External Ballistics of Pellets by Ballistician Miles Morris

[ballisticboy]

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

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

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

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

Fig 3
There are two basic types of stability working on any projectile as it flies through the air. These are static and dynamic stability.
To try to explain the difference between the different types of stability think about a weight hanging on the end of a piece of string (figure 4). If you do not touch the weight it will just hang down under the string. This is its original position, the position it likes to sit in. This is equivalent to a stable pellet pointing directly into the airflow at zero yaw angle. If you pull the weight slightly to one side and let it go, if it is stable, it will swing back towards its original position. This is because the forces and moments produced by the weight and the string are trying to push the weight back to its original position. If the weight and string were an unstable system then as soon as we release the weight it would move away from its original position. This type of stability is called static stability.
 
Fig 4
When we have pulled our weight to one side and let it go, the first time it reaches its zero yaw position, it does not stop but goes on the other side until it eventually stops and then returns towards its original position from the other direction. Our weight will keep doing this with each swing getting a little smaller until it eventually stops back in its original position. It does this because the weight and string are dynamically stable so the size of the swing reduces each time until there is nothing left. If the weight had neutral dynamic stability it would keep on going with each swing being the same size as the one before. If the weight and the string were dynamically unstable the swings would get bigger until eventually the weight would go in a complete circle even though it is statically stable.
 As far as pellets are concerned there are actually three types of stability acting on them and affecting their flight as there are two types of static stability. If we just think of normal dome type diabolo pellets they are what we call aero/gyro stabilised, that is they rely on aerodynamic and gyroscopic methods for static stability. The third type is dynamic stability, which is needed to stop the pellet continuously yawing about its zero yaw position as it flies along the trajectory.
When we fire a pellet it is highly unlikely that it will be pointing exactly in the direction of the air flow after it has left the barrel. This is due to many things including wind, barrel vibrations, pellet manufacturing problems etc. so it will usually have a yaw angle soon after it has left the barrel.  The diagrams below illustrate the effects on the yaw angle for the different stability states. In each case the vertical value is the angle of yaw in degrees and the horizontal is the range in yards. First (figure 5) we have a pellet which is both aerodynamically and gyroscopically unstable. That is it is statically unstable.

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

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

Fig 7
Last (figure 8 ) is the situation we want which is a pellet which is stable both statically and dynamically. The pellet swings through zero yaw and each swing is smaller than its predecessor.
 
Fig 8
In reality most conventional pellets appear to be aerodynamically statically stable at speeds well below the speed of sound (1116.5ft/sec), that is, if we fired one from a smooth bore barrel it will continue to point in the direction of the trajectory. However, its aerodynamic static stability is marginal and at high speeds disappears completely. Also no pellet, or any other projectile, is made completely symmetrical and any differences from one side of the pellet to the other will produce an aerodynamic side force which will cause it to try to fly on a curved path. To reduce the effects of any projectile asymmetry pellets and most other aerodynamically statically stable projectiles are given some spin so that any side force is not pointing in the same direction all the time. This will make the pellet wobble a bit but will not produce the curved flight path. The spin rate needed for this is very low, much less than is needed for gyroscopic stability.
Most barrels give pellets much higher spin rates than those needed to reduce side force effects. This is because, with the marginal aerodynamic stability, a degree of gyroscopic stability in addition to the aerodynamic stability is beneficial. This is why we say they are aero/gyro stabilised.
From the reported behaviour of pellets they would seem to have pretty much neutral dynamic stability, possibly changing to dynamic instability if fired at high speeds for long ranges. The change to dynamic instability is due to the increase in pellet spin rate relative to the pellet forward speed as the pellet flies along its trajectory. This apparent increase in spin rate is due to the pellet losing forward speed much quicker than it loses spin until it causes the pellet to become dynamically unstable. It appears to be the dynamic instability produced by the excess spin rate which may lead to apparent spiralling and accuracy effects at longer ranges or at higher speeds. The pellets are still statically stable, in fact the gyroscopic  stability has increased, but the dynamic instability is adversely affecting the pellet flight.
So next time you are shooting just pay those little pellets some respect and marvel at the way they still manage to go through all the complications of the different stabilities and still hit a small target. Or forget about all the science and just get on and enjoy your shooting.

[rsterne]

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

Bob

[WhatUPSbox?]

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

[rsterne]

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

Bob

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

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

 
Fig 1

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

 
Fig 2

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

 
Fig 3

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


Fig 4

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


Fig 5

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

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

[rsterne]

By Devil's Luck....

A very interesting read.

[rsterne]

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.



...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.

[rsterne]

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

[rsterne]

By superchikn (Ray)….

My head hurts!

[rsterne]

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.

[rsterne]

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.

[rsterne]

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.... 

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

[rsterne]

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

[rsterne]

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.

[rsterne]

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.... 

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

[johnnyfoos]

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

[rsterne]

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

[ballisticboy]

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.


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.


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.


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.


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.


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.


Fig 6

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


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.

[rsterne]

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

[MJP]

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

[rsterne]

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