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Old 09-11-2009, 11:47 AM   #1 (permalink)
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External Ballistics, and what to possibly expect from .50 PBs

Cross Posted from TechPB. What follows is an external ballistics based exploration of .50cal paintballs. The point of this exploration is to gain some insight on how various ".50cal" paintballs (based on density) will perform. My reference point for density is a .683, 3g projectile measured by punkworks. Original posting:

Hey everyone, I realized something today. The Punkworks dual chrono testing unlocked something that I believe will allow us to make serious predictions about how paintball projectiles (.50s, .68s, First Strike rounds) will perform. That something is the the ability to determine Ballistic Coefficients (BCs) for the various paintball projectiles on or, coming to, the market. The dual chrono testing via revealed the true Ballistic Coefficients for both .683 diameter paintballs as well as First Strike rounds.

WARNING: Skip to the performance data, the pretty pictures, and my conclusions unless you really like reading / discussing external ballistics. LOTS of math and acronyms follow:

So, what is the ballistic coefficient? Well, it is a measure of how aerodynamic a projectile is both in terms of it's shape (i.e. pointy nosed, round nosed, flat tail, boat tail, etc) and it's mass vs. size. Mathematically, it is expressed as:
BC = SD / i

BC: Ballistic Coefficient (how well does it resist drag)

SD: Sectional Density (how heavy is it vs how wide is it)

i: Form Factor (how pointy is it, how is the back end shaped, etc)

Now, let's break this down. Sectional Density is a mathematical representation of how heavy an object is versus how much of a cross section it presents to the wind. It's calculated as:
SD = Mass / Diameter^2

in shooting circles it's measured in grains* / inches

* 7000 grains/lb

i = Drag Coefficient / Drag Coefficient of the G1 model bullet.

WTF? Yeah, in ballistics, everyone is comparing their round to the G1 model bullet which is a projectile that has a Ballistic Coefficient of 1. Think of the "i" as a common point of reference. You express how your projectile performs relative to the standard model and, calculation software can then predict how your round will perform when given other variables (like mass, velocity, etc).
In the firearms ballistics community, some folks/corporations predict the Ballistic Coefficient through mathematics or computer simulations but, others often simply build the round, shoot it, measure it's flight and then, calculate the Ballistic Coefficient. Using a calculator designed for the velocity ranges of airguns, and the dual chrono data from Bryce and Cockerpunk, I have calculated the BC for a .683 paintball (I also did this for First Strike Rounds my posts for FS rounds can be found here).
.683 paintball BC = .0060

Now, I can take this number and solve for "i". I'm going to convert to grains (gr) / inches 'cause it's easier for me. (A .683, 3g paintball weighs approximately 46.3 gr). Once I have the "i" value, I can then use that for other small, mostly spherical, smooth projectiles with single seams with varying diameters and densities.


Let's start with the .683 paintball:

SD = 46.3gr / ..683^2 = 99.2521 (rounded)

BC = .0060 = 99.2521 / i

i = 16542.0167
This means that a smooth, imperfect sphere with a seam, has a form factor of 16542.0167 However, it must be noted that this number changes with velocity but, it should hold pretty true to the velocities we are typically dealing with (i.e. well below 1000fps).

We also know the approximate volume of a .683 paintball (not taking into consideration shell thickness, nor how out of round the balls are): 0.1668ci

Now, we can take this, and apply it to .50 paintballs since, all available information indicates that they are shaped similarly to .68s (smooth surface, a seam, and probably not perfectly spherical).

However, there are some unknowns. We do not know the mass (and therefore the SD of the .50s.) We also don't know what velocities they will be fired at. But, I will generate some data showing different possible scenarios (heavier / lighter, faster / slower).

Now, let's make some projectiles:

The "Mini-Me" (similar to the .683, just smaller- these are the worst values my calculator will accept).
Volume = 0.0654ci (39.2% of the volume of a .683)

Mass = 20.68gr (approx 45% of the mass of a .683)

SD = 20.68gr / .5^2 = 82.72

BC = 82.72 / 16542.0167 = 0.0050
The "Slug" (High density fill= mass of a normal .683)
Volume = 0.0654ci (39.2% of the volume of a .683)

Mass = 46.3gr

SD = 46.3gr / .5^2 = 185.2

BC = 185.2 / 16542.0167 = 0.0112
The "Compromise" (a fill density between the "Mini-Me" and the "Slug")
Volume = 0.0654ci (39.2% of the volume of a .683)

Mass = 33.49gr

SD = 33.49gr / .5^2 = 133.96

BC = 133.96 / 16542.0167 = 0.0081
Pictures (in all pictures, red line = normal paintball at 300FPS. All other projectiles based on the maximum velocity which keeps the starting energy (point blank shot force) lower than the .683 at point blank.









Performance Data:

.683 Paintball @ 300FPS
Maximum Energy (ME): 9.255ftlb

Maximum Range (MR): 97yds

Angle for Max Range (AMR): 26deg

Terminal energy (TE): .478ftlb
Mini Me @ 445FPS
ME: 9.095

MR: 108yds

AMR: 21deg

TE: .178ftlb
Slug @ 300FPS
ME: 9.255

MR: 144yds

AMR: 30Deg

TE: .892ftlb
Compromise @ 350FPS
ME: 9.112

MR: 132yds

AMR: 26

TE: .467ftlb
Conclusion:

Looking at the performance data and the charts, I would say that the .50cal round that GI Milsim is pitching is probably closest to the "Compromise" round. You get a higher velocity, you hit with slightly lower maximum force, a longer range, and you shoot a little flatter. and because it weighs slightly less, you will probably get a little bit more efficiency as well.

The key thing is that they claim a higher accuracy. This is most likely due to the fact that the "Compromise" projectile will reach the target distance in a shorter amount of time (due to less drag), and therefore will be subjected to vortex shedding forces (the key reason for poor paintball accuracy) for less time. This is combined with the fact that the higher density helps reduce the effects of vortex shedding as well.

I think they may be actually onto something here. However, these rounds simply do not have the ballistic qualities of the first strike rounds (better velocity retention, and spin stabilization). They're still spheres, just less sucky ones.
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Old 09-11-2009, 12:03 PM   #2 (permalink)
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So they will be allowed to shoot at higher velocities, have a smaller ball, and the ball is just as heavy at .68 cal? So they will travel faster and hurt more?
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Old 09-11-2009, 12:25 PM   #3 (permalink)
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Originally Posted by Kahnif View Post
So they will be allowed to shoot at higher velocities, have a smaller ball, and the ball is just as heavy at .68 cal? So they will travel faster and hurt more?
he's modeled three possibilities. we don't know how the final product will turn out. my guess would be that the final product would be more along the lines of UV's compromise.
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Old 09-11-2009, 12:28 PM   #4 (permalink)
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Originally Posted by brycelarson View Post
he's modeled three possibilities. we don't know how the final product will turn out. my guess would be that the final product would be more along the lines of UV's compromise.
What is you best estimate on the slowest speed a normal .68 cal will still break?
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Old 09-11-2009, 12:31 PM   #5 (permalink)
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Originally Posted by Harbinger[TG] View Post
What is you best estimate on the slowest speed a normal .68 cal will still break?
hmmm, not sure. really dependent on paint quality. what's the velocity of paint dropped from 8'?
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Old 09-11-2009, 12:35 PM   #6 (permalink)
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Originally Posted by brycelarson View Post
hmmm, not sure. really dependent on paint quality. what's the velocity of paint dropped from 8'?
No idea, but I am not thinking about breakage on concrete or wood, but the average player. I am looking at these graphs, and while they are great work, I have doubts any of them are going to work at ranges like 100 yards.

Maybe you can get Gordo to stand out at distance and see what breaks where.
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Old 09-11-2009, 12:54 PM   #7 (permalink)
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Originally Posted by Harbinger[TG] View Post
No idea, but I am not thinking about breakage on concrete or wood, but the average player. I am looking at these graphs, and while they are great work, I have doubts any of them are going to work at ranges like 100 yards.

Maybe you can get Gordo to stand out at distance and see what breaks where.
right, the FS rounds are the only way to reach out like that.

looking at the greater energy at range and the fact that you get less drop - I would think you might be able to reach out an extra 50-75 feet. That seems pretty reasonable.

I usually assume 200' is at the edge of usable paintball range. at that range the .68 ball is only going 70 fps. the .50 doesn't slow down to that until 100 yards - but that's assuming a higher initial velocity. UV is going to re-run these calcs using 300 fps as the starting velocity for the .50 and see what he gets.

If the .50 is allowed to shoot faster - then you might see some really significant improvement in range. If they're limited to 300 fps, whether by field rules or manufactuer spec - then I would think you would get 20-50 extra feet of usable range.

Now, this is assuming that the ball breaks just as easily as the .68 - if they can get a more brittle projectile - then I don't know.

Mike and Willie over on TachPB had a first strike round break at 517 feet. That's WAY out there - but those rounds are quite brittle on the nose.
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Old 09-11-2009, 01:05 PM   #8 (permalink)
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Originally Posted by brycelarson View Post
right, the FS rounds are the only way to reach out like that.

looking at the greater energy at range and the fact that you get less drop - I would think you might be able to reach out an extra 50-75 feet. That seems pretty reasonable.

I usually assume 200' is at the edge of usable paintball range. at that range the .68 ball is only going 70 fps. the .50 doesn't slow down to that until 100 yards - but that's assuming a higher initial velocity. UV is going to re-run these calcs using 300 fps as the starting velocity for the .50 and see what he gets.

If the .50 is allowed to shoot faster - then you might see some really significant improvement in range. If they're limited to 300 fps, whether by field rules or manufactuer spec - then I would think you would get 20-50 extra feet of usable range.

Now, this is assuming that the ball breaks just as easily as the .68 - if they can get a more brittle projectile - then I don't know.

Mike and Willie over on TachPB had a first strike round break at 517 feet. That's WAY out there - but those rounds are quite brittle on the nose.
My only other concern is how are these in relation to the impact force.
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Old 09-11-2009, 01:08 PM   #9 (permalink)
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My only other concern is how are these in relation to the impact force.
well the graph of velocity shows higher velocities at much longer ranges.
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Old 09-11-2009, 01:08 PM   #10 (permalink)
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Awesome; I was wondering about this myself. The ballistic ARE better, as long as the weight, or velocity, are increased to similar energy levels.

I've shot some very, very brittle paint lately. I hope if we ever do make the switch (not something I'd want to do) the new paint is super-brittle, too.
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