above for the .22 calibre pellets suggest a close to 50% reduction in downwind drift through using the new design compared to the diabolo pellet. The low drag also creates the possibility of using this design, for a pellet which has the trajectory of a .177 with the energy retention of a .22 in energy limited rifles.
I did fire a couple of the .22 pellets recently over two chronographs and got very similar energy drop figures. I do not fire any now as there are very few of them left. If the project was started again there are quite a lot of differences I would make in the detail design. For one thing I am not convinced of the necessity for a boat tail, which does not help dispersion, and the angle needs changing, but the basic design would remain much the same.
Title: Re: External Ballistics of Pellets by Ballistician Miles Morris
Post by: JohnnyPDX on May 15, 2020, 10:52:52 AM
To make it more appealing to the average person perhaps this simplification will help:



Title: Re: External Ballistics of Pellets by Ballistician Miles Morris
Post by: rsterne on May 15, 2020, 12:25:21 PM
Miles, thanks for sharing the development of that pellet with Gerald Cardew.... The one in Figure 2 looks similar to the idea of the BBT's I have developed, but with a hemispherical nose instead of the tangent ogive with Meplat I settled on.... I can see that for lower drag the RN would be better in the Subsonic range....

Bob
Title: Re: External Ballistics of Pellets by Ballistician Miles Morris
Post by: JungleShooter on May 15, 2020, 12:36:19 PM
Wow, WOW!
Thanks, Miles, for all your efforts at teaching us who haven't had the chance to study this. 👍🏼😊
Matthias
Title: Re: Early Experiments on Low Mass Subsonic Bullet Type Designs
Post by: ballisticboy on May 19, 2020, 05:45:03 PM
Just a small note. In an idle moment today I used Chairgun to calculate the BC of the .22 final design we tested. Based on the average velocity drop of five pellets the BC was 0.053 based on the GA drag law. Now the GA drag law is not a suitable shape for ths type of projectile but it does give a direct comparison with diabolo pellets.
Title: Re: External Ballistics of Pellets by Ballistician Miles Morris
Post by: WhatUPSbox? on May 19, 2020, 07:33:51 PM
Interesting, you didn't say how you made these, but there are low cost DIY injection molding machines that would work well for this. I'm envisioning a two step cast and mold process.
Title: Re: External Ballistics of Pellets by Ballistician Miles Morris
Post by: ballisticboy on May 20, 2020, 07:18:40 AM
Interesting, you didn't say how you made these, but there are low cost DIY injection molding machines that would work well for this. I'm envisioning a two step cast and mold process.

Gerald cast the metal first then molded the plastic with the lead in place. The plastic was not to touch the barrel in a production version, the plastic mearly acts as a lightweight aeroshell with the lead core providing the weight and the bearing surface in the barrel. In this way the inertias and the aerodynamic moments could be controlled.
Title: Examples of data simple tests can tell you.
Post by: ballisticboy on June 08, 2020, 08:08:40 AM
To start this one a warning, it is very technical and specialist and as such will not be of interest to the vast majority. Hopefully one or two may find it of interest.

This one is about analysing measured data from trials results to try to obtain some of the aerodynamic coefficients which govern pellet flight. When I was working one of the things I had to do was to analyse trials results. The trials were carried out according to strict trial plans which I usually had to write and which usually involved the use of extensive instrumentation including meteorological systems, survey equipment, and multiple radar systems one of which was a multimillion pound/dollar tracking Doppler system. To go with all this we also had the supporting instrumentation engineers. For most shooters this instrumentation will not be available when they are testing but that does not mean that the same analysis methods cannot be applied to some carefully measured results.

There are plenty of ways in which the aerodynamic properties of pellets, slugs or any other gun launched projectile can be calculated, so that pellet flight can be modelled. The problem with pellets is trying to find suitable measured data in order to confirm, or otherwise, the calculated data. For many aerodynamic coefficients it is very difficult to obtain measured values without very extensive instrumentation and facilities. However, if tests are carefully thought out it is sometimes surprising what can be derived from the resulting data.

Perhaps the easiest aerodynamic coefficient to obtain is drag coefficient and how it varies with projectile speed. It can be done with a couple of chronographs which have been calibrated against each other if they are used at different discreet ranges. The best method available for many shooters is to use the LabRadar to obtain a downloaded data file of measured pellet speeds at a large number of distances.

The problem with many radars is the amount of data from a number of shots (I would always recommend a minimum of ten shots), making sure there has been no form of smoothing applied to the data to make it look better and how best to analyse it. Using unsmoothed data and simple analysis, assuming you are firing as flat as possible and combining the analysed measured data from a number of shots, you may get data which looks a bit of a mess (figure 1).

(https://hosting.photobucket.com/images/oo221/rsterne/Labdata.jpg?width=1920&height=1080&fit=bounds)
Figure 1
 
It is at this point that you can start using different data smoothing techniques such as running average values etc. The reason you should not use smoothing before analysing is that the shape of the drag curve you obtain from the smoothed data will be mainly dependent on the smoothing method used rather than the true data derived shape. Excel can be used to give a curve fit to the data but I always found it more accurate to just put a line through the centre of the data by eye avoiding the limitations of the curve fit methods. Using this method the data above gives the fitted curve below (figure 2) for the Cd curve.

(https://hosting.photobucket.com/images/oo221/rsterne/Cdlaw(1).jpg?width=1920&height=1080&fit=bounds)
Figure 2

Some years ago Harry Fuller in Australia produced some interesting firing data when he fired some marked .25 JSB King pellets over a range of 200 yards through paper targets. For each of the data distances ( 2 feet, 75, 100, 150 and 200 yards) there were two targets a measured distance apart. The marks on the pellets left a mark on each of the paper targets so the angle through which the pellet had turned between the two targets could be measured and the effective twist rate at each range could be calculated. The initial and final pellet velocities were also measured. The twist rate data is shown here.

2 feet = 1: 18.9
225 feet/ 75 yards = 1:15.9
300 feet/ 100 yards = 1:14.9
450 feet/ 150 yards = 1:13.2
600 feet/ 200 yards = 1:12.8

One of the aero coefficients I had tried to calculate before was the aerodynamic spin damping coefficient. Because of the shape of a pellet and its Reynolds numbers it is not an easy calculation. However Harry’s data provided a possible method of obtaining measured spin decay data. Using the two measured velocities and a calculated Cd drag law I obtained estimates of the pellet velocity at each data point and from that and the measured effective twist rate the pellet spin rate in radians per second. Once we have the pellet speed and spin rate it is then relatively easy to derive the spin damping coefficient. The resulting spin damping coefficients obtained from the data are shown below after smoothing.

(https://hosting.photobucket.com/images/oo221/rsterne/spin_damp.jpg?width=1920&height=1080&fit=bounds)

The estimated drag law is a possible source of error in the calculations of the spin damping coefficients so the exercise was repeated using a different very simple drag law. The new spin damping coefficients were practically identical to the previous set suggesting the drag law was not a major error source.

One aerodynamic coefficient which most shooters have never heard of but which is arguably the most important coefficient of all is the aerodynamic overturning moment coefficient slope, usually called Cma which is a lot easier to write. This one coefficient is important since it is a major factor in aerodynamic stability, gyroscopic stability, spin drift, vertical cross wind effect and group size, amongst other things. It is however very difficult to measure without major facilities.

One of the things Harry Fuller did years ago, on a day when the wind direction was steady but the wind speed was varying, was to fire 15.9 grain .22 JSB Exact pellets over a range of 60 yards at a pan and compare the results with 25 grain JSB Monsters. Harry was interested in showing that the vertical crosswind effect is different for pellets and bullet shaped projectiles. Harry’s results can be seen in his photograph below (figure 3).

(https://hosting.photobucket.com/images/oo221/rsterne/Harry1.jpg?width=1920&height=1080&fit=bounds)
 
This test, which Harry carried out, is a brilliant example of what can be done with the simplest of instrumentation, in this case a chronograph and an old pan. Harry’s results clearly show the difference in the vertical cross wind effect between aerodynamically stable and aerodynamically unstable spinning projectiles. But there is more information there as well.

When I was looking at the vertical cross wind effects on pellets to try to help incorporate this effect into Chairgun one of the things which stood out was that the angle between  the line of pellets  and the horizontal was largely independent of muzzle velocity for speeds below 900ft/sec. Years later, looking at the theory again, it was obvious that one of the main factors in deciding the magnitude of the angle shown above was the distance between the centre of gravity and the centre of pressure which is a major component of Cma. Thus by comparing modelled results with the angle seen in figure 3 a good estimate for Cma can be obtained. The original estimated Cma for the JSB exact pellet and the values derived from Harry’s firing results can be seen below.

(https://hosting.photobucket.com/images/oo221/rsterne/Cmamea.jpg?width=1920&height=1080&fit=bounds)

Now those numbers won’t mean a lot to most people but they are highly significant being negative rather than positive and being a factor of 5-10 smaller than many projectiles.

This post is not meant to be a “look how clever I am” post. It is an attempt to show there are probably many other results around which could be used for simple analysis to at least get some idea of the values of certain important aerodynamic coefficients. It is however vital that the tests are carried out carefully and methodically in the right atmospheric conditions to be usable. The analysis also needs some idea of the atmospheric conditions, things such as air temperature and pressure.
 
The more we can find out from tests the greater our understanding of pellet flight can become and the more we will be able to say what is good, what is bad and maybe why.
Title: Re: External Ballistics of Pellets by Ballistician Miles Morris
Post by: JungleShooter on June 08, 2020, 03:51:47 PM
Miles,  😊

you are showing us that the deep dark HOLE that we have fallen into is far deeper than most of us imagined....

Keep writing! Thank you! 👍🏼


Now, you brought up some stuff that I've seen on my ballistic calculator, Strelok Pro.

🔶There are several settings in Strelok that I didn't know what to do with — and now I want to KNOW...! 😄

▪Vertical Deflection of Crosswind, with an optional manual setting (here set to 1.2345679 for fun)
▪Coriolis Effect
▪Spin Drift▪Twist direction of the barrel

For the first three of the four, see the attached screen shot....



Once the Peruvian government allows us to leave our homes again after this covid craze I finally want to really get into 100 yard shooting and shooting slugs....
➔ And I have an inkling that these four settings in Strelok might have a sufficiently large effect to be important....   


🤔 So, what do I do with these settings? Will there be a difference between pellets and slugs?

If this thread is not the place, I gladly start a new one.... 😊
 
Matthias
Title: Re: External Ballistics of Pellets by Ballistician Miles Morris
Post by: ballisticboy on June 08, 2020, 07:18:00 PM
Matthias

Vertical deflection of a crosswind is a difficult one to use. When a pellet is fired into a wind at 90 degrees to its direction of travel it will not only be deflected down wind it will also be deflected up or down depending on a number of things. In Chairgun, and it appears Strelok, a simple method was used which set the vertical deflection as a percentage of the downwind drift. The trouble is the percentage is not a constant with range and will be different for different pellets and slugs. (as can be seen in Harry's pan picture) For long ranges (50 yards or more) with conventional pellets a figure of around 30-40% would be a first guess but it will be heavily design dependent. For slugs figures closer to 10-20% are probably better but again design dependent. The barrel twist rate and twist direction will also change the vertical deflection in size and direction.

As for coriolis effect for airguns I am not convinced it will be relevant. For rifles shooting 1000 metres or more yes, but air rifles? If you want to include coriolis then you should have to include the direction in which you are firing and where you are on the Earth's surface.

Spin drift for pellets will be in the opposite direction to that for slugs. Pellets will normally drift to the left and slugs to the right assuming a barrel with right hand twist. If the barrel twist is in the opposite direction the spin drift will also be in the opposite direction. The program will again need extra input, gyroscopic stability factor as a minimum to give a crude guess with sweeping assumptions. To calculate it properly will need axial inertia, Cma, spin rate, spin damping and lift coefficient in a modified 4DOF program. Some of the old fire control systems used to use a fiddle based on, I think, time of flight but they needed to know what projectile and gun was being used. I am not at all sure the data to create such a system for pellets and slugs exists. Work may need to be done in the future if air gun ranges keep increasing.

Sorry I cannot be more specific. The main problem is people are trying to use point mass trajectory models for things which need extra abilities in the program and, with that, much more input data. This is a very similar situation to that which existed in the 1960s for artillery fire control systems. For pellets and slugs the necessary data simply does not exist or is not made available. I have created limited data on one or two pellet designs and some slug designs but it is not of much use without the specialised trajectory programs to use it.
Title: Re: External Ballistics of Pellets by Ballistician Miles Morris
Post by: JungleShooter on June 10, 2020, 09:49:01 PM
Thanks a lot for your time and input, Miles! 😊

Matthias

Title: Re: External Ballistics of Pellets by Ballistician Miles Morris
Post by: Spacebus on September 15, 2021, 01:43:18 PM
Does a tin pellet require a different twist rate than a lead pellet? I found the tin slug thread before this one and saw that tin slugs require a much faster twist rate. I'm getting very inconsistent groups with my .177 regulated Bandit firing Dynamic TM-1 9.5 grn tin pellets. Sometimes my groups will be 1/2" or less, but other times up to 1.5". The TM-1 pellets also aren't shaped quite like the traditional Diabolo pellet, they look like a pellet/slug hybrid. I remember it being much more accurate with H&N Barracuda copper plated 10.64 grn pellets, but I can't test right now due to a tropical storm moving through our area.
Title: Re: External Ballistics of Pellets by Ballistician Miles Morris
Post by: ballisticboy on September 15, 2021, 08:00:24 PM
I have looked at non-lead pellets compared to lead pellets, and the ideal twist rates seemed to be much the same for the two. This is probably because the pellets I looked at were aerodynamically stable and thus less dependent on spin stabilisation.

One thing which did stand out was that the non-lead pellets were much more affected by any pellet defects than lead pellets of an identical design. This would suggest that non-lead pellets need to be made to a greater degree of accuracy and consistency, and also are more critical of pellet barrel fit for good group sizes.

If there is any interest, I could put the modelling results in a thread.
Title: Re: External Ballistics of Pellets by Ballistician Miles Morris
Post by: Spacebus on September 15, 2021, 08:27:17 PM
I have looked at non-lead pellets compared to lead pellets, and the ideal twist rates seemed to be much the same for the two. This is probably because the pellets I looked at were aerodynamically stable and thus less dependent on spin stabilisation.

One thing which did stand out was that the non-lead pellets were much more affected by any pellet defects than lead pellets of an identical design. This would suggest that non-lead pellets need to be made to a greater degree of accuracy and consistency, and also are more critical of pellet barrel fit for good group sizes.

If there is any interest, I could put the modelling results in a thread.

If you don't mind I would like to see the modeling.
Title: Modelling Comparing Lead and Non-Lead Pellet Group Sizes
Post by: ballisticboy on September 16, 2021, 06:26:15 PM
With all the discussion of banning lead pellets in the future, I have had a look at a direct comparison of the group sizes between two pellets, one made of lead and the other made of zinc. I chose the usual 0.22 15.9 grain JSB type pellet and just substituted zinc for the lead. The zinc pellet weight came out at 10.04 grains, a bit lightweight but ok for this comparison. The results should be much the same for tin pellets, as the densities of zinc and tin are very similar (7.13 for zinc and 7.31 for tin).

Stability and group sizes are affected by a very large number of things, but one of them is the balance between the physical properties of the pellet, such as mass and moments of inertia, and the aerodynamic properties. If the aerodynamic and physical properties are balanced for a given design of lead pellet and you change from lead to zinc, then you are changing the all important balance, which should change how the pellet works. I am trying to see how much the group sizes change and if different twist rates are needed for the different pellet materials.

Many of the non-lead pellets appear to be the same or similar designs to the lead ones. This work compares the groups sizes for a lead and a zinc pellet of identical shape, fired at the same muzzle velocity (900ft/sec) and with the same defects present in the pellets. As the pellet designs are identical, the same aerodynamics have been used for both the lead and zinc pellets, but with the different mechanical properties.

The defects are based on some work I did some time ago looking at the effect of twist rates on group sizes for non-perfect pellets. For this exercise the pellets have a centre of gravity which is 0.1mm (4 thou) away from the pellet centreline, and a 1.25mm diameter flat spot on the front of the nose close to the pellet edge representing a dent or cavity. The barrel twist rates used range from one turn in 82 inches up to one turn in 7 inches.

The aerodynamic data is based on experimentally derived data as far as possible, with some extra coefficients estimated using standard aerodynamic estimation techniques. The pellet physical characteristics have been calculated using a simple program which has been tested for accuracy against standard shapes with known mass and inertial properties. The trajectory modelling program is a six degree of freedom model which has been fully tested to government standards.

The group sizes at 30 and 50 yards for both the lead and zinc pellets have been calculated and compared. The resulting variations in group sizes with barrel twist rate is shown in the two diagrams below for 30 and 50 yards range. Each dot represents two trajectory runs, one with no pellet defects to give a zero error point and one with the pellet defects to give the error size and thus the predicted group size.

(https://hosting.photobucket.com/images/oo221/rsterne/30znpbv.jpg?width=1920&height=1080&fit=bounds)

(https://hosting.photobucket.com/images/oo221/rsterne/50znpbv.jpg?width=1920&height=1080&fit=bounds)

Don’t worry about the size of the groups predicted, that is just a function of the size of the pellet defects used, which were pretty severe, for this exercise in order to show up the differences. The important things are the relative sizes of the lead and zinc groups and how they vary with barrel twist rates.

The 30 yard results are the easiest to look at first, as the lead (pb) pellet results are always better than the zinc (zn) results. The zinc group sizes are generally 30% or more larger than the lead ones. The results at 50 yards are largely the same, but there is something strange happening at twist rates around one turn in 50 inches, where the zinc pellet suddenly looks much better. Looking at the variation in the pellet yaw angle with range for this twist rate, the maximum yaw seems to increase to a much larger angle than normal, indicating a dynamic instability which then to slowly damps down. This can be seen in the diagram below, showing the vertical yaw angle as a function of range for this particular case
.
(https://hosting.photobucket.com/images/oo221/rsterne/zn79.jpg?width=1920&height=1080&fit=bounds)

One possible explanation is something known as spin yaw resonance producing spin yaw lock in, which happens when the yaw and spin frequencies are the same or very close. The yaw wave length shown above is close to the barrel twist rate, which would support the resonance theory. Resonance usually gives larger errors. In this exercise though, the orientation of the pellet defects used produced a vertical error giving a high impact point. The extra drag produced by the yaw angles shown above caused the pellet to fall as the range increased, so it may just be a coincidence that the error is small at the chosen range because the extra fall of the pellet due to the increased drag counteracted the vertical error of the pellet defects.

The best twist rates for both the lead and the zinc pellets seem to be similar, with the zinc having a slightly smaller bandwidth of suitable twist rates.

The results do not mean that a lead pellet will always give smaller groups than a zinc pellet. A zinc pellet with no defects which is a perfect fit in a barrel will be as good as a lead one in terms of group size. What it does mean is that a zinc pellet is much more sensitive to defects and is much more fussy about the barrel fit than a lead one. A zinc pellet will have to be made much more accurately and be a better fit in the barrel to match the lead pellet group sizes. Using lead pellet designs and production methods as a basis for zinc pellets is unlikely to give suitable results in a wide range of guns and barrels due to the above sensitivity.

The effects of cross winds have not been included in the above results for group sizes.
Title: Re: External Ballistics of Pellets by Ballistician Miles Morris
Post by: JungleShooter on September 16, 2021, 08:10:13 PM
Miles,

Very interesting!

You are an amazing guy. Your research, and your way of putting the results and implications into words that are comprehensible — great! 👍🏼

Thank you.

Matthias
Title: Re: External Ballistics of Pellets by Ballistician Miles Morris
Post by: Spacebus on September 17, 2021, 08:55:19 AM
Thanks for the data, Miles. It very much reinforces what I am seeing with my .177 lead free pellets. I wanted very much for the Dynamic 9.5 grn pellets to be as accurate as my H&N 10.64 grn copper plated pellets, but they are nearly unusable. Some groups come out at .5" at 25 yards and then I'll get two groups that are over an inch. They look very much like well made pellets, but I suspect that lead pellets do a better job of expanding and filling the barrel. My anecdotal evidence is seeing dented skirts on my copper plated lead pellets still hit exactly at the POA. I hope the big pellet manufacturers get better with their lead free options, as so far only H&N and Predator seem to make competent lead free ammo.

The below groups are from testing with H&N .25 Barracuda Green 19.91 grain pellets. The far right is with my Seneca Eagle Claw on max power and all eight shots. The third from the left is at two "clicks" less than max power and the "flier" is my attempt at Kentucky Windage to compensate for the different POI between the Green pellets and my NSA Slugs.
Title: Re: External Ballistics of Pellets by Ballistician Miles Morris
Post by: Spacebus on September 17, 2021, 11:17:04 AM
I'm hoping manufacturers will start making zinc and tin pellets with all new designs rather than just substitute materials.
Title: Pellet Wobble Effects on BC and Accuracy (Groups)
Post by: ballisticboy on September 23, 2021, 05:20:06 PM
One of the things which often gets mentioned is that pellet wobble will affect the BC of a pellet, leading to large differences in measured BCs. I have never been comfortable with this simple and logical conclusion, the reason being that, while pellet wobble will affect BC values, it also affects a whole lot of other things in the pellet flight which should make it obvious. I have never seen anyone mention seeing anything strange about their pellet’s behaviour when low BCs have been measured.

Since firing pellets with a known yaw angle to get consistent wobble is rather difficult, I used the usual easy way out of the problem by modelling the effects. The trajectory program is the usual one I use on pellets with the same data from the 15.9 grain .22 AA Field pellet. The modelling was simple with trajectories calculated for pellet yaw angles from zero up to ten degrees in two degree steps, with a muzzle velocity of 850 ft/sec. I took readings for the velocity at 30 and 50 yards along with the calculated error in the pellet position at the same ranges. I then used Chairgun for each range to calculate the average BC based on the calculated velocity.

The first figure shows the calculated velocity drop in ft/sec over 30 and 50 yards for each yaw angle.

(https://hosting.photobucket.com/images/oo221/rsterne/yawbc1.jpg?width=1920&height=1080&fit=bounds)

The figure below shows how the calculated BC varies with yaw angle for both the 30 and 50 yard ranges.

(https://hosting.photobucket.com/images/oo221/rsterne/yawbc2.jpg?width=1920&height=1080&fit=bounds)

So there is a demonstrable effect on the value of BC from pellet yaw angle. In this case, the value fell from .029 with no yaw down to .023 with ten degrees of yaw. So far, so good.

Below is a graph of the pellet impact point error in inches at 30 and 50 yards range for the different yaw angles.

(https://hosting.photobucket.com/images/oo221/rsterne/yawbc3.jpg?width=1920&height=1080&fit=bounds)

Group size can be expected to be twice the error value, as the error can be in any direction. Now, I think that most shooters would notice a group size of 34 inches at 50 yards range. Even a four-inch group size would be considered completely unacceptable, but you can get that with just over one degree of yaw at 50 yards, two degrees of yaw at 30 yards. Yaw angles of one or two degrees made no difference to the calculated BC value. For those who don’t like graphs, the table below sums the results.

(https://hosting.photobucket.com/images/oo221/rsterne/yawBC4.jpg?width=1920&height=1080&fit=bounds)

So the problem I have is that you cannot have a yaw angle large enough to cause a measurable change in BC without having a large error at the target, in many cases too large for the pellet to be in any way usable. All the work I have done in the past suggests that pellet angles have to be below one degree for an acceptable group size. My feeling is that the reason for BC variations is far more complex than some pellets having more yaw (wobble) than others.

The modelling may have errors in it, however the most important variables have been derived from experimental results. The fact is that even if the modelling is 50% in error, it still seems unlikely that pellet wobble, which is sufficient to cause significant differences in BC, will not produce large errors and groups at the targets.