Projectile Drag Coefficient versus Velocity at Trans-Sonic

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SkeeterHawk

SkeeterHawk

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Oct 23, 2021
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Florissant, Colorado, United States
Hello everyone,

I just can't stop reading up on and trying to get educated on ballistics. I came across some data today that I put into a chart relative to the Drag Coefficient of the projectile when going through the trans-sonic range. Here is the chart I created:
DragCoefficientVersusVelocity_ChartLabeled_2022-09-04.jpg

OK, so this is charted using a "Very Low Drag Bullet", so this would be more of a direct comparison to slugs than pellets, but the results are still relative to what we are seeing. As you can see, just below 976FPS, the drag is the least on the projectile, and this is right at the "Sweet spot" for pellets around 850-925FPS. This could be extrapolated to mean that we are shooting pellets at the point with the least drag. Now, when the projectile gets into the trans-sonic range, the drag varies significantly. This (to me) would almost mean that when you are shooting slugs, that you would really need to shoot for the 1300FPS range than the 1000-1100FPS range that seems to be the most common. According to the chart, only a small variation in the velocity would make a bigger difference in the drag, and thereby the point of impact.

Is there a gun that can shoot slugs at up to 1400FPS? This would be an interesting experiment to see if you got "ultra-stability" in slugs by pushing them up into the plateau that exists at the top of this curve. Sure, you have the most drag here, but the results should be really consistent. Thoughts??
 
There's a very good reason why even match grade 22lr is subsonic. Transonic does very weird things to a projectile as I'm sure most people are alreadyaware of. If you're going to break the sound barrier you need to break it by a significant amount so that you have consistent accuracy at longer ranges. I have a Savage 22lr that I use to poke out to 500m. A lot of people think high velocity ammo is the way to go. Unfortunately that ammo starts to "wobble" somewhere around the 150m mark for me and anything beyond that becomes pretty inconsistent. Subs on the other hand remain predictable.
 
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Nerd Warning :geek:: Supersonic projectile flight causes shock waves to form on every single edge of the projectile with the main shock waves being at the front and rear of the projectile. Like a boat's bow wake and stern wake.

These standing shock waves cause tremendous drag on the projectile (hench the higher Cd in the OP graph). But as long as the projectile is flying significantly above Mach 1.0 these shock waves are even and don't cause disturbances to flight despite the high drag. When a projectile slows down and goes trans-sonic the shock waves dissipate at different points at different times. These uneven forces cause a very brief buffet and instability to flight which "even out" once the entire projectile is free of standing shockwaves, usually below Mach 0.90-0.95. At that point the Cd drops drastically as noted in the OP graph. Regards, Badger
 
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🔶 The drag vs. velocity curve in the OP is of course projectile specific.
And a "very low drag bullet" is a far shot from a very high drag projectile that is the classification that all our airgun pellets fall under....

So, the relatively high velocity in the graph at which drag increases exponentially is much lower for our domed pellets (and lower yet for wadcutters).



🔶 The video by Ted referenced above has been discussed at length on the GTA, where we have a resident professional ballistician....

Things aren't as "conclusive" and "obvious" as one might conclude from just watching the video. 😉

Ted's surprising high BC results at 1100 FPS - Airguns & Guns Forum

Ted's surprising high BC results at 1100 FPS, Air guns, Airgun Forum
www.gatewaytoairguns.org


Cheers,

Matthias
 
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badger5th said:
as long as the projectile is flying significantly above Mach 1.0 these shock waves are even and don't cause disturbances to flight despite the high drag
Click to expand...
Thanks for the feedback!!! I love this nerdy stuff!

This was exactly my thought. If you can push a slug up to 1400FPS, you could see if this theory is correct. I mean, it stands to reason, no matter what. The numbers may be slightly different due the the BC of that actual projectile, but the concept should be the same. Once you get above the trans-sonic range, the drag will be greater, but more consistent. If you are shooting a 0.177cal 10.3gr slug at 1400FPS, that is only about 45FPE. This is still well within competition guidelines. If you are able to buck the insane cross-wind at (for example) RMAC, would this give the small caliber guys an advantage over the 30cal guys for a change?

Anyway, this is REALLY interesting stuff to a nerd like me.
 
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I'm new to airguns on the more "serious" level, but I've spent a lot of time shooting and hand loading powder burners. There's a reason that we try to find calibers/loads that avoid going trans-sonic before the projectile gets to the target. As another member mentioned, subsonic 22 is usually used when shooting long range for this reason. There are a lot of strange things that can happen in flight during the trans-sonic stage, it's pretty cool to watch as it happens. TiborasaurusRex has a long range shooting series on YouTube, not all of it will apply to airguns but it's all interesting and good knowledge to have.
 
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Jonathan, 😊

for nerding out on airguns, there's a dedicated forum for you:
Bob and Lloyds Workshop, a sub-forum on the GTA, here:

"Bob and Lloyds Workshop" - Airguns & Guns Forum

"Bob and Lloyds Workshop" , Air guns, Airgun Forum
www.gatewaytoairguns.org

You should try it sometime — read up on the questions being asked, and post your own questions.

The guys on that forum are all AG nuts.

Matthias
 
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JungleShooter said:
You should try it sometime
Click to expand...
Thanks for the tip, Matthias! I am SkeeterHawk over on GTA as well. I joined GTA and AGN about the same time, but I gravitated more to AGN, so I didn't know about Bob and Lloyd's workshop. I have about 60 articles to read through now (thanks to your suggestion), and if they don't touch on my concept of pushing into the super-sonic plateau, I'll post it there too and see what I get.

Thanks again for the tip! (y)
 
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lbc_PSI said:
Might give this a watch..interesting..

The Mysterious BC compliments of Ted

Enjoy!
www.airgunnation.com www.airgunnation.com

Maybe Ted's slugs are hitting a "magic" FPS in the transonic range?
Click to expand...
nervoustrig said:
Or cranking the power up by 20% produces different recoil and barrel harmonics.
Click to expand...
I would imagine that Ted owns a Lab Radar, so he "could" have used that to try and confirm his results. I also think the explanation of harmonics and barrel whip, especially in an 800mm thin barrel could be a plausible reason. All he really needed to do was shoot with is LR and get muzzle and 100Y velocities. Easy day and no brain busting required...
 
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JungleShooter said:
So, the relatively high velocity in the graph at which drag increases exponentially is much lower for our domed pellets (and lower yet for wadcutters).
Click to expand...
I've read your comment a few times, Matthias, and it is true from a number of different aspects, but I am not sure which you are speaking of. Are you saying that the extent of the knee of the curve is less "high" for a pellet, or that the velocity at which this trans-sonic destabilization occurs is lower than 970-1200?

I think both points are probably true. With a pellet, or lesser BC projectile in general, the knee probably won't be so sharp and will have more of an angle until the pellet or slug gets to super-sonic. Now the other point is probably what you meant and more true, that the velocity at which the destabilization occurs is lower, since we see Diobolos start to destabilize at around 900FPS, rather than 975FPS. Baracudas, and the Re-designed pellets like it over 900FPS, so they are obviously on another curve. There are so many variables here, but the resulting destabilization when the pellet passes through trans-sonic is a given. It would just be a matter of where the destabilization starts, and what the slope of the curve is.
 
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SkeeterHawk said:
Thanks for the feedback!!! I love this nerdy stuff!

This was exactly my thought. If you can push a slug up to 1400FPS, you could see if this theory is correct. I mean, it stands to reason, no matter what. The numbers may be slightly different due the the BC of that actual projectile, but the concept should be the same. Once you get above the trans-sonic range, the drag will be greater, but more consistent. If you are shooting a 0.177cal 10.3gr slug at 1400FPS, that is only about 45FPE. This is still well within competition guidelines. If you are able to buck the insane cross-wind at (for example) RMAC, would this give the small caliber guys an advantage over the 30cal guys for a change?

Anyway, this is REALLY interesting stuff to a nerd like me.
Click to expand...
The trick would be to stay above sonic all the way to the target. A 10.5 grain slug with a generous G1 BC of 0.030 and muzzle velocity of 1400 fps will be below sonic in the first 25 yards. Hence the reason for starting out subsonic at the muzzle to avoid going through the trans sonic region.
 
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Centercut said:
I would imagine that Ted owns a Lab Radar, so he "could" have used that to try and confirm his results. I also think the explanation of harmonics and barrel whip, especially in an 800mm thin barrel could be a plausible reason. All he really needed to do was shoot with is LR and get muzzle and 100Y velocities. Easy day and no brain busting required...
Click to expand...
Also posted on the other thread..


I understand how the velocity of the pellet/slug might have a effect on group size (e.g. barrel harmonics, muzzle flip, etc.) , but I don’t think that is what Ted is describing.

Sure, it could be that “barrel harmonics, muzzle flip, etc.” are the most likely reason(s) for the groups shrinking as the velocity is dialed up. Totally agree. But. After the projectile leaves the barrel, “barrel harmonics, muzzle flip, etc.” have zero effect on the trajectory.

You might be able to make the case for “barrel harmonics, muzzle flip, etc.” being the reason for the POI difference at 100 yards, except for the fact that Ted said he re-zeroed at 50 yards before shooting the 100 yard groups. With a 50 yard zero for both tunes, the slugs have to follow the trajectory path determined by the muzzle velocity and BC.

A POI change like Ted describes can only be explained by a change in BC..since the velocity change alone cannot explain it.

A doubling of the BC seems crazy, but there is probably something related to the slug drag envelope as is hits a certain velocity..unless of course, Ted just made a mistake in his testing results.

It would be great if someone else could duplicate similar results.
 
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lbc_PSI said:
You might be able to make the case for “barrel harmonics, muzzle flip, etc.” being the reason for the POI difference at 100 yards, except for the fact that Ted said he re-zeroed at 50 yards before shooting the 100 yard groups. With a 50 yard zero for both tunes, the slugs have to follow the trajectory path determined by the muzzle velocity and BC.

A POI change like Ted describes can only be explained by a change in BC..since the velocity change alone cannot explain it.
Click to expand...
I don't know if this is true. If your barrel is indexed, if you are changing the nodes, it could cause a POI shift up when the velocity is changed, which seemed like what Ted was seeing.

lbc_PSI said:
It would be great if someone else could duplicate similar results.
Click to expand...
I agree. With a Lab Radar, like Centercut said so we can see what the BC is actually doing.
 
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SkeeterHawk said:
I don't know if this is true. If your barrel is indexed, if you are changing the nodes, it could cause a POI shift up when the velocity is changed, which seemed like what Ted was seeing.


I agree. With a Lab Radar, like Centercut said so we can see what the BC is actually doing.
Click to expand...
No. I think Ted said he re-zeroed at 50 yards after settling on the 1100fps sweet spot. When you re-zero at a intermediary distance like 50 yards to check drop at 100 yards, you basically eliminate barrel harmonics or indexing as a possible source of the shifting POI.
 
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SkeeterHawk,

glad some of my comments were helpful. 👍🏼
And yeah, some of those articles are worth reading again after a few years of sliding down the AG rabbit hole — they make much more sense (or, any sense at all for the first time to me.... 🤦🏻‍♂️).


🔶 Several very well written articles by Bob published by HardAir Magazine are just now entering my brain, before they were just words that passed through my eyes.... 😄
Here's the index to those:
hardairmagazine.com

The Definitive Index To Bob Sterne's HAM Technical Articles

As the stories are spread over two years of publication, this post brings together an index of Bob’s HAM technical articles, together with their titles.
hardairmagazine.com hardairmagazine.com


Yeah, my main point was the the turbulent and drastic drag increase happens with low BC projectiles at lower velocities than with high BC projectiles.


Nice to nerd out....

Matthias
 
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lbc_PSI said:
You might be able to make the case for “barrel harmonics, muzzle flip, etc.” being the reason for the POI difference at 100 yards, except for the fact that Ted said he re-zeroed at 50 yards before shooting the 100 yard groups.
Click to expand...
(Posted the following in the other thread last night but it is equally applicable to this thread so...)

You’re right. I misunderstood when I watched it the first time. I thought he was extrapolating between two different states of tune. My apologies for adding to the confusion already swirling, and thank you for the polite correction.

Looking back at Ted's video again just now, I notice in his Chairgun screenshots that he is using a custom drag profile...which means there is a very simple but not so satisfying answer: the drag profile is wrong. If it were correct, the BC would not vary with velocity. That's the whole point of a drag profile.

Elsewhere Bob Sterne pointed out that ballistician Miles Morris found the commonly used G1 profile is wildly off in the transonic region for typical slugs, so if Ted used it as the starting point for his custom profile, that would represent a significant source of the discrepancy.

The good news here is that drag doesn't mount up nearly as quickly as we approach the speed of sound as we might have expected based on the "best we got right now" G1 profile.
 
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