The Future Of Airgun Ballistics Coefficients
In this post, HAM Technical Editor Bob Sterne discusses his thoughts about current drag models and the future of airgun Ballistics Coefficients.
In the last article I mentioned that we need a better drag model for Diabolo pellets, and also one for the common shapes of slugs that we shoot in airguns. In the past, the only way to determine the Drag Coefficient (Cd) and then calculate the Ballistics Coefficient (BC) was to use two positions for Chronographs, separated by a known distance, and measure the velocity of the pellet or slug at those two points.
That gave us data for only one narrow velocity range, or an average over a wider velocity range if the Chronys were widely separated. Shooting though a Chrony at 100 yards is a great way to destroy it through an accidental hit, of course. Fortunately, there is now a better way.
A Canadian company, Infinition Inc. has produced LabRadar, a ballistics doppler radar at a price within reach, and it can track a .30 cal. projectile to about 100 yards. Smaller pellets can’t be tracked as far, but with care, we can collect data over a wide range of velocities with just a few shots, and no danger of hitting the unit, as it sits on the bench beside the muzzle.
You can preset five downrange distances where it will report the velocity, and if you graph those results you will end up with something like this:
Once you know the velocity at two distances, by using the frontal area and mass of the projectile, you can calculate the Cd between those velocities, and plot that on a graph as well. It might look something like this:
If you collect enough data, showing how the Cd varies with velocity, we are hopeful that we can come up with a better drag models than the current GA model for Diabolo pellets, or the G1 model for slugs.
Currently, we have to use one of the existing drag models, and because none of them are a perfect match for our pellets or slugs, we end up with a graph for the BC that might look like this:
You can see in this example how the BC is not a constant, as it should be. If the drag model was an exact match to the Cd curve of our pellet, the BC would be a constant over all velocities. This would allow precise calculation of trajectory and wind drift.
It is my goal, and that of several other keen individuals, to try and refine the drag model for pellets to improve the accuracy of BC values.
Some Actual Data
I was recently awarded a LabRadar by the AirGunGuild forum in recognition of sharing my research about airguns. This generous gift will allow me to pursue my dream and goal of improving our body of knowledge of airgun ballistics coefficients for both pellets and slugs.
I will be retiring in February of 2021, and beginning that summer plan to start seriously working on this project.
There are other airgun aficionados who are already using their own LabRadar units for similar research. I have been fortunate to be in contact with one such individual, Ron Burnett, who has shared with me some of his data. With his permission, I have condensed some of his results to present to you here.
One of the problems with obtaining a complete drag model for pellets is the wide range of velocities involved. While LabRadar can track a pellet over quite a long distance, you can still only view one “window” of velocities at a time. In order to get the complete picture, we will need to “stitch together” several sets of data for each type of pellet.
For example, we might shoot a series of pellets at 950 FPS, collect and analyze the data, but it is only good down to, say, 700 FPS before the pellet is out of range of LabRadar. So we will then shoot another series of pellets at 700 fps, to extend the data down to 500 FPS, and so on until we assemble all the data we need.
Ideally, when we plot all the data, we will see a high level of correlation, like this data from Ron:
The blue line was shot at a muzzle velocity of 945 FPS, and the orange line at 875 FPS. They are completely superimposed below 800 FPS, and plenty close enough above that velocity that you could use this data for the drag model for that pellet from 620 to 940 FPS.
Let’s have a look at how that Cd curve matches to what we are using now. The best fit we have currently for this pellet would be using the GA drag profile, with a Form Factor of 1.6, to produce a Cd curve like the black line on this graph:
The data from Ron’s testing produces a Cd curve like the red line above. This is a good start for a drag model for that pellet.
When exploring new technologies, that can give you more information, you are bound to run into problems that you didn’t even know existed. In a perfect world, all the Cd curves you plotted for a given pellet would stitch together to form one continuous curve over the entire range of velocities. Unfortunately, this is not always the case.
When Ron tested a different pellet, instead of getting data that behaved nicely, he got three different Cd curves, depending on the muzzle velocity, like this:
What we would expect to see is three curves, starting at the upper right, that merged into the orange curve. In other words, all three curves would only differ on the right side, because they started at different muzzle velocities. Obviously, that is not what we got!
So, what happened? It is my guess that when this pellet is shot at higher velocities from this particular twist barrel, that it experiences dynamic instability, and starts to wobble and/or spiral. This causes an increase in drag, which slows the pellet more rapidly, and shows up as a higher Cd. The higher the Muzzle Velocity, the sooner it starts to wobble, and wobbles worse, so the more rapidly it slows down.
The only way to determine for sure if that is what is happening would be to repeat the tests in a barrel with a slower twist rate. The lower RPM resulting should reduce or eliminate the dynamic instability and subsequent wobble/spiraling and drag increase. At this point, this is only a guess.
I am hoping that by testing many different types of pellets, we can come up with an “average” Cd curve that is a better fit than today’s GA drag model for airgun Ballistics Coefficients. It may be that we need several curves, one for wadcutters, one for round nose pellets, and some sort of “compromise” curve in between. Only when I start testing will I (hopefully) know for sure.
I also intend to do similar testing of slugs, to see if we can come up with a better drag model than the G1 we use today.
The G1 projectile is a pointed, flat based bullet, whereas we usually use a slug where the nose is “cut off” to form a Meplat or Hollowpoint. While that may not have a huge effect on the drag in the Subsonic range, it definitely increases the drag when Supersonic, and logic would state that in the Transonic range the drag of our slugs would also increase faster than the G1 drag profile.
I also firmly believe that boattails can be used successfully to reduce the drag of airgun slugs. That is another thing I wish to investigate once I am retired. So many projects, so little time!