More on Ballistic Coefficients

BCs

On my recent article “Ballistics 101: What Is Ballistic Coefficient?”, commenter Anthony asked for clarification on some points:

Thanks for the info, but I don’t feel I know what ballistic coefficient is after reading the article. You state, “A ballistic coefficient is a comparative value for a given bullet,
showing its relative resistance to drag versus a model projectile that
has an empirically established set of drag characteristics.” Could you give an example? Is a lower number better? What happens when one used the incorrect drag model? What does any given coefficient tell us about a bullet?

Your wish is my command, Anthony!

Ballistic coefficients are essentially an estimate of how aerodynamically efficient a projectile is. They are derived by comparing a projectile with a known model projectile that has been empirically tested. True ballistic coefficients have to be derived empirically as well, but the resulting value is a very convenient figure for use in subsequent ballistic models. Essentially, the value is a modifier, so for example a 0.250 G7 BC means that the projectile flies similarly to the G7 model, but is 1/4th as efficient (i.e., it suffers 4 times as much from drag). Because the aerodynamic effects involved in a bullet’s flight are so complex, a comparative value like this is extremely useful for boiling down a projectile’s aerodynamic characteristics into a single piece of information that can then be quickly plugged in to simple ballistic calculators.

So, to answer one of your questions, higher ballistic coefficients are better, lower ballistic coefficients are worse… Unless of course you need a reduced-range projectile!

When you use the incorrect drag model, you get an incorrect result. For example, here I have created ballistic outputs for a given bullet, one with G1 and one with G7 BC (note that while G1 can sometimes be approximated as 2 times G7, that is not a true equivalency, although it happens to work here; you can verify it with JBM’s BC converter, a very handy tool indeed!):

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Now, G7:

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You can see that the G1 gives substantially better results at long range, but this is because the model is a poorer fit. Incidentally, this is one reason manufacturers like using G1, it makes their products look better!

G6 and G8 are not often used because they aren’t that different than G7, although they can give different results over long enough distances. For example, we know that .30-06 M2 Ball has a .210 G8 BC, which converts to a .202 G7 BC, but the results are still quite different:

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So it is important to use the right drag model!

Ballistic coefficients can also be accurately approximated by comparing two projectiles of the same shape and adjusting the value based on their relative sectional densities. Since ballistic coefficient is a dimensionless value, all it tells you is just the ballistic coefficient itself. If you also know the sectional density, you can then derive the form factor, and make a guess as to the projectile’s shape characteristics based on that value, but that’s about it.

And, of course, you can plug the BC into a calculator to learn a lot more about how it flies, too.



Nathaniel F

Nathaniel is a history enthusiast and firearms hobbyist whose primary interest lies in military small arms technological developments beginning with the smokeless powder era. In addition to contributing to The Firearm Blog, he runs 196,800 Revolutions Per Minute, a blog devoted to modern small arms design and theory. He can be reached via email at nathaniel.f@staff.thefirearmblog.com.


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  • Giolli Joker

    To all readers: do not google “drag model” to get more info about ballistics.
    The results may not be satisfactory.

    • M.M.D.C.

      I’m just like that kid who has to do it if someone says “don’t.” I got these Model Ts and quit while I was ahead:

      • iksnilol

        Lemme try:

        Just a lady next to a bicycle. I really don’t see the big whoop. EDIT: Giolli is kinda right. I didn’t learn anything about ballistics from this.

        • M.M.D.C.

          You’ll have to do an image search to see the big whoop. I did but it was rather unimpressive.

  • Mark

    Thinking that drag model number should be given with the coefficient: it would be much easier to deduce performance if we were given a figure like 0.35(G8).
    The coefficient may be dimensionless but this is only accurate if we’re all using the same model!

    • MPWS

      Correct. On top, as mentioned Drag co-efficient is of measurable value. This “black magic” around various comparative models just does not make lots of sense. Accurate numbers of uncertain value. But tradition has deep roots, right?

    • I try to always give the drag model with the coefficient, yes.

  • Matrix3692

    Are there any web based apps that allows you to roughly calculate a bullet’s ballistic coefficient?

    I’ve at many times thought of many bullet shapes, and like to simulate them out…….

  • iksnilol

    “Black magic for dummies”?

    I disagree heartily, I mean, there’s no info on what to do with these vulture guts that are all over my reloading bench.

    • ostiariusalpha

      Well, what exactly did you think you were going to form your reloading homunculus from?

  • MPWS

    Therefor and excuse me my slowness, BC is an hypothetical (in your words “comparative”) value, not supported by an exact measurement. As much as I understand it as a source for common ballistic calculation, I personally lean on more exactly measureable data such as drag coefficient (Cx) which in obtainable in aerodynamic tunnel test.

    I do not intend to fuzz the subject, neither to put what was written into a doubt; just to be understood properly.

    • ostiariusalpha

      The G models are what you use to quickly obtain the coefficient of form, which gives you just as accurate a prediction of ballistic coefficient as carefully measuring the drag coefficient in a wind tunnel, just in a more convenient form. Now, it is true that the coefficient of form isn’t going to tell you that your polymer tip is going to melt at 880m/s, but good luck finding a wind tunnel that can do it either. Your better off just firing the bullet, and measuring velocity changes with Doppler radar.

      • MPWS

        All right, I hear you. Natural question which is bound to arise is: what if my bullet shape does not fit into strictly defined models G1-8. What then? Here are the are variables I see a critical: ratio of diameter and length and tip’s envelope angle (say measured tangentially somewhere in mid of ogive) and take it from there. That would be good enough to me. I do not want to be bound to exact location of tip radius, size and O/A length. In practice, if you analyse shapes of bullets historically you come to similar conclusion.

        My point is – I cannot see something which is estimate to be “accurate” on 3 decimal places. Not in my books.

        • ostiariusalpha

          If you come up with a useful shape for a projectile that doesn’t conform to one of the G models, then good on you. That’s innovation that would open up at least a decade of research. The hybrid tangent/secant ogive comes to mind, but that’s fairly simple to create a hybrid G model for, as are other “in between” profiles. I suppose even a heeled/secant model wouldn’t be difficult to generate; the new shape would have to be rather radically different.

          As for three decimal accuracy from the G models, in the real world minute, variations in powder charges, bore size, and bullet consistency make that kind of moot. A ballistic coefficient should remain a guide, with empirical data from the actual firearm having the final say.

      • MPWS

        To add to previous: I understand that all what is defined as G form profiles is ‘tried and true’; no sense of inventing the wheel. For practical use and within conventional solutions it has sense. I look at problem more generally, outside of conventional bounds.

    • Bjørn Vermo

      I believe the various “models” were developed because classical aerodynamics only work in the subsonic realm. Cx can be found with a 200 km/h wind tunnel, but that will not be very accurate if you want to compute drag at Mach 1.5.

  • Anthony

    Thanks for the follow-up, Nathaniel.

  • GreyGeek77

    Meters used in one column, inches in another, feet in yet another and then joules for energy?
    Isn’t it time to stop being schizophrenic and switch completely to the metric system? The rest of the world, and our own military, have.

  • Cmex

    Thanks for this — always wanted to know that the different G’s were, though my fave is still G3. 😉

  • rcantor

    What’s PBR?