There is a ton of misconceptions about what REALLY is the B.C. (acronym of Ballistic Coefficient) of a projectile.
Probably, the most noxious one is the one that equates a high B.C. to a "good" projectile and a low B.C. to a "bad" projectile.
B.C. is NOT a measure of the "design qualities" of a projectile.

So. . . . ¿What is BC?

First and foremost, BC is a SCALE FACTOR.

To explain this we need to go back almost two hundred years, to the heroic days when small, field worthy artillery pieces were truly coming into their own. When smokeless powder first became a commercial and military reality, and when the value of a soldier's life was less than the value of the musket he carried.
So, imagine yourself living from the 1840's to the late 1880's:
The US has just doubled its territory by waging war on México.
Crimea has just been lost by the Russians to a Western European bloc
Germany has just annexed all the Alsace Lorraine
The French have just invented the "75" and Captain Dreyfus is spending some time in "Devil's Island" because it is easier for the "Establishment" to send an innocent person to his death in a tropical island than to accept that the ring of spies is so well entrenched in the government circles as to make it a "Reason of Sate". 
Russia is trying to assert its role in the "modern world" and the Czar decides to support the Army because supporting the Navy, with no warm water sea port is senseless. There is a peculiar alliance being established between France (the 3rd Republic) and Russia (an Imperial Autocratic State).

Out of England (THE Maritime Power of its day), comes a young chap by the name Francis Bashforth; developing on the (by then 200 years old) ideas by Benjamin Robins, he creates in the late 1860's an electromechanical chronograph that is capable of measuring velocities of projectiles to much greater precision than the ballistic pendula of the day. Consider that to measure ACCURATELY, a ballistic pendulum has to have a mass at least 200 times greater than the projectile it tries to measure. Now consider the size of ballistic pendula for artillery ogives.
Bashforth measures and creates tables for all his measurements, and then comes up with a flash of brilliance:
¿What if ALL the effort was devoted to a "standard" projectile, could he then prove that all other projectiles would have a SIMILAR behaviour? 

Similarity, in the mathematical context, is the capacity to change one thing into another using a scale factor.

And so, he proposes the Ballistic Coefficient; a SCALE factor that can tell technicians how a given projectile will behave BASED on a LOT of firings of a STANDARD projectile.

Being a good Yorkshireman, and VERY British, Bashforth uses a Standard Projectile (S.P.) of 1.00" Caliber, with a 1.5" tangent Ogive, weighing (¿What else?) 1 lb. And this becomes the B.C. = 1.00

Now, let's come to the present and analyze this a little: ¿What on earth can be MORE DIS-SIMILAR than a flat base, 1.5 calibers tangent ogive, parallel sides projectile, weighing all of 7,000 grains in 1.00" Cal. AND an 8.44 grains, diabolo shaped (waisted) pellet with an ogive barely 1.25 calibers in cal. 0.177"?

Caliber of the S.P. is more than 5½ times the caliber of the projectile we are interested in. 
Mass of S.P. is more than 800 (eight HUNDRED) times the mass of the projectile of interest.

There is NOTHING of the S.P. that barely resembles our pellets. How can we HOPE to use a simple SCALE factor?

Well, we can't.

And neither can do many others interested in the exterior ballistics.

Going back to the late 18th Century, the Russian Mayevski, then the Italian Siacci and then the American Ingalls, conducted a LARGE number of tests. At the same time, Krupp was conducting their own experiments and by 1875-1890 all nations had a pretty well informed knowledge of what exterior ballistics truly meant, as far as field artillery pieces were concerned. Just in time for the Balkan Wars, and then World War I.

Let's get this chart clear. The chart illustrates how the DRAG changes with speed. It is NOT a B.C. change chart, but it is close in an inverse sort of way.

Now, please consider: IF drag changes like this for every speed along the pellet's projectile, then the B.C. that is trying to scale a whole trajectory is much more dependent on how closely the projectile of interest is to the S.P.

It was the Russian, the Italian and the American, the ones that first proposed a DIFFERENT way to look at things: ¿Why not develop a mathematical model that, taking into account the physical characteristics of the projectiles will give us firing solutions?

Ah! that sounded GREAT!, let's call it Drag Function and then we can PREDICT what things will behave like as long as we know how those physical characteristics relate to the external ballistics.
At first it seemed that a "form factor" could be established that related the B.C. to the sectional density (the weight of the projectile -in lbs.- divided by the square of the caliber), BUT then the form factor became something to be qualitatively assigned. Tables were prepared where by graphical observations, shooters could ascertain which form factor they could use for their bullets.

REAL problem is that reality is a little too rich in details and too complicated to actually be able to do this with any really good precision. Few functions are linear, and since the old days, the exterior ballistics solutions have been, in reality, approximations by velocity regions. One set of equations, constants and coefficients apply from 0 to about 850 fps, another from 850 to about 1,100, another from 1,100 to about 1,400, then another between 1,400 and 2,200, and another between 2,200 and 5,000 fps.

Even at present, military applications use one Drag Function and commercial applications use another.

In the market there are several programs and types of software that use the drag coefficients. BUT they all have the same caveat: Use only by sections and make sure that YOUR case is not close to the boundaries of the sections. A few really good and conscientious manufacturers publish the B.C.'s for their bullets by MV regions.

In more recent times, with the advent of cheap and relatively reliable and precise chronographs, it has become easy to determine the "deceleration" (loss of velocity) of ANY projectile, and there have been some rather interesting approaches to solving the firing solutions. 

Among the more imaginative is Pejsa's "Velocity Retention Factor", and similar approaches whereupon some of the modern airgun pellet ballistics programs work.

Another aspect about shooting pellets as opposed to bullets, is that our pellets deform upon firing.
The BEST mathematical model taken from the dimensions of the newly produced pellet will NOT be true once you fire that pellet through ANY barrel.

Modern pellets and modern barrels do this less dramatically than those made only a few decades ago. Compare the above picture to this one:

And, I think it is obvious, but I will say it again: EACH pellet/barrel combination will do this in a slightly different manner.
So, there is NO way to use a "table" B.C. for your pellet calculations, if you want them to be precise.

One of the peculiar differences between airgun shooters and powder burners is that, for them, some differences are "small" or "inconsequential". For airgunners where the targets are measured in fractions of an inch, there is no really inconsequential difference. 
Especially for FT shooters. 
A 40 Troyers target (a measure of relative difficulty) is a ½" target at 20 yards. The pellet occupies 0.177" of that, so the real wiggle room is about 0.32" If you consider that the pellet needs to be LESS than one caliber off to any side from center, you realize how accurate FT shooters and gear have to be.
And that is not the hardest target in an FT course, Match Directors can place these ½" targets all the way out to 30 yards! for a 60 Troyer shot.

Anyway, coming back to B.C.:

It seems to be one of those things that you are bad with it, and even worse without it.

For years I used Pejsa's approach and tried to calculate and keep good records of Velocity Retention Coefficients for all pellets in all my rifles. And then we went to Norway to shoot at the FT World's Matches and  I got faced with wind drift.

This is the OTHER side of B.C.: ONCE YOU HAVE A TRUE B.C. then wind DOES become a scientific calculation.

Not only that, Wind drift is proportional to normal velocity (velocity vector measured perpendicular to the trajectory plane). So, if you could have the B.C. for YOUR pellet, shot from YOUR rifle, at the place you ARE shooting, then wind drift is really more a matter of learning how to "guesstimate" this normal wind velocity.

BUT. . .  chicken and egg situation! How can I find the B.C. of my pellets shot at places as dis-similar as Norway (coastal location), Germany (mountain location), Texas (lowland, dry location), or Baton Rouge (humid, coastal location). ¿Should I take my two, matched, Chronos and do all my testing all over again?
¿At EVERY venue?

Well, enter a different point of view and a recently modern mathematical approach called "Fuzzy Logic", where one quantity can have not only A value, but a RANGE of values. Then you go on the next "test case" and check that range of values against the new one, and by discarding those values that are OUTSIDE BOTH ranges, you have a narrower range. Then you take a THIRD test case and come up with a different range of values, when you compare all three and come up with the value that meets all three test cases, then you have your solution.

This is how P-P Calc works.

And that is why I came back to the B.C. method. By using a zero range and THREE more ranges and POI's, the software calculates the B.C. by sections of the pellet path, it will give you a weighted average and use that for the calculations, but more importantly, it will calculate the wind drift.

While discussing the error in B.C.'s  vs. the Wind Normal Velocity reading error with a very good shooter, Scott Hull, he came up with this example:

As you can see, an error of 0.006 in the B.C. (six thousandths, from 0.021 to 0.015) will move your POI as much as an error of 1 mph in reading the wind.

As much as we dislike the idea, we cannot fault our pellets for having such a low B.C. (just to illustrate, some modern 0.50" cal bullets have B.C.'s GREATER than 1.00)
The low B.C. is what makes the use of our pellet rifles relatively safe in urban environments and at close distances.
The low B.C. of our pellets is what gives us the same challenge shooting out to 55 yards as the H.P shooters get shooting at 600 yards.
The low B.C. of our pellets is what makes our sport unique.

In conclusion:
Pellet shooters CAN use the B.C. concept, but they need to be careful to apply it by sections.
"Fiddling" with the B.C. is not too smart unless you REALLY know your rifle/pellet combination well. You may arrive at a scale factor (the B.C.) that has nothing to do with reality.
P-P Calc will allow you to MEASURE the B.C. from YOUR rifle/pellet combination at EVERY venue. You can then store that venue for future reference.

Hope this has been informative and I hope to see you at some FT Match soon!







HM

As promised in our previous article, we performed some more extensive tests. We had the support and help of the Eastern Field Target Competitors Club (EFTCC) in the person of Ray Apelles who, very kindly, opened the DCPA Range up for a Sunday fun session of testing, shooting the breeze and general airgun camaraderie. THANKS!

We arrived at the appointed time and found Ray in the process of opening Range 3 (the airgun range), so we took all our impedimenta up the hill and settled on some shooting positions, setup paper targets and quadrant spinners and called a hot line.

First thing was to test in a comparative manner how the well-used and trusted HW-95 was performing vis-à-vis the “new to Veronika” Diana 54. She decided she would shoot two targets at 20 yards and then two targets at 40 yards with both guns and then compare what was happening.
Here is the first target, the HW-95 with a Hawke Sidewinder scope at 24 X:

As the reader can see, the 2 groups shot at 25 yards (#6 & #10), show a reasonable performance, yes group #6 opens up, but that is normal when shooting a recoiling springer shot after shot after shot. Shooting springers does require some effort and physical tiredness is not to sneeze at when dealing with fine motor coordination tasks.

What raised a red flag for us was groups #13 and #14 at 40 yards. Not so much because the group opened, that was expected, but because the groups shifted dramatically from left to right of the target when there was no appreciable wind at the range. Hmmmmmm . . . .
So she settled down and tested a Diana 54, WFTF version with a Barska 12X scope, and these are the results:

As you can see, the groups at 20 yards (#10 & #6) were not too different from the groups shot with the HW95. In fact, careful measurement revealed that the difference between the two groups was 2 mm’s.

So next came the test groups at 40 yards, on targets #14 and #15. Again, not a large difference between one rifle and the other.

After some more practice and a little bit of further familiarization, I decided to test the HW95 because something was not working right in there, so we changed papers and while I was shooting targets #19 and #20 with the 95 first from the bench and then from the knee, Veronika was shooting targets #2 and #7 using the Diana 54 BUT with one important change: She was holding a sight picture. And that sight picture was, as per my suggestion, to cradle the center of the bullseye on the upper right corner of the reticule’s crosshairse. Some shooters believe that when using a scope, there is no sight picture. Yes there is. And the lower the magnification of the scope, the better the consistency of the sight picture has to be preserved.  

As you can see from targets #2 and #7, ALL of those hits would have meant a fallen target and a point added to the score, at 40 yards, in the hands of the shooter with a somewhat disadvantageous scope (only 12X).

The tests on the Hawke/HW-95 system did not go well and demonstrated that there was something amiss. The gun is perfectly capable of much better accuracy.

So, we decided to change the scopes. The scope my rifle was wearing, a Hawke Eclipse 6-24X50 got replaced for her much fancier Hawke Sidewinder 6-24X56.

After some messing around with the alllen wrenches and just getting things reasonably in order, Veronika allowed me to sight in the scope and then shoot some tests. We returned to 25 yards for expediency, as it was getting on with the day and hunger started to show its ugly teeth.

So, this is the final test, the 5 shot witness group on target #1 (with the flyer that I probably pulled) was just to make sure that the sight settings were not completely off; and target #7 was a consistency confirmation group with 20 pellets through that hole.

Veronika shot groups #15 and #16.

She being left handed and having completely different sight parameters was hitting a little left and high, but the main thing was established:

There is no real handicap shooting non-lead pellets in a WFTF environment because the KZ’s are not that small.

Wind does play a role and it is my honest opinion that in WFTF what is tested is more the shooter than the gear.

Due to some questions arising from our first little note, I am hereby addressing some of the issues:

Flight characteristics of the Barracuda Green are not that different. Compare the JSB 8.44 and a Barracuda Green shot at the same ENERGY level (sub-16 Joules); please note that the red curve is the Barracuda Green, the Blue curve is the JSB 8.44 .

NOT a lot of difference, ¿is there? 

Now see the windage curves, first the JSB; for a 10 kph wind and a 50 meter range, the deflection is a little over 2 miliradians:

And now the Barracuda Green for the same wind and the same range:

A little over 3.5 miliradians. Yes it takes some getting used to, but not Impossible.

On the energy side, calculations performed with actual, measured BC’s yield that at 50 meters (55 yards), the Barracuda Green still has 4 ft-lbs of energy. So, as long as the targets comply with AAFTA’s recommendations (page 31 of The 2013 Handbook), there should be no problems.

Transferring energy and momentum are two different things and, while silhouette is one game where momentum can take the field, FT is not. And the reason is simple: The PADDLE of the FT is a relatively light element that only needs to be taken over the dead-point and then the full weight of the FT plays a role in its fall. The paddle is captive, it cannot spin, nor can it “totter”, a properly set target will fall. Yes it is true that for MD’s the requirement for leveling and setting is a little more stringent. But as long as the targets fall with 4 ft-lbs, the Barracuda Green has no problem performing where it counts.

As for durability of the FT’s themselves, it has to be stressed that tin is not as hard as steel, a steel BB WILL damage the FT’s much more than a tin pellet and the use of BB’s is a risk to be avoided because of the potential for a ricochet with a faceplate hit.

Some other offerings out there use steel inserts, I do not think those are a good idea.

One should always bear in mind that the last shaping tool a pellet sees is the barrel, and therefore EACH gun will be different. How a specific barrel shapes each type of pellet is something that cannot be predicted.

That is why we all need to try different things in different guns.





Good shooting!

Many years ago, when I first introduced my (then) girlfriend Veronika to airgun shooting, little did I know that she would one day be shooting right alongside me and going to world-class events.

In all these years I've seen her evolve as a shooter and develop definite ideas, likes, needs and wants.

And it has been my pleasure and my privilege to try to come up with solutions to those requirements.

About two years ago, she decided she wanted to shoot non-lead pellets. Out of conviction to be doing the right thing, she has persevered and we have managed a decent accuracy from her standard (and only) airgun: an HW95.

Husbands being males and males not being able to leave a good working thing bloody well alone, I have been trying to get her to switch to a more stable platform, stable as springers go. So I got for her an older model Diana 54 , the one with the slim stock, lightened the action as much as possible, changed all the internals to my “WFTF” model, and then started to fulfill what was, in mind, the most important requisite: Shoot well with non-lead pellets.

For the last few years, Veronika (now my wife) has been shooting “green” pellets, made by Haendler & Natermann , in particular, the Barracuda Green.

But with the possibility of a new gun, the possibility of new pellets also opened up, so I decided to make a trial run between the available non-lead pellets. Here in the US, the only really available non-lead offerings are limited to the Dynamic line by Prometheus and the Green line offered by H&N.

Having learned some time ago that the trick in shooting non-lead pellets is to drive them fast and use a good lubricant between pellet and barrel, I settled down to do some test shooting wich yielded the following results:

The reader can appreciate at the top left two “witness” groups shot with JSB Exacts (8.44 in this case),  made by Schultz Diabolo in the Czech Republic they are arguably some of the best pellets for Field Target shooting. So we compared the performance of the Dynamic pellets to the JSB's. 5 shots at 22 yards (20 meters). Not bad. Quite good actually. All the groups would fit comfortably into a ½” kill zone. Perhaps a little re-zeroing between one and another of the different models of the pellets, but nothing too drastic.

But,: ¿How would the old stand-by's shoot?, well, here is the result of 4 consecutive 5 shot groups at the same distance:

We will be conducting more extensive tests with this pellet/rifle combination.

Non-Lead pellets can be driven a little faster than their lead counterparts, and this offers some advantage in the limited-power world of WFTF. Yes they are more susceptible to wind, but wind is something we all have to learn anyway. If you are a serious FT shooter, you owe it to yourself to test the Barracuda Green pellets by H&N.