DIY Ballistic Coefficient or Getting the Data Yourself

[Mole2017]

Not being one to always believe what data I can find on some pellets and wondering what my BSA R10 can really do at longer ranges, I set about doing some low budget estimation of ballistic coefficient. Here is my story and results.

I suppose low budget can go a couple of ways, but my case starts with having a chronograph that only gives me muzzle velocity--the Combro CB-625. It is useful for some things, but muzzle velocity is all it can do. After that, I had to depend on calculators and whatever data they had on the pellets.

But recently I picked up a ProChrono PaintBall for cheap at a yard sale ($7), which now gave me something to work on that terminal question. Of course, you can always set the ProChrono at the range in question and shoot at it, but I was wanting a ballistic coefficient I could calculate with. OK, ballistic coefficient is actually a slippery little devil that changes with speed and drag model, but I just wanted to have a number for which I knew its source...Now having two chronographs, I could shoot pellets and have simultaneous muzzle and terminal velocities from which to extract a BC.

First I tested both for muzzle velocity. I strapped on the Combro and put the ProChrono as close as I could to the outlet of that for a simultaneous measurement. Here's some velocity data in FPS for five shots that is worth noting some things about:
         Combro          ProChrono
            889                896
            893                897
            903                904
            892                897
            902                897

What I noted right off that it wasn't going to be easy to do this comparison shot by shot--sometimes the Combro was higher than the ProChrono, sometimes lower, and sometimes the same. This brings up an interesting question of the ultimate precision of any chronograph and the true meaning of any observed spread, but suffice it to say I felt I'd be better off to compare averages of five shots. Going that route, both chronographs gave averages that agreed to within 1 percent or less. Good enough for engineering, as they say.

Now for the tests. I strapped on the Combro and set the ProChrono out at 30 yards with a suitable armor plate to protect the electronics (1/2" thick acrylic I had laying around). Five shots each of seven or eight different pellets and a repeat set of one pellet just to see. I calculated the average velocity for each pellet at the muzzle and at the target, then fed these into my favorite (i.e. easy to get at) online calculator over at American Airguns to find the BC that fits the two velocities best. Here's what I got:



I've sorted that data by "best energy retention" and boy was I pleased to see how the NSA pellet turned out! Over 30 yards, it only lost 13 percent of its energy, compared to a somewhat lighter wad cutter (the RWS Supermag, actually a "heavy" wad cutter), which lost almost 50% of its energy. Things to note:

• For a given pellet shape, the trend for higher BC essentially follows weight of the pellet. I think the actual factor is sectional density, but in general this supports the thinking that a heavier pellet was the direction I wanted to go for some terminal smack-down potential. The NSA has both weight and shape going for it.
  
• The BC is just an average number representing a complex interaction and is sensitive to all the factors that go into finding it. Look in the middle of that table: I duplicated a test of the JSB Heavy, shooting one set early on and another after I did the other pellets. Between the variability of the measurements and a few shots that didn't register on the ProChrono resulting in 3 good shots for one set and 4 for the other, I got two values for the BC. Not a huge deal--they are within 5% or 6% of each other and are useful at this point. Lesson: don't go nuts about decimal places here.
• Likewise, the BC values I have are "mine"--my conditions are different than those for others reporting BC values. For example, NSA lists a BC of 0.062 for this "slug" or bullet. After I get done tuning the R10 to launch these babies at higher velocities, hopefully with excellent accuracy too, I may in fact get a similar BC. For the JSB pellets, HardAirMagazine didn't have a BC for the 10.34 grain pellet. Now I have numbers I can work with. Like I said the BC is a slippery one: check out Rsterne's results, particularly his comments below his table: https://www.gatewaytoairguns.org/GTA/index.php?topic=51607.0
  
• ...and on top of this, I've been assuming the list values of the pellet weights are correct. Technically, I should verify these and that would slightly change the results as well. Testing can get complicated.
  

To tell the truth, I may not use the BC for much more than some "what if" calculations at the longer ranges. I'll ultimately depend on shooting some targets to work out my hold over and such for hunting, but the calculators can help estimate what to expect for drop and wind drift.

[Bayman]

Great piece, thank you for posting.

[Pandur_HR]

You will need ballistic calculator which support GA drag, multiple BC (for different velocities) or Cd, MV temperature correction, spin drift.

I use Strelok Pro which support all of mentioned. After it had been properly configured, it calculate POI inside 2 MOA accuracy on 150m (162 yd). 1 MOA on 100m (109yd). 4 MOA target, I usually hit with a first few pellets (wind estimation), not rarely with a first one. And I am shooting with a .22 springer, that is far.

I will see when I get the weather station (for true weather data on shooting line) is that 2 MOA on 150m is going to decrease, now I use live weather forecast from internet.

[Arch_E]

Great piece, thank you for posting.

+1


Essentially, the heavier pellets arrive with more retained energy - am I reading this correctly? And, Wadcutters perhaps have the worst design for BC; hence, the admonition not to depend on them for over 25-30 yards?

[Mole2017]

Great piece, thank you for posting.

+1


Essentially, the heavier pellets arrive with more retained energy - am I reading this correctly? And, Wadcutters perhaps have the worst design for BC; hence, the admonition not to depend on them for over 25-30 yards?

Essentially correct, but don't rule out a wad cutter too quickly. I was using that RWS Supermag effectively on grey squirrels out to 45 yards in a .177 Gamo CFX (a springer). It was my most accurate pellet at the time. However, the lighter wad cutters do "drop like rocks" past about 30 yards; I saw that when I was testing pellets years ago. Later, I discovered that the Crosman Premier Ultra Magnums (CPUM) were very good in this rifle too, but I then stuck with the Supermag because my shooting was almost exclusively within 35 yards, for which I liked the terminal performance of the Supermag better--wad cutters simply hammer squirrels! For some of the same shots, the CPUM would pass through and the squirrel would run like nothing happened, whereas the Supermag would knock them off their perch or feet almost every time and kill them more quickly.

The heavier pellets are benefiting from that sectional density property and, for most of those in this test, the rounded nose. Which would you throw for a long distance: a hollow ball or a solid ball of the same size? The "density" equates to extra momentum to keep going against the same drag levels. But that shape isn't as aerodynamic as the NSA bullet, so that's how the NSA did so well. I did have a really heavy JSB pellet available, the Beast at 16.2 gr, but didn't include it in the test. Indeed, I only threw the NSA in there because I thought I still had enough air in the gun and test conditions were still favorable (I needed the glare of the cloudy skies to make the ProChrono work well). It probably would have had a BC around or slightly above 0.03, but nowhere near 0.05 like that NSA.

[Mole2017]

You will need ballistic calculator which support GA drag, multiple BC (for different velocities) or Cd, MV temperature correction, spin drift.

I use Strelok Pro which support all of mentioned. After it had been properly configured, it calculate POI inside 2 MOA accuracy on 150m (162 yd). 1 MOA on 100m (109yd). 4 MOA target, I usually hit with a first few pellets (wind estimation), not rarely with a first one. And I am shooting with a .22 springer, that is far.

I will see when I get the weather station (for true weather data on shooting line) is that 2 MOA on 150m is going to decrease, now I use live weather forecast from internet.

Great shooting with that springer!

I've heard of the Strelok app before, but I'll need a smart phone first  . My girls insist I really would benefit from one, but I'm not ready to pay for one yet.

I lieu of the apps, this is the low-tech approach. And there probably still are options if you don't have two chronographs. I think there is one where you work out the BC from the measured drop at several distances and some measurements of your scope set-up relative to the gun. I even did something like it years ago. I had the drop at four or five ranges and wrote a pretty good simulation that let me estimate both the muzzle velocity and a drag coefficient to match that data. For two unknowns and five measurements, it represented a "best fit" scenario, but it was sufficient for the modelling I was doing at the time, which was to work out was happening at high inclination angles. Very informative.

[Arch_E]

super, informative post--for newcomers like me.

[Pandur_HR]

I am not sure can the BC be calculated from relation between center view of barrel and scope setup. Different projectiles will leave barrel at different way, due to different vibrations and barrel  harmonics. Something similar to aerodynamic jump due to wind.

I did something else other way around. I calculated POI and then elevate the scope without shooting.

When I went to range to verify calculation on 25m (I still have that data).

Cal .22

Deviation from calculated value:
JSB 18.13 was 2 MOA down, 1.5 MOA left.
JSB 15.89 was  3 MOA up, 0.5 MOA left
Metalmag was 4 MOA down, 1.5 MOA right
G-Hammer was 3 MOA down, 2 MOA left

This is way too much deviation for BC calculation.

Now I use those data in scope offset settings in Strelok, so that I don't have to re-zero scope when changing between pellets.

I calculated BC for Metalmag based on POI, by shooting at 25,50,100m. It cost me a lot of pellets, in various conditions, to get reliable groups and representative POI.

By velocity is way easier.

[Mole2017]

I am not sure can the BC be calculated from relation between center view of barrel and scope setup. Different projectiles will leave barrel at different way, due to different vibrations and barrel  harmonics. Something similar to aerodynamic jump due to wind.

I did something else other way around. I calculated POI and then elevate the scope without shooting.

When I went to range to verify calculation on 25m (I still have that data).

Cal .22

Deviation from calculated value:
JSB 18.13 was 2 MOA down, 1.5 MOA left.
JSB 15.89 was  3 MOA up, 0.5 MOA left
Metalmag was 4 MOA down, 1.5 MOA right
G-Hammer was 3 MOA down, 2 MOA left

This is way too much deviation for BC calculation.

Now I use those data in scope offset settings in Strelok, so that I don't have to re-zero scope when changing between pellets.

I calculated BC for Metalmag based on POI, by shooting at 25,50,100m. It cost me a lot of pellets, in various conditions, to get reliable groups and representative POI.

By velocity is way easier.

If velocity is known, it certainly is best to use it. In fact, to really get the BC calculations, one would prefer to have velocity at multiple points downrange. The LabRadar has been a godsend to those that can afford it, allowing them to determine a velocity dependent BC.

However, at modest velocities and ranges, the "no velocity" method does work, though it is not nearly as accurate. I had POI at 5, 10, 15, 20, and 25 yards as seen through the scope. Maybe even 30. The scope views along an axis that is hopefully in the same vertical plane as the barrel, but even that is not a rigorous requirement. Once you have measured distance between the center line of the scope and the bore, you are just dealing with an intersecting line and pellet path. Mathematically, all it is a transformation of coordinates applied to the simulation output. By trial and error you dial in the muzzle velocity and whatever coefficients needed for the drag model until you get a good fit to the observations. Of course, the key to this method is having a simulation tool. In my case, I wrote one for a pellet under the action of aerodynamic drag. It was a simple model, but was again sufficient for the purpose. The final output was a graph of POI in mildots at different ranges and angles. No windage calculations were included.

Now for target work and really long range stuff, it may seem pretty crude. Barrel harmonics creates problems for certain guns, like you said, but I suspect other factors can be present (e.g. clothing, changes in grip, fatigue affecting technique) which similarly cuts into the validity of any predictions. That is why I ultimately go with field testing over simulation results.

In addition to the different ranges were are talking about, we also use our scopes differently, I think. These days, I've set my scope zero somewhere around 30 yards and I leave it there, preferring to know where the POI is relative to that setting and holding over or under as needed at any range. I've seen others develop "dope sheets" and then turn the knobs on the scope for whatever range and wind conditions the sheet says to use. There an good app would be supremely useful, but field testing can also generate some of that information if you lack the instruments to measure velocity in the first place. I have recently acquired a scope for long range work, and I see myself learning to use this method, as the drop at those ranges exceeds the markings on my reticle. And if you change the zoom...more shooting is needed, or some good math must be applied, or just use the app 

[rsterne]

David, first of all, let me congratulate you on your methodology.... and your conclusions.... You are correct that for a given pellet shape and caliber, the BC is proportional to the weight.... Over differing calibers, you would use the Sectional Density, instead of the weight, of course.... You are also correct that using too many decimals in the result is unnecessary, I would not go past the third decimal, ie 0.0226 and 0.0234 should both be recorded as 0.023, IMO.... Using a larger sample size would be a good idea, because the accuracy of the average increases, particularly if you are getting errors that are reducing your sample size even further.... I couldn't find out what Drag Model you used in your calculations, but currently the GA model is the best we have for Diabolo pellets, although it differs only slightly from the G1 model, which is the best for the NSA slug.... Since you are testing with one gun, and that means that heavier pellets are starting slower, the calculated BCs for the lightest pellets will likely be low and for the heaviest ones may be high, relatively speaking.... That, again, depends on the drag model chosen, and how well it matches your projectiles....

The best thing is that for YOUR gun, you have a valid comparison....

Bob

[Pandur_HR]

Or, instead of changing zoom. Think about shims (Hawke has good 25 MOA ones) or adjustable mount. I use both, giving me total of 90 MOA boost available.
That is more trigonometry and math involved. I like it too.  Recently I re-zeroed scope on 150m, now I wll re-zero it back to 100m, since on 150m is not usable on short range.

If you are going to do longe range shots, it is better to use high zoom on long range and low zoom on short range (field of view), not the other way around. Simply elevate the scope, and leave it in optical center.

Not to change calculations, I entered elevation as offset in calculator and left the scope as zeroed on 25m.

If you are good with math, elevation can be done without shooting with few MOA mistake.

I use feeler gauges to messure clearances of adjustable mount, messure the lenght of mounth, and use trigonometry to calculate the new clearance. If you know adjusting bolt thred, things are done very fast in 2-3 MOA precision.

Note that by elevating scope you will change scope height in relation to the end of barrel. That is more trigonometry to do.   

[Mole2017]

Thanks Bob! Yeah, I wasn't pleased with the short sets, but the weather was briefly uncooperative and I just had to keep moving--and take more care to put the shots over the gates....You have to make sure the ProChrono isn't slightly cockeyed to your line of fire.

It's not like the cosine error will eat you up so much as you might miss the sensitive zone of one of the gates. I was putting the shots about 4 or 5 inches above the top of the ProChrono. I happened to leave the rods in place without the diffuser while setting up, and after I realized how easy it was to flub a shot, I used them to stay lined up with the ProChrono. (It was easy to bump the ProChrono out of line each time I walked up to get the reading.) Yes, every shot required walking up to the ProChrono, maybe lifting the armor out of the way to get the reading, and heading back. The acrylic was thick and dirty and you couldn't just flip the zoom to 16x to read it from the firing line. That's a mile and a half of walking--a huge waste of time, but that's what I get for owning a ProChrono Paintball. I could have put a video camera up there and reviewed the video afterwards to get the readings and have finished everything faster. 

I was surprised the Power Ball and Hunter Extreme fared worse than the lighter Diabolo Exact, but the shape of that dome does the trick, apparently. I see it also has a slightly different angle to its skirt.

[Mole2017]

That's some pretty cool shooting you do Ivan. Zero at 100 and 150 yards...When you mentioned the adjustable mount I remembered I had seen someone with a really steep angle on their scope mount because they were shooting so far. Have a look at this--you have to wonder how much his gun is blocking the view