External Ballistics of Pellets by Ballistician Miles Morris

[ballisticboy]

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.

[WhatUPSbox?]

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 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 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 .
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 .

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. 

[rsterne]

Stan, those are some excellent links.... Thank you for posting them in this thread....

Bob

[ballisticboy]

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 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 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 .
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 .

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. 

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.

[rash]

Thanks Miles!

I figured most of your work was and still is, classified.

[TPL]

I couldn't imagine how secret this is. Please save me about all the details you could tell but then have to kill me. 

[rsterne]

Timo, no reason to be rude.... 

Bob

[rgb1]

I have Blunt Body Aero and McCoy corrections if anyone wants them.


                                                                     Ron

[rsterne]

It would be helpful if you explain that, please, Ron.... and I would love a copy....

Bob

[WhatUPSbox?]

The blunt body handbook is available on DTIC https://apps.dtic.mil/dtic/tr/fulltext/u2/776586.pdf

[rsterne]

Thanks, Stan.... but it's way beyond me.... 

Bob

[ballisticboy]

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.


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.


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.


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.


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.


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.

[rsterne]

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

[WhatUPSbox?]

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.

[ballisticboy]

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.

[ballisticboy]

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.



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.


 
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.

[rsterne]

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

[WhatUPSbox?]

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.

[ballisticboy]

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.

[ballisticboy]

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.


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.


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.


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).


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.