Ballistic coefficient: What is it? Part 2

by Tom Gaylord
Writing as B.B. Pelletier

Part 1

Last week I republished Part 1 of this discussion about ballistic coefficients because I was out of town helping my sister. I’m back in the office, but Part 2 of this report is necessary to close the loop. So here we go.

This report covers:
• Review
• Today’s discussion
• Round balls
• Conical bullets
• Smokeless powder
• A big point
• Shape
• Round balls — again
• The bottom line

I’ve taken 11 months to return to this subject of ballistic coefficients (BC). That was in spite of some tremendous interest in Part 1 of this report last May.

I’m purposely avoiding all discussion of mathematics, which is difficult, since ballistics is a discipline that heavily employs mathematics. But I’m not qualified to write about the math; and, more importantly, I know that 99 percent of my readers would be turned off if I were to write the report that way.

Review

Last time we learned that the BC of a pellet:
• Is an extremely small decimal fraction compared to the BC of a conical bullet.
• Varies with the velocity of the pellet.
• Varies with the shape (form) of the pellet.

We also learned that the stated BC of a pellet can be forced to vary by the distance from the muzzle at which the measurements are taken.

We understand that diabolo pellets are designed to slow down rapidly in flight, and that the BC is a measure of the velocity retained in flight. So, a pellet’s BC rapidly changes over a short distance.

We learned that a pellet’s BC varies between 0.010 and 0.045. We also learned that pellets that have a relatively high BC (the larger numbers) will take longer to slow down than pellets that have a relatively low BC. Even though all diabolo (wasp-waisted with a hollow tail) pellets slow down rapidly, the higher BC numbers are given to the pellets that slow down the least in relation to all diabolo pellets.

Today’s discussion

Today, we’ll look at the impact that shape (form) has on the BC. We’ll also look at the impact velocity has on the BC. Let’s begin with that.

Round balls

When firearms were first invented (we now believe that was in the 1300s), the earliest formal shape for missiles was either a shaft (arrow or dart) or a ball. The earliest ball-like projectiles were probably just stones, but that soon gave way to uniform lead projectiles that were easy to cast. Cannon balls were still chiseled from tough rock for many years before they, too, were cast from iron into spheres.

The round ball became more than just a projectile of choice. It became synonymous with the title — bullet. From some time in the 1400s to around 1840, the word bullet meant a round ball. Round balls are easy to enter into formulas and ballistics tables because the form is always the same. The weight varies with the caliber, but not the form (shape). Because of this, the early science of ballistics was built around a spherical bullet, and everything was fine.

Conical bullets

Conical bullets (oddly referred to as conical balls in their early days) changed everything. Ballistics had to expand to adapt to these new projectiles. Several ballisticians worked out new formulas to account for the different new forms, but by now the forms were changing faster than the science could keep up.

Smokeless powder

Then, smokeless gunpowder came on the scene and things changed again. Velocities with black powder (which, up to that time was just called gunpowder) topped out somewhere around 1,600 f.p.s. Within 20 years, smokeless power doubled that speed; and in another decade, it added another thousand f.p.s. Suddenly, bullet makers had to be concerned with shapes that flew at ultrasonic velocity. This was decades before anything else approached that speed, so things like wind tunnels weren’t even available for modeling.

It may seem like I’m getting far from the topic, but here’s why I am telling you this. In 1870, the Rev. Francis A. Bashforth — the inventor of the first (?) electronic chronograph — discovered that drag increases with the square of the velocity at speeds between 430 f.p.s and 830 f.p.s. — but with the cube of velocity at speeds between 830 f.p.s. and 1,000 f.p.s.! That higher range is the trans-sonic region that we tell airgunners to be wary of. We used to think it caused inaccuracy, but I disproved that in 2011 in an 11-part blog series titled Velocity versus accuracy. But what it definitely does do is increase the rate at which projectiles slow down.

I could easily get into a discussion of the ideal shape for supersonic projectiles, and there are many airgunners who would like that. “Just design a solid pellet that has a boattail, and all your problems are solved,” they say. Yes, all problems are solved, save one — accuracy. No airgun I know of is capable of accurately shooting those solid pellets (that I’ll now call bullets) at supersonic speeds. In fact, very few airguns can get them up to supersonic speeds at all! So, the discussion is over before it begins.

A big point

If something can’t be done, it makes very little sense complaining about what “they” should do. The blog readers know that I’m not a negative person. I’m willing to try anything that has a chance of success. But physics is physics! I’ve learned in all my experiments and reading that airguns have practical velocity limits. We may not be at the limit today, but we’re very close. Because, to push a pellet any faster than about 1,500 f.p.s. (1,486 f.p.s. is the fastest pellet I’ve ever observed), requires us to do things with compressed air that it just doesn’t want to do. The speed of sound governs how fast air can flow. Pellets can be pushed faster than the speed of sound; but to go much beyond 1,500 f.p.s., we’re going to have to use a different compressed gas.
So, pellets that top 1,000 f.p.s. are slowing down at least at the cube of their velocity. That’s what Bashforth tells us. Take another look at the chart I showed you in Part 1:

BC chart
The ballistic coefficient of a single pellet can change this much with velocity changes.

The chart isn’t real, which means it wasn’t generated by actual test data, but the relationship of the BC decline at the trans-sonic region is representative. Lighter pellets fall off their BC at lower velocities, so take the entire curve and move it to the left. The same thing happens — just at lower velocities. Heavier pellets fall off at higher velocities, too. But all of them fall off in the same way.

Shape

Enough talk about velocity; now let’s look at what the shape (form) of a pellet does to the BC. Just as certain shapes work well at supersonic speeds, there are also good shapes for subsonic speeds, where most pellets live. A domed nose with a solid cylindrical body is very good at subsonic speeds. And the more it weighs, the higher the BC will be.

pellets
The shape or form of the pellet has a lot to do with the ballistic coefficient.

The wadcutter, by contrast, is the worst shape — or at least it’s down there with the worst of them. Some people feel that hollowpoint pellets are even worse because their hollow points act like air brakes. Others believe the hollows fill with air under pressure, and the pellets then act like wadcutters.

The pointed pellet is not as aerodynamic as its shape seems. While it looks sleeker than a dome, it doesn’t turn out to work that way at subsonic pellet velocities. A point is great for supersonic speed, but it does very little below the speed of sound. Pointed pellets do penetrate deeper in solid media; but in the air, they aren’t that different from domes.

Round balls — again

Round balls — remember them? As it turns out, a round ball is sleeker at subsonic velocities than any diabolo pellet. Only when the pellet weighs considerably more than a ball of the same caliber (and may be too heavy to shoot effectively) will it have a superior BC. Round ball BCs hover around the 0.07 mark. That’s about double what the best diabolo pellet offers and several times what the average diabolo has.

So, why not just shoot round balls? Simple answer — accuracy. Round balls don’t have any accuracy at longer distances. The high drag of the diabolo pellet — the very thing that destroys their BC — is also what helps them be so accurate.

The bottom line

Yes, the BC of a pellet is important, but only after you know that it’s accurate. If you can’t hit what you’re shooting at, the retained velocity of your pellet means nothing.

So, search for accuracy first and a high BC second. Or, in some cases, such as long-distance hunting, look among the pellets with high BC numbers for the one that’s the most accurate. Don’t just shop for the highest BC unless you also understand the relationship of your gun to that number (re-read Part 1 to understand).

Is that all there is? Of course not. We could go on and talk in more detail about form, but I think the basics have been covered.

I know that many of you use the Chairgun program and find it very useful. One of the things Chairgun requires is the input of the BC of the pellet in question. Sometimes, you only discover how close that BC is after shooting your gun and matching the results to the Chairgun predictions.

I don’t know if I’ve helped you understand ballistic coefficients or if I’ve just confused you more. If you remember the basic things I’ve outlined in this report, it’ll stand you in good stead in your future shooting.

35 thoughts on “Ballistic coefficient: What is it? Part 2

  1. BB et al..
    Apologies for being so far off topic!!
    The Carpal Tunnel surgeries that I have had to both hands over the winter are healing just fine. My right hand, done the end of last October is now nearly completely healed and the left hand, done the end of March is coming along fine. The left hand was a little more complicated as I had ‘Trigger Finger’ surgery for my left middle finger done at the same time. It is still causing a little pain and numbness but is also healing well.
    Towards the end of March I found an airgun shop in British Colombia that was selling the new Crosman Bushmaster ACR (Adaptive Combat Rifle) without the sub 500fps modification. At the higher MV of 800 fps it is considered a firearm here and requires a PAL (Purchase and Acquisition License) in order to buy.
    I’ve always thought the Crosman MK-177 was a great looking gun but at the time the only ones available were the sub 500fps guns being sold in the big box stores for exorbitant prices – just not for me at the time. This gun, however, I scooped up immediately! It had just been posted on their website and I was told that I was the first owner in Canada.
    When I received the gun I was unable to shoot it because of the surgeries but was able to do a few mods that would make the gun more comfortable for my kind of shooting.
    First and foremost was to mount a sling. Not an easy thing to do on a pumper and I decided a single point sling would work well because of the small size of the gun. On the Crosman site I found the expanded parts diagram for the gun showing a moulded in hex type of bolt on the rear receiver that could be drilled out on both sides and not interfere with any of the guns internals. A clevis pin, some metal and rubber washers, a ⅝” high quality key ring and some liquid blueing to blend the colours and a perfect mod was completed.
    The second mod was done because the iron sights were no longer completely made of metal. The bottom clamp part that went on the rail is aluminum with the rest of the sight made of plastic and held together with a tiny hex screw accessed under the clamp part. The bits and pieces, both front and back, were a sloppy fit which I didn’t think would stand up for long. I replaced the rear sight with an AR style full metal rear sight. It has adjustable windage and elevation with very tactile and audible click settings. Sold by PA about 15 years ago. The matching Leapers front sight is also now on order. What a difference now in useability and not having to depend on tiny tools.
    The end of last week saw me shooting the gun for the first time. The first pellets I grabbed from my pellet stores were the Daisy ‘El Cheapo’ wadcutters, 8.0gn at $4 for 500 count belt box. After wondering why the groups were so small I got the gun zeroed at 10 meters and on a brand new gun, basically just out of the box, 5 pellet clips later I was getting .31in. 5 shot groups on 5 pumps! With the cheapest pellets! And Oh Ya, don’t forget with AR Combat Peep Sights!
    This gun is definately a keeper. With that kind of accuracy I may not even bother putting it on the chrony. We shall see. I think with some more practice on the peep sights I may see even smaller groups.
    This gun is accurate, handles nicely but has one, to me at least, major drawback. It is noisy – not the shooting but the pumping! It clacks very loudly when pumping, way louder than the shooting.
    Trying to reduce the clackity – clack pumping noise may be my next mod to this gun!
    Apart from having different trades the Bushmaster ACR and the MK-177 seem to be identical. The Bushmaster ACR seems to be quite a bit more accurate when compared to your MK-177 blog entry
    Cheers
    Dave


    • Dave,

      Glad to hear that you are back to shooting and have a new toy to play with. I love the peeper sights, like on the 499. I imagine that yours uses a front post? On the 499, I use an O front insert and at the right range, it is practically a no miss proposition. Hat’s off to you as well for getting in there and modifying it to your liking.


      • Hi Chris
        The front sight is a standard screw – in post. Plastic and wobbly that came with the Bushmaster.The new Leapers on order is all metal. These AR sights will probably outlive the gun. The rear is a dual flip over with a large aperture for close – in CQB shooting and a smaller aperture for distance shooting. Both apertures are picture window apertures with the CQB being almost 5/32 in. diameter and the distance aperture about ¼ of that. I am still amazed at how accurate these large apertures can be.
        As far as new toys I have several more that I will mention in the upcoming week or so – an action bb pistol and an anti-material sniper rifle as well as finishing my blog on the B3 – 1 and the Hatsan Torpedo 155 springer that I was unable to finish because of my gimpy wrists!
        Cheers
        Dave


      • Everyone should own a 499.
        Who could ever have believed a BB gun would be that accurate? I have shot it 10m and gotten results that for me were the same as I could get with pellets free hand.


        • Yes; I bought one for my pastor’s son; our pastor is not a “gun guy” and was unsure what to get his son and asked my advice; so I gave him the 499 (after shooting it myself a bunch, of course =>); now the whole family is shooting it and loving it! =D



    • Dave
      I have to say I have good luck with those Daisy wadcutters. My Wildfire loves them. And I have a Python Co2 pellet pistol that loves them too. They surprise me especially if you look at them compared to higher dollar pellets. People should get at least a tin of them and try them in their guns.


      • Gf1

        I didn’t read till late last night. Springing for the hw30s? Very nice! I almost like looking at mine as much as shooting it. I remember you saying awhile back you were wanting one.

        Let us know what u think. Mine was buzzy and had the gauling while cocking problem. I accidently fixed mine and mine cocks butter smooth now. I will tightened it up inside after I finish my new (pre safety) hw35. I’m also refinishing my salvia 618 stock. Just ashooters finish with some tru oil.

        Glad to hear ur Wi-Fi is working out well. I’m going to have to sit that one out again as I can’t get over these low to mid power springers. I have a slavia 630 headed my way as well. 😉

        P.S. I’m somewhat curious if you will try jsb 10.34 in the new hw30s. I am somewhat joking but hey I guess you never know 🙂


        • Punching Holes
          Thanks about the HW30s. And for sure happy about getting it. And for a good price. I had $5 in bullseye bucks and the 20% off and free shipping. Ended up with about $80 off the guns price. That’s a heck of deal. I think the sale is still going on too. People should jump on getting one while they can. Probably not going to happen again. Or for some time again.

          And I had a HW50s about 5 years ago I think it was. Mine had that as they called it at that time. New anti galling plastic insert in the cocking groove. So hopefully the new HW30s I’m getting has that now. How old is yours since you said yours don’t have it? And I think at the time I had my HW50s someone was selling the aftermarket inserts for the 50’s don’t know about the 30’s. So if mine don’t have it I will be doing something about it.

          And yes I really will be trying​ the JSB 10.34’s in my 30. Plan on the cheapy Daisy wadcutters too. I’m going to use it for pesting starlings and plinking out to around 35 yards. I have had good results with both pellets in lower velocity guns like the factory tuned FWB 300s and the 1377 conversions with the steel breech and Discovery barrels and 1399 stocks. And as well as mid and high power guns. People should really try both pellets.

          And nice on the Slavia. And yes I’m happy with the Wildfire. But I did do some tuning on it for trigger pull and fill pressure. It’s got a better trigger pull than the 1077’s I had and velocity and shot count at a fill pressure around 1400 psi.


          • Gf1

            I got it last summer but not sure when. I would say you got a heck of a deal on that rifle! O yeah it will fit the bill for that. I have a peep sight on mine and any army man or empty co2 cart inside of 20yds or sparrow out to about 25yds was an expected direct hit offhand.

            Which makes me wonder what kind of optics do you think you’ll use? I keep looking utg but haven’t decided anything yet. I like the open sights on my hw35 way better and I plan on shooting it that way for awhile. I also use the slavia open sight (obviously) and often I can out shoot the 30 in my garage. Its the sights and the little slavia just excels there for me. I shoot it horribly off a bag.

            I had read in the past about you making a modification in order to change operating pressure. That’s very cool and efficient in more ways than one.

            One more thing. In the same thinking as the 10.34s h&n makes the sniper light and sniper medium (don’t know weights offhand) I wonder if those would perform similarly, although I think part of the 10.34s success is due to the length and with length comes weight. Idk I guess the only way to know would be to buy and test. 😉


            • Punching Holes
              What’s kind of funny that I noticed with the 10.34’s is they seem to fit a little looser in guns than other pellets I used. And the skirts are on the thin side. So I think that helps seal them in the barrel on weaker powered air guns. And they chrony faster than the normal diablo shaped pellet of the same weight. And from the guns I have shot them out of they also have a flatter trajectory and don’t need as much hold over or under as the same weight diablo shaped pellet. So in other words they act like a lighter weight diablo in flight but still retain their energy at farther distance than the lighter pellets. Shot em out of alot of guns. They work.

              And I really want to shoot the HW30s open sighted which I wanted to do with my Wildfire too. But my eyes just didn’t want to cooperate. I ended up putting that Tasco red dot on the Wildfire that I posted a link to the other day. I have had that sight on many guns also including a Discovery and my Air Arms Tx 200.

              But I think possibly with the globe front sight on the HW30s. I might be able to use it in a sense like a dot sight. If I can keep that front sight aimed center mass of what I’m shooting at and just ty to line the back sight up the best I can. I might be able to do good with the HW30s sight. I’m for sure going to give it a shot though. 🙂


      • Gunfun1
        The cheap Daisy wadcutters were the first box of pellets that I grabbed out of my pellet drawer. I wasn’t expecting any kind of accuracy from a brand new gun so I just continued on with them as a break in pellet. I normally zero with 2 or 3 shot groups and that’s when I began to notice the super small group sizes.
        The Daisy wadcutters have never worked for me in any other rifle or gun that I own so I’m really impressed with the group sizes the Bushmaster is throwing. As the saying goes ” if it ain’t broke don’t fix it” so the Daisy pellets will be the pellet of choice for this gun!
        Cheers
        Dave


        • Dave
          Don’t you love​ when you find a pellet that works in a gun. And one that don’t cost a arm and a leg.

          That’s what I try to save some pellets that I have tryed over time. You just don’t never know what a gun may like. I know I have been surprised more than once.


  2. B.B.

    Your comments on hollow points vs domed headed pellets is very interesting. Perhaps in future tests you could include Crossman Premier Hollow Points AND Crossman Premier Domed pellets. FWIW-I swear that CPHP’s are more accurate in my Hatsan 95 than their domed fraternal twin. If we could do a 20 yard crony test we should see different velocities with basically the same pellet. That would be cool!
    Thanks,

    -Y




      • I’m really intrigued by that LabRadar (I think that’s the name) Doppler radar chronograph. It can measure a single projectile’s velocity at multiple distances downrange. AND it doesn’t sit in the line of fire! Money no object, seems an ideal way to measure the BC of _your_ projectiles from _your_ barrels.

        Anybody have hands-on experience with this gadget? Any difficulty picking up little airgun pellets at airgun ranges versus say a 168 gr .30?

        -Jan

        PS, I’m way behind on stuff and not following along with the comments, so apologies if this is something you folks already talked about!


    • Yogi,

      I’ve actually done that at 20 yards and although I don’t remember the exact velocities, I do recall that there was almost no difference. The gun was a Remington express .22. I concluded that since the hollowpoint was not really constructed the way most are, being just a domed pellet with a tiny hole in it instead of a scooped out wadcutter shape, that the two pellets were just too similar. I thought I might try sometime with two different pellets if I can find two that are similar in weight. RWS Superdomes and Super H-Points are within .3 grains, I think.


  3. Nice recap and always a fascinating topic. Chairgun is nice, real nice,.. and gives you a real good idea of what the pellet will be doing in flight. I think it’s great for beginners, armed with a few basics in knowledge. The visual depiction/chart/graph is nice and by changing some of the input data, you get to see how the chart will change.

    Of course, it is no replacement for actual shooting/testing. You got to do that. Suffice it to say though that Chairgun will cut your learning curve/time way down and at least give you a very good idea of what to expect.

    Good Day all,… Chris


  4. B.B.,

    I wonder how an H&N Piledriver (solid, conical, boat-tail) might do BC-wise in a Condor at 100 yards. If the Condor were in .177, the 21 grain Piledriver would perhaps go supersonic, but at .22 the Piledriver is a weighty 30 grains.

    Michael


  5. Redrafter

    You may be able to reduce pumping clack noise quite a bit. Get some black ponytail ties at any drugstore, the kind girls use to fix their hair style. They are elastic so take 3 or more and slip on your rifle so that they are in the way of pumping arm at completion of the stroke. This does wonders for a Webley Rebel. Hope your rifle’s design allows this. The ponytail ties are not expensive and come in packs of 50-100.

    Decksniper


  6. So the pellet skirt performs two functions it acts as an aerodynamic brake to keep the pellet pointed in the right direction, and to expand upon being hit with the blast of propellant Gas to engage the rifling? Is one more important for accuracy than the other?


  7. Wow 3/8 group in a smooth bore I would have to agree that aero drags influence is Probably greater than twist. That might also help explain choked barrels impact on accuracy.


  8. B.B.,
    I find the smooth bore very interesting. I’ve talked with a guy who deer hunting with nothing but smooth bore muzzle loaders (black power of coarse). He told me that at 50 yards, his guns were dead on. But if he extended it out past 100 yards, starts falling apart. I’ve always wanted to try one. He claimed it was easier to load and easier for him to clean? Also you’re own tests with the Umarex Colt SAA in smooth bore shows pellets can do very well in those too vs a bb. I also have thoughts of those shotgun slugs shaped like a pellet. Very accurate for a smooth bore when shooting those types. I shot mine up years ago. I’m not even sure they still make that type. All I see are the foster type slugs again.
    Doc.



    • Doc

      If you have never seen Taofledermaus’s YouTube channel you should take a look. He shoots all sorts of diabolo shape projectiles from a 12 gauge with and without a rifled choke. He films them in ultra slow mo so you can see the inherrent stability of the design.


    • Doc
      My smooth bore 760 loves wadcutters.

      I’m really, really waiting for a 30 grain .25 caliber wadcutter pellet to be made by one of the pellet makers. I want to try them in my modified .25 Marauder even though it’s not a smooth bore. If I could get a 1″ group out at 40 yards that would be a deadly combination.


  9. B.B.,
    Just thinking out loud, if two air guns had the same power plant, be it spring piston, C02 or what have you, with one being a smooth bore and one being rifled, wouldn’t the one in smooth bore shoot the pellet “faster” than the rifled barreled gun? It would seem so due to the force to “spin” the pellet and friction involved.

    Doc


  10. “Pellets can be pushed faster than the speed of sound; but to go much beyond 1,500 f.p.s., we’re going to have to use a different compressed gas.”

    B.B., for some reason that made me think of an article I once saw about NASA research into meteorite impacts on spacecraft. They used a “light-gas gun” ( https://infogalactic.com/info/Light-gas_gun ), which is kind of like a giant spring-piston airgun…if you replace the spring with an explosive charge. =D

    Anyway, they were firing small pellets at nearly 30,000 fps at an aluminum plate. What fascinated me was the shape of the pellets, raindrop-shaped, with the round side toward the target and the pointy side trailing. Even more amazing was the high-speed photo of the aluminum melting BEFORE impact from the shock wave in front of the pellet…cool stuff! =>


  11. Here’s some trivia for you all. Our first electronic computer, the Eniac which was dedicated at UPENN in 1946, was originally used to calculate ballistic tables for the Army Artillery command. Then the military discovered a better use for it – the feasibility of a thermonuclear device!

    Fred from GA


    • Fred,

      And here is more trivia on top of that. As late as the 1970s the US Army was still calculating mortar fire (indirect fire, similar to artillery fire) manually, with plotting boards and hand-held drafting compasses. We got meteorological data from the weather service that we plugged into paper tables and charts! And it all worked! It was slow, but it worked. In fact, watch the movie, “Hidden Figures,” to see what life was like just a half-century ago, when computers were people!

      B.B.

      B.B.



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